Hello! Welcome to Hexcells and my 100% No-Mistake Walkthrough. Hexcells has been likened to the classic game Minesweeper, and that's not a bad comparison. In each puzzle, you're given certain pieces of information, which will be explained in more detail during the walkthrough. Your basic goal is to use that information to determine which of the hexagonal cells should be colored blue, and which should be eliminated from the game. A counter in the upper-right corner of the screen shows how many of the remaining cells should be colored blue; a second counter shows the number of mistakes you have made. Our goal is to have no mistakes whatsoever, thus unlocking every achievement the game has to offer!

The purposes of this strategy guide are two-fold. First and most obviously, I want to present ways to solve all 30 puzzles presented by Hexcells. But I also hope to accomplish more than that. Instead of this being a straight walkthrough from Point A to Point B, this guide will also explore the logic behind each move--that is, WHY a puzzle can be solved in a particular manner. By delving into the actual puzzle-solving mechanics behind a given solution, you can actually become a better player, potentially able to solve some of the more advanced puzzles without the need for this or any other walkthrough. That is the primary goal of this guide, but it will also be here to help you if you become completely stuck on a particular puzzle, or even if you just need to be pointed in the right direction before you make your next move.

So to begin with, we'll take a brief look at the simple control scheme used for this game, as well as how to play the game and some helpful hints.


Controlling Hexcells is very straightforward and requires only your mouse. The Left Mouse Button is your confirmation button; you use it to select the cells you wish to color blue, to confirm menu selections, and to highlight rows of cells to work with. Think of your Right Mouse Button as your strike-out button; use it to eliminate cells you are confident should not be marked blue, as well as to dim the numbers outside of lines or columns you feel are completed. Below is a sampling of one of the opening puzzles which illustrates most of these basic concepts.



To begin the game, just click on one of the save file images. You'll then be taken to the game's puzzle index:



Initially, only the first chapter of puzzles is available to you. Completion of a puzzle awards you a certain number of hexes; a tally screen will appear after you finish a puzzle to show you the number you earned for that puzzle. In the center of each chapter ring in the puzzle index is a single blue hex with a number inside; this tells you the number of total hexes you must earn to unlock that chapter's puzzle. Any mistake you make during a puzzle will subtract from its final score. You don't have to perfect every puzzle to unlock all of them, but you will need to in order to unlock all of the game's achievements. You'll earn a corresponding achievement with each chapter you unlock; the final achievement, "Perfectionist," will be unlocked with the completion of every puzzle without any mistakes.



This picture is from my 100% complete file; that number on the right will be much lower when starting out!


No doubt you will want to try working ahead of this guide; that's only natural, and it is encouraged. It will be here if you get stuck. Here are some of the more useful tips I have picked up as I have played the game:

• Start with the most obvious moves first. For example, if you see a "0" somewhere on the grid, eliminate everything around it and see what's left.
  
• Watch for shared hexes. One of the most important concepts in Hexcells is that each blue hex you mark is likely to touch more than one empty hex. In such a scenario, it will contribute to the blue hex requirements for each empty hex it touches. This will often tell you which additional orange hexes need to be eliminated.
  
• Where there are many empty cells in the same general location, try to work the one with the least number of surrounding orange hexes first. Often, you will be able to solve one, which will show you how to solve the other empty hexes in the region.
  
• In the later puzzles, you will start working with rows and columns of cells. Every time you solve a sufficiently large number of cells on the grid, check the line restrictions to see if you can solve an entire row or column in one fell swoop. Be sure to do this periodically; it's important to be able to manage both kinds of restrictions at once.

With our introduction to the game concluded, let's dive right in! Click on the cell marked 1-1 to begin our journey into Hexcells!

Welcome to the first series of puzzles. For the most part, Hexcells does an admirable job of introducing you to the game's concepts and easing you in feet-first, gradually increasing the difficulty as you gain more experience. Let's take a look at the introductory puzzle below.




The first puzzle gets the game off on the right foot, allowing us to begin learning the basic concepts without throwing anything very challenging at us. Notice the footnotes at the bottom of the board. Often, when introducing new mechanics or concepts, Hexcells will give you a written hint about the puzzle you are attempting to solve. The hints in Puzzle 1-1 are designed to introduce you to the basic relationships between the different types of cells you will encounter.

Let's use this information to see if we can solve the puzzle right off the bat. First, remember that for any "empty" (black) hex on the board, the number inside tells us how many of its adjacent cells should be colored blue. Starting with the first cluster of hexes on the left, we are given an empty cell with a "6" inside. This means that six cells directly bordering it should be colored blue. As basic as it may be, counting is actually a very important puzzle-solving mechanic in Hexcells. It's a good idea to check the number of orange cells surrounding a particular empty hex before trying to work it. For this initial cluster, we can see that the "6" here has exactly six orange cells surrounding it. In fact, as you might expect given that these are hexagons, no given cell can ever have more than six additional cells surrounding it. We therefore want to color all six of these hexes blue by left-clicking slowly on each one.

Notice how the "REMAINING" counter in the upper-right has changed to reflect that only one of the puzzle's remaining cells should be colored. So let us now focus our attention on the empty cell marked "0" in the center of the second grid. The "0" here tells us that none of the cells bordering it should be marked blue. Therefore, using similar logic to the "6" on the left, we can eliminate all six cells surrounding the "0" by right-clicking on each one.

Notice that there is now only one short column of orange hexes remaining. The first one is below an empty hex with another "0" in it. So that one is automatically elminated; right-click on it. This gives us another "0" to follow; go ahead and right-click on the next cell down to clear it, as well. This time, we uncover a "1". Notice that the only "active" cell left in the puzzle is that orange hex beneath it. Using this and the "REMAINING" counter as guides, you know what to do. Puzzle complete!



Hexes Earned for Completing this Puzzle: 1

Before moving on, it's important to define what I mean by an "active cell" or "active hex," because it is a term that will come up repeatedly in this walkthrough. This term refers to any blue or orange hex. Orange cells are considered "active" because they are still in play; we haven't confirmed or eliminated them yet. Blue cells are considered "active" because they are confirmed to be part of the puzzle's solution; they aren't empty hexes.


Congratulations for completing your first step on the journey to Hexcells puzzle mastery! Click the Next arrow at the bottom of the hex tally screen to advance to Puzzle 1-2. Or, if you prefer, you can click the button with a curved arrow on the left to retry the puzzle if you made a mistake. You can also return to the puzzle index by clicking on the center button marked with a ring of hexes.



The next puzzle is a relatively gentle step up in difficulty from the first one. Let's take a quick look at it and see what information we have:



We again have two grids of cells, one of which is comprised primarily of empty hexes with a "2" in them. So for each one of those, two adjacent hexes should be colored blue. The grid on the left is a bit more complicated, with only a few empty hexes and lots of possibilities.

It may actually be slightly easier to begin with the grid on the right this time. If you look closely, you'll notice that several of those empty hexes only have two adjacent hexes to color, which gives you this:





So what exactly did that do? If you look closely at all of the empty cells in the grid, you'll see that now, they all have two blue hexes bordering them. This introduces us to the concept of shared hexes. Often, the active hexes on a grid will be sandwiched in between one or more empty hexes. In such a case, those active hexes are "owned" or "shared" by each empty hex that they touch. So when dealing with multiple empty hexes in a cluster, check to see if the blue hexes you mark border several empty ones at a time. If they do, it means that they contribute towards the blue hex count for each empty cell they border. Understanding this relationship early on is critical to solving later puzzles. But don't worry if it's a little fuzzy right now; the concept of shared hexes, as well as more advanced applications of the concept, will be discussed repeatedly during this walkthrough.

Now, what of the remaining two orange hexes in the grid? The one right above the middle borders two of the empty "2" cells, each of which has the two blue hexes it needs. This means we need to eliminate that one by right-clicking. This reveals one final "2"; only two of its adjacent hexes are "active," and one of them is already colored blue. So we know that the final orange cell should now also be colored blue, thus completing the grid.

Pay close attention to the puzzle logic used in completing that grid, as you will need to both utilize and expand upon that in the upcoming challenges. For now, let's tackle that other grid. The pattern is different, but we can actually apply similar logic to all of the empty "2" cells on the outside of the grid, as well as the individual cell marked "1" at the bottom; see if you can come up with this next pattern by building upon the previous solution:



We're almost finished. Let's turn attention to that big "5" in the center of the grid. Count the total number of hexes around it; we have six, but it turns out that when we marked the blue cells for all of the surrounding empty hexes, we also gave five blue hexes to the "5". In other words, the "5" shares a blue hex with each of the other empty hexes. This means we need to eliminate the final orange hex on top of the "5" by right-clicking on it. Doing so gives us a "3". We can immediately see that there are only three active hexes surrounding it, two of which are already colored; we simply need to color the last one to complete the puzzle.

Hexes Earned for Completing this Puzzle: 3

The game starts to get just a little more challenging with this one. One of the most important rules of Hexcells is that you don't want to just jump right into a puzzle immediately. Instead, take a little bit of time to ponder what information you have; many times, there are some moves that are obvious right from the outset and which can help make the solution easier.

If you look carefully, we have at least one obvious move. In the top-right section of the puzzle, a "0" is glaring at us; remember that this means nothing around it can be colored, thus allowing us to immediately eliminate the two hexes bordering it. Both of these new empty cells contain a "1", immediately telling us to color the final orange hex in that grid. That's the easiest part of this puzzle.


Let's finish out the top section now. The second grid up here looks a little more ominous since there's more room for a mistake; just take it methodically. The "1" on the far right only has a single cell adjacent to it, meaning it automatically gets colored. Notice how this blue hex is shared with the "1" directly under it. This automatically eliminates the remaining orange hex bordering this "1". With only one orange hex remaining in the grid, and the remaining empty cells still requiring one blue hex apiece, we need only color that one to finish the grid.

You're doing great if you've kept up to this point. The final grid on the bottom may look daunting for a newcomer to the game, but let's see what we have. There isn't too much information; again, let's look for something obvious. See that "0" at the bottom-right of this grid? That's our starting point. Go ahead and eliminate the cells surrounding it. We now get another "0" and a "1". Let's continue with the "0" and see where it takes us. Going around that side counterclockwise, we eventually get another "1". If we look at the empty "1" cells we just uncovered, we see they each only have a single active hex bordering them; color those hexes.

It may not look like it, but we still have a couple of pretty easy moves to spot. At the top, again going from right to left, the "2" along the top edge only has two adjacent active cells, one of which is already colored. Coloring the second one actually completes both of the empty "2" cells in this region. Now, all empty hexes on the right side of this grid have the blue hexes they need; this means we can actually clear the entire next column over.

This is a tricky spot. Notice how the "2" right around the center of the grid doesn't have much around it; it has a "1" on its top-left edge and only a single orange hex on each side. Both of these need to be marked; when we do so, we also give a second blue hex to both empty "2" cells in the column we just eliminated in the last step. So the final orange hex at the very bottom-center of the grid can now be eliminated.

The other major thing we need to observe now is that the "1" bordering the "2" we just solved has now been given a blue hex. We need to erase the other orange hex to its left. The "2" that this reveals is in the same relative position as the last couple we worked; therefore, it only has one remaining choice for a second blue hex. When it's colored, we also give the "2" directly below a second blue hex, and the final two cells of the puzzle are eliminated.



Hexes Earned for Completing this Puzzle: 3


We are now halfway through the first chapter. By now, you should have a pretty clear idea of how we can isolate and eliminate individual hexes from a puzzle. The puzzles will only get more complicated from here, and you'll need to be able to identify those moves that are 100% safe before diving in to solve them. To that end, let's take a look at the layout for Puzzle 1-4:



Cute, isn't it?? It sort of looks like a baby owl to me. Anyway, on to actually solving it. At first glance, it may not look like there is much you can do; most of the empty cells have more active hexes surrounding them than the number of blue ones they need. But look closer; see the "4" near the bottom-center of the puzzle? It only has four total adjacent cells. So start by coloring all of them. This will actually open up some additional moves, but for now let's look at the "2" on the far left edge of the grid; notice that it only has two adjacent cells--one above and one below--so we can also complete it right off the bat.

This setup allows us to now eliminate several orange hexes. Notice that some of the empty "1" cells now have their single blue hex, meaning that any others adjacent to them can be eliminated. Doing this reveals two empty "3" cells and a couple of zeroes. You know what to do with the zeroes; afterward, you'll find that each "3" at the bottom only has three active cells to deal with. Marking the final orange hexes around them also solves the empty "2" cells in the same region.

We now have much more information to help us solve the top half of the puzzle. The "2" in the center claims the orange hex above it because we've either eliminated or colored all the others surrounding it. To the right, next to the "0" near the bottom-right corner of that section, the "1" has only one active cell bordering it, meaning it is automatically colored. This blue hex is shared with the "1" just up the final column. We now eliminate the remaining orange hex above that "1". This gives us yet another "0", putting us in position to color a single remaining hex adjacent to the resulting empty "1" cells in the top-right corner.

If you've gotten this far, you may be able to finish the puzzle on your own, but take it slowly. Our last move did satisfy some additional requirements. The next empty "1" cell to the left of where we just were now has its single blue hex; the other two bordering it are now eliminated. We will reveal a "2" and also another "1", which has an adjacent blue cell. The "2" that we just revealed only has one other cell that needs to be colored. Can you finish the puzzle from here?



Hexes Earned for Completing this Puzzle: 4

This puzzle as a whole really expands upon the concept of shared hexes; you'll need to pay attention to any blue cell touching multiple empty hexes to avoid trying to incorrectly mark extra cells. Also remember to, as much as possible, work the empty hexes with the least number of active hexes first.

We're almost ready to finish Chapter 1. We'll move on to the next-to-last puzzle in the series next.

Here's the layout for the next-to-last puzzle in this chapter:



Interesting. This time, we are given just a single large grid with a few empty cells revealed to us. Where do we even begin?

Remember the core rule of Hexcells: Look for obvious moves first. They're a little harder to spot this time; as the puzzles grow larger, you will need to spend more time studying them to find out what is immediately open, and what you will need to come back to later. This is a good introductory lesson to that idea of problem-solving.

While they may not be immediately obvious, we do have a few opening moves. We'll work from left to right this time. Note the "4" near the left-center of the grid; it only has four active hexes surrounding it, meaning it "owns" all of them. (Remember that the empty "2" cell in this cluster is not considered active since it has been eliminated.) Color them all. Next, look at the cluster of empty "3" cells at the bottom-center; if you look carefully, you'll see that the middle one only has three orange hexes to deal with, meaning it "owns" each of them. Color them, as well. Now look at the right side of the grid; we have another "4" in an identical situation to the one we just handled. Go ahead and mark all of these cells, too. Finally, just up and to the right of this, on the outer edge, is a "3"; we just gave it two of its three blue cells. Can you see why it also "owns" the final remaining hex right above it?



Before moving on, let me briefly describe one concept I like to use when solving these puzzles: Ownership. Since Hexcells is all about determining which cells around a particular numbered hex should be colored, I like to think of those cells as being "owned" by that empty hex. So when I talk about a particular empty cell "claiming" or "owning" a cell or cells surrounding it, I mean that these are the ones which satisfy the requirements for that cell and the rest of the puzzle. Also note that as the game progresses, the idea of blue hexes being shared by multiple empty cells is becoming more and more important. We just used the concept in solving the "4" and "3" on the right side of the puzzle, for example.

So with our opening moves having been made, let's see what they did to the rest of the puzzle. Try working from left to right again, along the same general track. Notice that solving the cells around that first "4" also gave the "2" right next to it the two blue cells it needs; we can eliminate all three of the other cells around it. We reveal a "1" directly below the "2"; the blue hex under the "4" is shared with this "1". When we clear the orange hex to its left, we get another "1", which also shares that same blue hex. So do the same again, unveiling yet another "1" which shares that blue hex. With this, we find that this single blue cell is actually shared by five separate empty hexes.

We can now go back to the cluster of empty "3" cells in the middle; we eliminated two possibilities for coloring cells around the first one, leaving it only one left to claim. Skip the third one in the set for just a minute; the "2" on the right has its two blue cells, eliminating three additional hexes around it. Return now to that remaining empty "3" cell; we eliminated two of its remaining possibilities for getting a third blue hex, leaving only one which becomes the correct answer. As for the empty "1" cell we just revealed? If you work carefully, you'll see that this entire corner is treated exactly the same as the other one.



Now what? It may take a little bit of time to see our next move. But careful examination shows that the two empty "2" cells we revealed a little bit ago already have their two blue hexes, allowing us to eliminate two more from the puzzle. Each of these reveals an additional empty "2" cell; remember what we said about shared hexes? It turns out that the blue hexes owned by the cells we just solved are also owned by the ones we just revealed. In total, we can now eliminate five more hexes.



We're almost done; be careful if you try to finish the grid on your own. We can complete the top section by working from right to left. The "4" in the upper-right corner now only has four adjacent active cells, two of which are already colored. Simply color the other two to solve that corner. Doing so gives the empty "1" cell to the left its lone blue cell, and we simply eliminate its other adjacent orange hex.

Now, we can finish the center section; the only way the "2" in that cluster of cells can even have two blue cells is to color the ones above and below it. The "1" just over from that only has a single possibility, as well; when we fill it in, we also give the "3" in that corner its third blue cell. We can now finish the puzzle by eliminating the other orange hex surrounding it and coloring the two final cells to complete the empty "4" cell in that corner.



NOTE: If you saw it before, you could actually have colored in that center cell without working the top section first. The empty "2" cell two spaces down from the top and just left of center only has two possible blue hexes to claim by the time you complete the previous series of steps; with one already colored, that center cell immediately satisfies its requirements. It just illustrates that there may be more than one approach than the one I am presenting in this guide; if you see something that you're confident will work, go for it!

Hexes Earned for Completing this Puzzle: 5

Congratulations on reaching the final puzzle of Chapter 1. At this point, Chapter 2 becomes unlocked; feel free to take a look at the upcoming challenges if you wish. Notice that Chapter 2 only has four puzzles in all. Chapter 2 will build upon the skills we are learning in Chapter 1, introducing more complicated setups in which to apply the rules we have learned. Here's the layout for the conclusion of Chapter 1:



Um, right. As weird as this one may look, remember that every one of these puzzles has an opening step you can take that will always be 100% correct. The trick is to identify it and then figure out how it feeds into the rest of the puzzle.

There isn't a right or wrong approach to a particular puzzle, only to individual moves you can make. With this one, we can go around the grid and try to locate all the possible starting moves, or we can try to find one or two initial moves and see how they relate to the cells in the immediate area. For this guide, we'll try the latter approach first.

One thing that may jump out at you immediately is that "0" on the left side. Finding a "0" is always helpful because you can eliminate hexes immediately. So we'll start with this, opening up several empty "1" cells, one of which only has a single orange hex that will now be colored. Just making this one simple move will allow us to handle the other empty "1" cells in that same part of the grid. In fact, with some careful thinking, we can finish that entire corner!

If you need a little more guidance here, be aware that a couple of the empty "2" cells will only have two active hexes bordering them. Pay close attention to all of the empty "1" cells you will deal with, and make sure you have no blue cells touching one before you try to mark a hex. Save the "3" on the right side of the section for last; you'll be able to eliminate enough hexes to make the choice of blue cells obvious.

So let's try to finish the left half of the grid. Moving back towards the top, you'll see a "2" on a corner with only two active cells, which we will color to satisfy its requirements. This simple move is also going to fulfill the requirements for the empty "1" cells in the same general vicinity, allowing for the elimination of more hexes. Using a similar approach to the bottom-left corner, we can work our way around the cells of that loop and down the column near the center of the grid.

At this point, let's skip to the small cluster at the upper-right section of the grid. Hopefully, you will notice fairly quickly that the "3" here only has three active hexes around it for us to color. Doing this will also give the empty "1" cells in that corner their single blue hex; we thus eliminate the two remaining orange hexes surrounding them. This gives us another "1" at the top, and another "0" below; you should easily be able to see what to do next.

We're basically at the end of the puzzle now; we just have to be careful not to make an obvious mistake. Let's start in the center; notice that both of the empty "2" cells here only have two active cells around them. Go ahead and color them all to solve each "2".

We'll solve the final cluster in a similar manner to the one we just completed. Start with the "2" at the bottom-right corner; since it has only two active cells around it, they both will need to be marked. Doing this also gives the "1" next to it a blue cell, so clear the remaining orange hex on its top-left edge. The "1" revealed from this shares the same blue hex we just colored, allowing us to eliminate the two along its top rim. Oh, look: Another "0". If we get rid of its only remaining adjacent cell and finish off the "2" beside it, completing the puzzle is easy. As for the one lone cell just hovering there? Once the main grid is filled, your hex counter will show one final blue hex to identify. Color the final cell to complete Chapter 1!



Hexes Earned for Completing this Puzzle: 5

Welcome to Chapter 2 of Hexcells, and congratulations on successfully completing Chapter 1. If you've been playing on your own and using this guide as a reference, you probably understand all of the basics by now. You may still be making a silly mistake occasionally, but your basic grasp of the game is solid. Chapter 2 will build on the skills you have learned, as well as their application towards more complicated layouts.


Here's the layout for the next challenge:



I'll just go ahead and say that I really like the music for this chapter. This puzzle gives us a little more information than some of the previous ones. Notice that in addition to a few empty cells, some of the blue hexes are already given to us! Be aware, however, that the "REMAINING" counter still accurately reflects the number of cells that we have to color to solve the puzzle.

Since the two grids are not connected in any way, you can choose which one to start with; nothing we do in one grid will have any effect on the other. This is actually important to understand; later on, you will begin working with entire lines of cells, some of which may be a part of different grids. Don't worry about that for now, though; we'll go over this concept in plenty of detail when the time comes.

I prefer to start working on the bottom grid, but you don't have to; if you wish to start with the upper grid, that's totally fine. In my opinion, the bottom grid simply has a little more information to get started. So let's check it out. We already have two blue hexes, and everything we have to work with is all in the same general grouping. Can you identify our opening move? Start with the "2" at the end and notice it already has a blue cell, with only one additional active cell adjacent to it. If we simply color that one cell, we solve the "2" immediately. Similarly, that "3" right next to it only has a total of three active hexes around it, so they all need to be marked. Notice that now, we have also given the second "3" to the left the two remaining blue hexes it needs, allowing us to eliminate the final cell surrounding it.

The last cell we eliminated gave us a "2". You should immediately see that it already has two blue hexes from the last set of moves. We eliminate the orange hex adjacent to it, revealing a "1"; this cell shares the blue cell under the "2", meaning we automatically eliminate the other orange hex adjacent to it. This gives us a "0"; we know what to do with zeroes. The rest of the grid is extremely easy; just don't go too quickly and make a careless mistake.

Let's move on to the other grid now. Most of the information for this section is located in that top-left corner. We start with the empty "2" cell at the top; can you see that it's already been solved without us even doing anything?? So the orange hex beneath it is automatically eliminated from the game. We get another "2" from this; again, it is already solved, and we eliminate two more hexes. This grid is apparently coming in twos, because we get two more empty "2" cells! The one to the left needs a second blue hex and has only one choice for it to the left. The second "2" of this new pair, however, is already solved; we eliminate the sole remaining orange hex to its right.

We're almost finished. The "1" that we just revealed shares a blue cell with the empty "2" cells from before; just get rid of its remaining orange cell. You should be able to finish the rest on your own. Just be a little careful towards the end. When you're working the cells surrounding that final empty "1" cell at the end, don't let the numbers that pop up throw you for a loop. You will have already given that cell its single blue hex, so you can safely eliminate all five of the other orange hexes surrounding it to win.



Hexes Received for Completing this Puzzle: 4

The next puzzle will be the lengthiest challenge you will have faced so far...

The last puzzle was a nice warm-up to the chapter. This next one is a bit more complicated, however:



The solution to this puzzle is much longer than any you have encountered so far, and more reliant on moving around to different sections to progress. Despite its complexity, it still only ranks in the middle on the difficulty scale; the most complicated puzzles near the end are true brain-teasers! If you fare well on this one, however, your ability to solve these later puzzles will be greatly enhanced. As always, look for obvious moves first, but don't get ahead of yourself as you clear out the grid; that's when you will make a mistake.

A decent amount of information is already given to us. We again get a few blue hexes for free, and several empty hexes. Remember: Find the obvious moves first. We have several; see the zeroes around the outer edge of the grid? Also, the empty "3" cell in the center already has its three blue hexes, allowing us to eliminate the one directly above it. So our opening move looks like this:



In a puzzle that's a little more complicated like this one, always spend some time investigating how your initial moves affect the rest of it, and anything else you may simply have missed the first time. In the hardest puzzles, it's not uncommon to have to retrace the same sections many times before you find that one move that will open it all up for you.

So let's take a closer look. On the left side, we got a couple of empty "1" cells, but we can't yet determine which of their active hexes will be marked. On the right side, however, we can eliminate a few hexes because a couple of the empty "1" cells there already have a blue hex assigned to them. So let's do that next. Finally, in the center, we have an empty "1" cell that is easily missed in the initial analysis; it, too, already has a blue hex assigned, eliminating a few more cells. These changes look like this:

You may already have seen another move or two we can make. If you wish, you can go ahead and complete them, but don't rush through. The best way to proceed in larger puzzles is simply to pace yourself; make sure you aren't missing something fairly obvious. Near the upper-right corner, the same blue hex is shared by all three of the empty "1" cells, allowing us to eliminate quite a few more cells. In that same general area, some of the empty "2" cells now open to us only have two adjacent hexes apiece, allowing us to now mark several cells. We get a similar situation in the bottom-right corner; the empty "2" cell on the edge only has two adjacent orange hexes. Once they are marked, we find that the "2" right next to it shares both of those blue hexes, and we can eliminate the other three surrounding it.



Before we move on, we want to do some clean-up work. You may already have spotted some moves we now have available to us. Near the top-right corner, that "1" has its blue cell already, so we get rid of the orange cell touching it. The "1" revealed from this shares that same blue cell, so the orange cell next to this "1" is also eliminated. That gives us yet another "1"; we'll come back to it shortly.


But now, if we go back to the center-right section, where there is still a cluster of four orange hexes, we see that the "2" right above them has both of its blue hexes. That lets us clear the orange hex right below it. The "3" just over to the left has its three blue hexes, clearing the final orange hex still bordering it. The "2" revealed from this only has two possible blue hexes to claim, one of which is already marked. Marking the other also gives the "2" we revealed a moment ago the second blue hex it needs, and we eliminate the final orange hex on this side of the grid.

We can go to either the top or bottom now. Since we're already there, let's continue around the bottom. There's only one choice for the "2" near the bottom-center to get a second blue cell; when it's marked, we give the nearby "1" its single blue hex and can eliminate the orange hex still bordering it. The "1" revealed shares that same blue hex, eliminating three more cells. The "2" at the bottom of this cluster now only has a single possibility for claiming a second blue cell. That's as far as we can go here for now, though. Here's what it looks like:

If we now look right above where we just were, we see that another "2" already has two blue hexes, eliminating two more. Now we can finish the bottom section; the "2" directly below the empty "1" cells we just revealed only has a single choice for a blue hex. When we mark it, we also complete all of the nearby empty hexes below and just to the left, eliminating that final remaining orange hex in the section.

Not much more to go. We can pretty much finish the third column from the left now; all of the empty "1" cells in the fourth column have their single blue hex, eliminating all the remaining orange hexes adjacent to any of them. I went from bottom to top in clearing them; the "1" unveiled in the fourth column from doing this only has a single choice for a blue hex. It will be shared by the "2" a couple of cells to the right, completing it and allowing us to erase the orange hex above it. The "3" that this reveals claims the cell above it for a third blue hex; this blue hex will be shared by the pair of empty "1" cells at the top of the grid, eliminating the orange hex to their left.

We can now finish the puzzle. Notice how the three empty "1" cells in the top-center of the puzzle all share the same blue hex. We clear the next orange cell over to their left; this reveals another "1", which has only one choice for a blue hex. This new blue hex will be shared by the "1" on the corner, eliminating the cell below it.

This is a tricky part; the "1" we revealed from that last elimination has two possible choices for a blue hex, but look more closely. The adjacent "1" on its bottom-right edge has only a single active hex to claim for its blue one. Since this blue one is shared between each "1", we can now clear the remaining active hex from the first "1". The final move of the puzzle is to mark the orange cell below the "2" in the first column--its only remaining choice for a second blue hex--and then eliminate the final orange cell. We know this one has to be eliminated because all of its adjacent empty cells have the blue hexes they require.



Hexes Earned for Completing this Puzzle: 6

Congratulations on making it to the halfway mark of Chapter 2. At this point, Chapter 3 is unlocked if you would like to take a peek at some of the more advanced puzzles. That last one was quite a bit more challenging than those before it. If you understand the underlying processes for solving it, however, you will be able to handle the more advanced challenges later in the game. Remember that even the most complex puzzles have their solutions rooted in the basics that we are learning through these opening challenges. Here, then, is the layout for the next puzzle.




Kind of looks like a ragged old blanket to me! We do get several blue cells for free, and several empty cells to get us started. Our opening move will again be to eliminate several cells. See the two zeroes at the top- and bottom-right corners? Not to mention that the empty "1" cell near the bottom-left corner already has its single blue cell. So here's what that leaves us:


We now have quite a few moves open to us in the bottom-left corner. In the first column, the "2" has only one choice for its second blue hex. As this hex is shared with the "1" on its upper-right edge, the bottom cell of the second column is now erased.

Moving up the second column now, the empty "2" we uncovered halfway up already has two blue hexes, clearing the two remaining cells around it. You may also notice that both empty "1" cells in the third column also share the blue hex on the upper-right edge of the "2", which clears several more cells.

After clearing all of these other cells, it's not hard to solve the first two columns. Notice that the "2" halfway down the first column shares a hex with the "2" on its upper-right edge, as well as the "1" right above that "2"; when we mark it, we complete the blue hex requirements for all of them. We now have to clear the cell above the one we just marked, uncovering another "2". It will claim the top hex of the column; that of the second column will then be erased.



Let's go to the fourth column now; the empty "2" cell three spaces down only has two possible choices for its blue cells. Believe it or not, just coloring those two hexes will help us solve most of the empty hexes in the same general vicinity; we'll clear a large number of hexes now, as many of the empty hexes we uncover will already have their required number of blue hexes as soon as they appear. For those that do not, their choices for blue hexes will generally be obvious.

We'll continue working from left to right. The "1" at the top of Column 6 already has a single blue hex; when we clear the two orange hexes to its right, the "2" below it will only have two cells it can claim. Marking both gives the "2" directly below that one a second blue cell. Since the "2" and "1" at the bottom of Column 6 already have their required blue hexes, the two remaining cells at the bottom of Column 7 are now eliminated.

Notice that now, Column 7 has only a single orange hex at the very top. Our last move gave the "1" about halfway down the column a single blue cell below it. If we clear the orange hexes still to its right, we'll reveal another empty "1" cell with a blue hex to its right, which was given to us at the start of the puzzle. The cell above it is cleared, and the lone hex at the top of Column 7 is colored.

Let's see if we can finish the puzzle from the right and meet in the middle. To start, the "1" at the top of the final column has only one choice for a blue hex, and it will be shared with the "1" at the top of the previous column. Clearing the cell under this "1" gives us another "2" with only two active hexes to worry about marking. That gives a second blue hex to the "2" right below this one, clearing away two more cells. The same basic logic will solve these two columns. As a bonus, all three cells in Column 12 will automatically be eliminated; all of their adjacent empty hexes will already have the blue ones they need!

To complete the puzzle, start near the bottom of Column 11 and work upwards; Columns 10 and 11 are basically solved in tandem, using the existing relationships and uncovering some new ones. Starting from the "1" at the bottom of Column 12, which already has a blue hex, clear the remaining orange hex on its bottom-left edge to reveal another "1". It shares shares the same blue hex with the first "1", letting us clear three additional cells. We'll get two additional empty "1" cells from this, with the hex at the bottom of Column 10 becoming an obvious blue hex for them. Continue working your way around these columns, and you'll see the relationships needed to complete the puzzle. Here's what the end looks like, minus the final blue hex:



Hexes Earned from Solving this Puzzle: 7

By now, you should have a pretty clear understanding of the relationships between the various types of cells, as well as how to recognize a blue cell that is owned by multiple empty cells. This is pretty much the driving force behind the last few puzzles we have attempted. Going forward, I'm not going to point out every single relationship in a given grid; I will, however, point out relationships that can be very easy to miss and how they can open up new avenues toward a given solution. Your actual puzzle-solving skills should be solid by now; it's their application in more complicated situations that may leave you scratching your head for awhile.

We have now reached the conclusion of Chapter 2, with only one more puzzle remaining. We'll begin learning new skills and mechanics in Chapter 3, where the concept of working entire rows and columns of cells is taught. This presents new challenges when trying to solve puzzles that otherwise might be more straightforward. The mechanics will be discussed in great detail as we move forward.


Here's the layout:



The pattern reminds me somewhat of Puzzle 1-6. We do get an assortment of blue cells given to us, and a number of empty cells, primarily in the outer part of the grid. As before, our first step is going to involve elimination of cells. See the two zeroes? We'll start with those as a reference point to the larger solution and see where they take us. Work slowly, and you'll be able to see additional relationships between the cells we uncover, and those already present:

And just like that, almost the entire upper portion of this puzzle is solved! While there isn't much more we can do on top for right now, we can finish a couple more small clusters. First, in the upper-right corner, the empty "2" cell in the third column from the right has only one choice for a second blue hex, which will also give the "2" next to it the one it also needs. So we can clear the last hex from the section.

The only other thing we can do on top for right now is over on the opposite side; the "2" with a blue hex below it only has one other active hex to worry about marking.

Now, let's scan the rest of the puzzle. Do you see anything else that can be done around the edges of the grid? I sure don't. All of the empty cells have multiple options for getting their blue hexes, and the one blue cell already given to us has no empty cells we can give it to for right now. We're stuck, right?

Not completely. This is one of those situations where it may take a little bit of looking before we find the next move. Notice that in the very bottom-left corner, the "2" only has two options for its blue hexes, so fill in both. We'll find that these blue hexes will be shared with the "2" on its upper-right edge, as well. We now eliminate all other cells adjacent to that second "2". We're left with this:


Moving up slightly, the "1" at the top of this cluster shares a blue hex with the "2" below it, letting us eliminate the orange hex above it. For now, the "1" this reveals is a logical dead end; we have no way of determining which active hex it will claim. So let's move towards the center. Our only other move right now concerns the empty "3" cell; it only has three total hexes around it, so color the other two that it needs.

Let's move to the left of this. The "1" touching the bottom-left corner of the "3" now has the blue hex it needs; we can eliminate the other orange hex to its left, which gives us a "0" to follow. In doing so, we'll join back up with the column leading to the loop in the top-left corner; we should now be able to finish that area of the puzzle. Here's the setup after the last few steps:


The fourth hex down the third column--the second empty "1" cell in that string of five such cells--is the key to this next section. It is adjacent to only one orange hex, which we will now color; this blue hex is shared with the other two empty "1" cells in the cluster, and we can get rid of two more cells from this. To complete this corner, all three remaining hexes must be colored. Can you see why?


We're almost done with the chapter now. Go back to the bottom-left cluster. The "2" on the bottom edge there only has a single remaining cell for it to claim. Mark it, also giving a shared blue hex to the nearby empty "1" cells. This basically sets up a series of eliminations, as we keep uncovering empty "1" cells which share the same blue hex.

We'll eventually uncover another "0", as well. Erasing its two orange hexes gives us a pair of empty "2" cells; the one on top already has the two blue hexes it needs, getting rid of one more cell to reveal a "3". It "3" also has the blue hexes it needs, and we clear the two remaining cells from it:



Let's finish the small cluster in the center-right section. The "1" we just revealed by completing the "3" obtains its blue hex from the "3"; clear the next hex over. This uncovers another "1"; the "1" above it--with the two zeroes on its upper rim--then has only one choice for its blue hex. This one is shared by both empty "1" cells, as well as the "2" at the end. When we erase the remaining orange hex from the lower "1", the "2" claims the final blue hex of this section.

Only that small cluster on the bottom remains. The "2" near the bottom of the central column has only one choice for its second blue hex, also giving the "1" at the bottom the one it needs. Clear the cell on the bottom-right edge of the "1"; the "1" just revealed from this shares that same blue hex. Clearing the remaining orange hex to its right reveals yet another "2". This is a tricky spot!

The answer lies with the other "2" positioned two cells above this one. Notice that the orange hex in between these cells is the only possible one that upper "2" can claim for its second blue one. It is shared with each "2", as well as the "1" to the right. The final two cells under the "1" are thus cleared, and the final cell of the puzzle is marked to clear the chapter!



Hexes Earned for Completing this Puzzle: 7

Congratulations on completing Chapter 2! The last few puzzles were a ramp-up of the skills we learned in Chapter 1 but didn't really introduce anything new. That all changes starting with the very next puzzle. We are now going to deal with entire rows and columns of cells, which can dramatically change the way you interact with a puzzle, especially those which are disjointed into multiple grids of cells.

To be fair: This chapter only focuses on vertical columns of cells; later, however, you will be working with entire diagonal rows of cells. Just consider the introduction of columns to be a primer as the exact same concepts will apply when the time comes.


The best way to demonstrate how to work with rows of cells is to simply jump right into the next puzzle. Here's the layout:



Oi. So what do we know from this? Here again, Hexcells does a good job of introducing the concept by giving us a hint: "Numbers outside the grid show the number of blue hexes in that column." Look at the first two columns in the grid on the left. The first has a "2" above it; the second has a "3" above it. So this literally means the first column can have no more than two blue hexes, and that the second column can have no more than three. Can you solve these two columns using that information combined with the total number of hexes within each?



Before you say it: Yes, I know I could have gone ahead and solved the grid by marking the final hex. However, I feel it is more prudent to focus only on the lesson being discussed for the time being. We are going to now go ahead and mark that cell to satisfy the requirements of the adjacent empty cells before moving to the second grid. What do we know about this one?

Well, two of the columns (if you want to call a column of one cell a "column," that is...) have a "0" above them. If you ever see this, it means the exact same thing as an empty "0" cell: That literally NOTHING in that entire column will be colored blue. I think you know what to do next...




So the big variable is which three cells in the middle column will be shaded blue. We'll start eliminating cells from the zeroes we just uncovered and work our way in. We'll reveal some empty "1" cells and another "0". What we end up with is only three active hexes in the central column, and a "2" at the bottom of that column with only two active hexes of its own to deal with:


That was a warm-up; the next puzzle throws in another mechanic on top of what we've learned here...

Hexes Earned for Completing this Puzzle: 2

Let's start with the in-game hint: "Numbers like this {3} give the additional information that the 3 hexes are consecutive."

My only criticism of this is that it uses a specific number when clearly, that's not what is used for the bulk of this puzzle. What it's really saying, though, is that if you see any number written inside of braces, you're being told two things. First: That row or column has only that number of hexes shaded blue; and secondly: All of those hexes are in one continuous line.

These concepts also introduce us to a different type of puzzle logic that we can sometimes use to immediately include or exclude cells in a line. Let's start with the middle column in the first grid. While simplistic, it lets us see the concept. The line header is a {2}, which means the column must contain two blue hexes linked together; there cannot be an empty hex between them. The line contains only three total hexes, but as the bottom hex is empty, the top two will both be colored.

Let's now look at the other two columns in the grid. They also have a {2} outside of them. Well, in these cases, there are three active hexes in each column; how do we determine which two to mark?

We can actually guarantee one of the blue hexes in each column from the outset. Since the columns only contain three active hexes apiece, there are only two possible combinations which will give us two blue hexes linked together: Cells 1 and 2, and Cells 2 and 3. The middle hex is the constant; no matter how we go about pairing up the two blue hexes, this one will be marked. So we want to mark the center hex in each column:

We now want to look at the grid itself to determine our next move. Notice that our last two steps actually gave that empty "3" cell the three blue hexes it needed. If we now eliminate the remaining hexes around it, we'll leave only the top cell in each column as the ones we shade to fulfill their own requirements.



So far, so good. Let's move to the second grid. This one is much more thought-provoking than the first. To start with, there are no obvious candidates for getting that empty "2" cell the two blue hexes it needs. The column in which it resides can only have a single blue hex; the middle column needs four consecutive blue hexes but has five cells; and the first column gets a total of two hexes which can be either connected or disjointed.

So let's use a similar approach to the center column that we did for the two columns in the first grid. If you count it out, you will find that the three middle hexes in the column all must be marked. Here's how we can determine this:



This logic will help us solve the third column; we've just given our "2" a pair of blue hexes, letting us eliminate its remaining orange hexes. This leaves only the final cell in its respective column as being marked.





To finish the grid, realize that the "1" at the top of the third column has its blue hex; we'll eliminate the top hex in the middle column as a result, giving us our endpoint for the four continuous hexes it requires and allowing us to mark its final hex. We now can finish the first column; the top cell of the middle column is another empty "1" cell, which obviously has a blue hex right below it. The top hex of the first column is now eliminated. Since that column has to have two blue hexes, we simply color both which remain!

Only one column left. We know that it needs three consecutive blue hexes but unlike before, there are far too many total cells in the column to accurately determine either an endpoint or a middle point.

So looking at the column, we have an empty "1" cell at the very bottom. Since the only adjacent orange cell is on top of it, that dictates the entire column. The first three cells above the "1" will have to be colored, and the rest of the column eliminated. Puzzle complete!



One final note before we move on. The way this column is solved introduces a little bit of a monkey wrench into the whole "consecutive cells" theory. Gaps between cells within the same row or column do not count as obstructions! Only actual empty cells count! You may have seen the three continuous orange cells in the center of that column, thought they must be the three needed to satisfy the column requirement, and gotten zapped with an error as a result. Remember this concept as we move on to later puzzles with more complex layouts. Also, make sure that you consider what's going on both on and off the grid; you'll have to combine your thinking in both areas to complete the hardest puzzles.

Hexes Earned for Completing this Puzzle: 3

A fish maybe?? Anyway, this puzzle builds upon what we learned in the last two. Notice that except for the last one, all of the columns have a number outside of them. You may notice that two of them have zeroes; we can eliminate those cells from the outset.

We'll actually get an empty "0" cell from doing this, which gets rid of a couple more cells. The "1" revealed on the far right side from doing this actually allows us to fill in our first blue cell of the puzzle, while eliminating another hex from the left side of the "1" which shares that blue hex. We can then finish the third column from the right by coloring its lone remaining cell.


Now, let's look at the empty cells revealed by clearing out the empty column towards the middle of the grid. The top one is a "2", and it borders only two active hexes. When we mark both, we find that the one to its right falls into a column headed by a "1". Since we've just marked its required blue hex, we need to erase the other cell from the column.

Let's next work with the empty "1" cell below the "2" we just solved. The "1" immeidately popped up next to its required blue hex. We now need to erase the cell to its left. This one falls into a column headed by a "2", and we have left it with only two active hexes. Mark the other one to solve the column.

Finally, let's look at the empty "3" cell we revealed a moment ago. It only has three total hexes around it; one is colored, so simply color the other two. These two hexes fall into one of the columns headed by a {3}. We don't know yet if the hex above or below that pair will be marked, but the first hex of the column clearly won't be connected to them. We want to erase it next.


The "0" we just revealed tells us how to complete its respective column; when we erase the zero's three surrounding hexes, we leave its column with only three continuous active hexes, allowing us to mark the last one at the bottom. Notice that this also leaves the next column over, which is headed by a {4}, with only four total active hexes; now, just mark all four.



The zeroes we've uncovered from this also set up the solution for the next column, which is headed by a {2}. The top hex was just eliminated, leaving the "1" on its bottom-right edge with only one possible blue hex to claim. Marking it gives the column its first blue hex; since we know to ignore the gap between it and the next cell down, we can mark the third cell and erase the fourth to solve the column.

We're almost done, but the first and second columns are a little trickier. Begin with the "2" in the center of the third column; it still needs another blue hex, and its only possible choices fall into the second column. The second column is headed by a {3}, meaning that it needs three consecutive blue hexes.

The trick is that if we were to start the column's chain of blue hexes with the cell on the top-left edge of the "2", we have to go up the column, since the cell below cannot be marked without giving the "2" a third blue hex. We can't do this; there aren't enough available hexes! So the answer is that the bottom three cells of the column must be marked blue. Afterward, erase its top two hexes.

And finally, to solve the first column, also headed by a {3}, we need to erase its top hex; the "1" we just uncovered to the right already has a blue hex to its right. This leaves only three active hexes for the column. Mark them all to complete the puzzle.



Hexes Earned for Completing this Puzzle: 6

We get another new game mechanic for this puzzle:



Here's the in-game hint: "Numbers like this -3- give the additional information that the 3 hexes are NOT connected."

So this one is saying that if a row or column has a negative number outside of it, that number of blue cells still exists within that row or column; however, they won't all be linked together. There will be at least one empty hex separating them. This gets a little more complicated the larger the number is. Let's say for the sake of argument that we had a -5-. The line's five blue hexes won't be consecutive, but that doesn't mean that some of the cells won't be connected. In this example, the cells could be clustered such that four are consecutive with the fifth somewhere else; three connected with two separated from them; or, if it's really convoluted, five individual blue hexes with empty hexes spaced in between all of them.

Before jumping into this puzzle, let's review the basic rules for dealing with numbered rows of cells:

• A standard integer, such as 4: This just means that number of blue cells exists in that row or column; they may or may not be connected in some fashion.
  
  
• An integer in braces, such as {4}: This means that number of blue cells exists in the row or column and that they all must be consecutive. Remember that gaps within the same row or column do not count as an obstruction between consecutive cells; only actual empty hexes do.
  
  
• A negative integer, such as -4-: This means that number of blue cells exists in the row or column but that they won't all be connected. Depending on the total number of active hexes, some of the required number may be connected, but you will always have at least one separated from the group.

Please refer to this any time you may need a refresher on how numbered rows work. It can take awhile to get used to this, especially now that we're working with groups that will always have disjointed blue hexes.

Let's start with our opening moves. Any time you have an empty "0" cell, it can be incredibly helpful. It's the only empty cell we get to start out, so we might as well get rid of the surrounding cells. Let's now look at the column in which our lone blue hex is sitting. It has a {2} at the top, meaning that either the cell above or below it has to also be blue. We just got rid of the one below it. Color the one above it, then get rid of the other two cells to complete the column since no others are allowed to be colored.

We just revealed another "0"; go ahead and follow it. This will give us a couple of empty "1" cells to work with; we can go ahead and safely mark the cells adjacent to them as no other active hexes border them. Let's now look around the rest of the grid; we don't have very much more that is obvious to start with. But I do want you to focus on the column headed by the -2- near the far right edge of the grid; notice that this column only has three cells total. Since the two hexes cannot be consecutive, we can mark the top and bottom cells and eliminate the middle cell to solve this whole column.



The most important thing we accomplished by solving that column was to open up the immediate area around it. The empty cell we revealed is a "2"; of course, we just colored its required two hexes just by solving the column. We now eliminate the four other cells around it. To the right, we reveal two more empty "2" cells; we can thus color the lone cell at the very right edge of the grid to give each of them the second blue hex they need.

In order to find our next series of moves, we'll need to return to the center section of the puzzle. The empty "2" cell we revealed at the bottom of the center column only has two options for blue hexes, so they will automatically be colored. Similarly, each of the empty "2" cells surrounding the "0" in the central cluster all only have two options for their blue hexes. Notice that marking all of these hexes also satisfies the column requirements for all four columns we were just working in, eliminating a huge number of cells.



Let's try to solve the right half of the puzzle now. The empty "1" cell on the bottom row, just right of center, already has a blue cell, so we can clear the one to its right. That gives us a "1" with only a single choice for a blue hex. This brings us to a second column headed by a -2-, and we just marked one hex for it. The next blue hex in this column cannot be connected to this one; as such, erase the cell directly above the blue one.

The "3" that this uncovers is immensely helpful; it not only has just three active hexes to deal with, it also reduces the "3" on its upper-right edge to three active hexes. Marking all of them gives this second -2- column its second blue hex, meaning its other two are eliminated. The "2" in the next column to the right now also has two blue hexes, eliminating the final orange hex at the top of that column. The "1" at the top of the second -2- column now has only one choice for its blue hex, which we now mark to complete this half of the puzzle.

Again starting at the bottom, let's solve the other side. The empty "1" cell just left of center already has a blue hex; get rid of the one to its left. We again reveal a "1" with an obvious choice for a blue hex. When we fill it, we solve that whole column; notice that it is headed by a "1". Clear all the other cells in that line. Next, clear the cells around the "0" we just revealed.


Let's return now to the empty "2" cell at the bottom of the column we just solved. It only has one choice for a second blue hex. Mark it, then go to the "1" directly above the "0". It has only one choice for a blue hex, which is shared by the empty "1" cell directly above it. The orange cell directly to the right of this one is now eliminated.



We're almost done, but this may be the trickiest part. We must now solve the third column, which is headed by a "1". The problem is that each empty "2" cell in the fourth column needs a blue hex apiece, with their only choices coming from the third column. Naturally, if we mark the top and bottom hexes, we break the rule established by the column header. So we need a blue hex which will be shared by each "2". That means the middle one is the correct choice.

Clear the top and bottom hexes in this column to reveal two more empty "2" cells, which each already have two blue hexes. This eliminates both cells from the second column and leaves only the lone hex on the left edge to color, thus completing the puzzle.



Hexes Earned for Completing this Puzzle: 8

Congratulations on reaching the final puzzle of Chapter 3! Working with entire columns of cells adds another dimension to the mechanics we learned in the previous two chapters. This puzzle will put your new skills to the test.




If you're like me when I saw this puzzle for the first time, you probably have no idea where to even start with this one. Looking at the empty hexes, there aren't really any obvious choices for filling in cells. We do get a "0" at the bottom of one of the columns, but the rest of the information we are given simply comes in the form of various column headers establishing different conditions for the cells we must mark. Don't be frustrated if it takes you a few times to perfect this puzzle. Even while working on this guide, it took me a couple of attempts to fully understand the logic of how this one works, even after having already completed the game once.

Let's at least go ahead and clear the cell above that "0." It gives us a "1"--again with no definite option as to which cell it will capture. We'll need to look at the column headers to figure out how to approach this one. The ones of most interest are closer to the center and are headed by a {3} and a {4}. We'll need to do some cell counting for these. The column headed by the {4} has five total cells that could fit the requirement of four consecutive hexes. We can mark a few of these immediately; try numbering them in your mind from top to bottom, 1 through 5. Then count: 1, 2, 3, 4, STOP. Now start over from the second cell: 2, 3, 4, 5, STOP. These are the two possible sequences that can form a line of four continuous blue cells; notice that in both sequences, we include cells 2 through 4, meaning that those three cells must be marked.

Let's do the same thing for the column headed by the {3}, which also has five possibilities to color. Numbering again from top to bottom and counting them out gives us this:

1, 2, 3, STOP
2, 3, 4, STOP
3, 4, 5, STOP

So we know the middle cell of the column has to be marked. See what this did to the empty "3" cell in the center? It now has its three blue cells! The lone remaining cell around it can be cleared now, and we have some new avenues open.

While it may not be immediately apparent, we can now solve the rest of the puzzle. Let's stay in the {3} column; we just revealed an empty "2" cell that serves as the boundary for the continuous three blue hexes required. As such, we now know that all hexes above the "2" are colored, and everything below it eliminated.

Let's now look slightly to the left; the empty "2" cell in the next column now has its two blue hexes. The orange hex to the left can be cleared. Doing this gives us a "1", but we can almost ignore it because the "2" directly underneath it only has two possibilities for blue hexes. We'll go ahead and mark both. The "2" shares one of them with the "1", and the other with a number of other nearby empty hexes. The "2" near the bottom of the column headed by the {3} has only one remaining choice for a second blue hex, which will be shared with the "1" below it.

We should now immediately be able to finish the left half of the grid. Let's start from where we ended the last step; the empty "1" we just revealed shares the blue hex directly above it, so the next hex to its left is cleared. This reveals a "2", but more importantly, it eliminates one of the possibilities for the "3" right above it to get a third blue hex, leaving only one for us to mark. When we do, we'll solve both the "3" and the "2", and we'll be able to clear the other cell beside the "2". This reveals another "1"; it shares the blue cell we just shaded. We can pretty much just continue with this logic.

To solve the last few cells on this side, realize that the empty "1" cell furthest left on the bottom now only has a single choice for a blue hex. When we mark it, we also satisfy that column's requirement for one blue hex and can clear the one on top. The "1" this reveals will guide our next moves. Mark the only cell it can claim to give the nearby "2" a second blue hex, then clear the remaining orange cell on top of it. The "3" we are encircling with this pattern then claims the final hexes on this side.

We now need to take a hard look at the right side to see what our next move is. Going to the final column, headed by a {2}, we can mark the center cell using similar logic to solving the central {3} and {4} columns earlier. Doing this gives us...absolutely nothing.

Our next move is arguably the hardest one to figure out on the first try, but it's also the move that will open the rest of it up. We need to focus on the column headed by the -2- towards the right side. This one took me awhile to understand. We have four cells total; cells 1, 2, and 4 are orange, while 3 is an empty "2" cell. The column requirements dictate our first step: We must have two blue cells total, but they cannot be consecutive. This means that either the first or the second cell can be colored, but not both. So we know that the bottom hex of the column must be colored.

Coloring the bottom cell of the column also gives the nearby "1" the lone blue hex it needs. By getting rid of the other three orange hexes around it, we can also solve the final column, headed by a {2}, since it now will only have one cell left to claim. Notice how the empty "2" cell nearby already has its two blue hexes, which eliminates the cell below it. The "3" that this reveals will then get the cell below it for a third blue hex.

We should be able to solve the rest of the puzzle now. The "1" at the top of the next-to-last column only has one choice for a blue cell; filling it also gives the third-to-last column its second blue hex, eliminating its final cell at the top. This reveals another "2", which similarly only has one choice for a second blue cell--which is shared by the "1" to its left.

Next, go back down the column headed by the -2-; the second empty "2" cell has a blue cell above it, and one below it. The two remaining hexes to its left can be cleared. We can now complete the column headed by the "2"; it has a blue cell already, and with everything else in the column eliminated, only one active hex remains to be colored. That cell will fulfill blue hexes for the empty "1", "2", and "3" cells bordering it. The orange hex to the left of the "1" can now be erased, clearing one of the choices the "3" originally had for a third blue hex. The "3" will now claim the final hex surrounding it, which also gives the {4} column the last consecutive blue hex it needs. Notice the counter of remaining blue hexes now reads "0." The puzzle is now solved; we need only clear the final two orange hexes to finish.



Hexes Earned for Completing this Puzzle: 8

We are now exactly halfway through Hexcells! Puzzle 3-5 was the first true brain-teaser you've faced. Chapter 4 takes the concepts of working with lines of cells and applies them to individual clusters of cells. Eventually, both concepts will be combined, and you'll have to consider even more restrictions on the grids themselves to solve the later puzzles.


Here's the layout of our next puzzle, which introduces the concept of working with clusters of consecutive blue hexes:



"Numbers inside brackets {} give the additional information that adjacent hexes are connected."

What this hint is saying is that if we have an empty cell with a number inside of braces, then all of the blue cells surrounding it will be consecutive, similar to the lines of cells we worked with in Chapter 3.

Special Note: I know that the game calls them "brackets," but in math, these are actually called "braces," so for consistency, that's how I refer to them; the terminology has no bearing whatsoever on the game itself, however. By the way, true brackets are like this: [ ].

For the first grid of this puzzle, notice that the "4" only has four cells surrounding it; we mark all of them, giving a shared blue hex to the {3} at an endpoint in its respective ring of hexes. This is important, because the fact that we mark an endpoint means we just have to mark the next two cells in sequence and erase the final two from the {3}. So in essence, we get six consecutive blue hexes from this!

This grid is actually really easy if you think it out. The second grid is only a little harder, but we have to be more careful with the {4} in this one. It actually has five active cells surrounding it, but we can use a numbering trick similar to what we utilized in the last chapter, ensuring that the middle three hexes in its ring are marked:



Marking these hexes also gives a shared blue hex to the "1" at the end. When we eliminate its remaining two orange hexes, only one active hex remains to be colored, thus solving the puzzle.



That puzzle was pretty easy; the next one isn't quite as straightforward...

Hexes Earned for Completing this Puzzle: 3




Well, well, well. We have no information other than a few empty cells, all of which have numbers in braces. This is one of the few times where the opening moves may not be as obvious as in most puzzles. The trick to this one is paying very close attention to your shared blue hexes as you uncover them. They will feed into the sequences required by multiple empty hexes.

I like to work the opening of this puzzle from top to bottom, and just take each empty hex roughly in order. We'll number surrounding cells like in the previous puzzle to try and come up with a few obvious blue cells to start with:



I hope the relationships established with the steps in that picture are clear. Also: You may notice that I did nothing concerning the {4} in the middle of the grid. That's intentional; since the maximum of six hexes surrounds this one, it's impossible to know for certain which ones to include without more information. We did obtain some of this information in the previous step; we'll return to that region later. For now, though, we've opened up some new avenues from our previous work.

We've managed to solve a couple of the hexes at the bottom with our last steps. We can clear away the remaining hexes surrounding the {4} and {3} now. When we do this, the choice of a second blue hex for the {2} at the bottom-left corner becomes clear. Notice also that we have already given the {2} above that one the two blue hexes it needs, so we can eliminate the other two surrounding it. One of the empty cells revealed is a "0"; go ahead and clear the lone cell to its left.

These last few steps help set us up to clear the top half of the puzzle now. The "1" we revealed at the center of the grid has a blue cell below it, so we can clear the orange hex above it. As to the empty {3} to the left, we've eliminated or colored all of its choices for blue hexes except for two, which will now be colored. This gives us an endpoint for the {4} in the middle now; we can complete the sequence and eliminate the final cell around it. The "1" revealed from this tells us to eliminate the orange hex from above the {3} to the right, and we can now complete its sequence, as well:



We're almost done now. The {2} at the upper-right has one blue cell, with only one other orange cell remaining as a possible capture. We'll go ahead and color it, leaving us only with the {3} on the opposite side. We actually don't have enough information yet about which of the remaining cells it will capture; however, we do know the two it will not. Naturally, the very top cell is not possible; it doesn't even border the {3}. Look at that: a "0". That eliminates two of the final three cells, leaving only the last one to color and solve the puzzle.



Note: You also could have eliminated the hex directly above the {3}; this is also correct since it falls outside of the possible captures for making three continuous blue cells. As that hex also reveals a "0", the outcome is exactly the same.

Hexes Earned for Completing this Puzzle: 6

That last puzzle was a decent jump up in difficulty from Puzzle 4-1. It's going to get harder as we move on to the final puzzles of the game.




Eek, a bat!! That's what I see when I look at it, anyway. It took me awhile to understand the logic to this one, too. Admittedly, when I played through it in a practice run before writing out this solution, I tackled parts of it completely differently. I think the solution given here is a more logical process than the one I ended up using in the practice run. As always, though, if you discover another way of tackling parts of it, feel free to experiment. Remember that this guide is designed to give solutions based on one person's throught processes and the logic behind them.

So starting out, there's very little to go on in this puzzle. We get two empty {3} cells towards the top-center, and a "0" at the bottom. That's it! Nothing else.

The problem with the empty {3} cells is that with the maximum of six hexes surrounding them, there's no clear way to determine any of the cells that can be marked. Do they share blue hexes or not? So our only obvious move is to clear away the cell above that "0" and see where it takes us. Well, we at least get another "0" which allows us to clear away three more cells. One of those is yet another "0", so let's just clear the path ahead of that one, too.

Perhaps the most obvious place to start after clearing everything around the zeroes is with the two empty "1" cells on top of each other on the right side of the cluster. The one on the bottom has only one obvious blue hex to claim; when it is marked, however, the "1" above shares it, allowing us to clear the remaining orange hexes around it.

When we clear those other orange hexes, we reveal a "3", which only has three active hexes of its own to work with. So all three will be colored blue; this will give the empty "2" cell we just revealed a second blue hex (it also shares the one we just marked at the bottom). We eliminate the other two orange hexes bordering the "2". One of the cells revealed from this is a {2}, which also shares that same blue hex at the bottom. We'll automatically color the hex to the right of the blue one to give the {2} a second consecutive blue hex, then clear the other hexes surrounding it.

We can't quite finish the right side yet, but this made some substantial progress. We've revealed quite a bit more towards the middle now, so let's see if anything opened up there. We actually have a second {2} with only two active hexes surrounding it--and one is already colored. We know to immediately color the second one, which will be shared with the "1" on the bottom-left edge of the {2}. This clears the remaining orange hex bordering the "1".

We get a {3} from this elimination, and it already has a blue hex at an endpoint. We need to color the next two hexes over from that one to give it a continuous series of three, and we then eliminate the fourth hex around it. This gives the "1" under the {3} only one remaining choice for a blue hex, so we'll go ahead and color that one, too. And now guess what? That "2" we just revealed now has its two blue hexes, clearing the two orange hexes to its left.

Notice now that both of the empty "1" cells we just revealed at the end of the last sequence already have the blue hexes they need; this is going to eliminate five more hexes from the region. We can now finish the bottom-left corner; notice that the "2" we revealed in the middle of all of that has only two choices for blue hexes. When we mark both, we'll give the "1" directly below it the lone blue hex it needs, and we can clear the bottom orange hex to the left of the "1". The "2" revealed from this will then claim the final cell in the corner.

Let's now go roughly halfway up the left side, where we have a {2} and a "1" clustered together. It doesn't matter which of these we solve first. The {2} has a blue hex on its right; marking the next cell above that one will give the {2} a second consecutive cell. Now, since the "1" already has a blue hex, just clear all the remaining orange hexes touching both cells.


We're almost ready to complete the puzzle. Let's start with the {3} we just revealed. It already has a blue hex; since it's an endpoint, we know the next two hexes we must color to give it three in a row, and we'll then eliminate the fourth hex above it. We'll reveal a "2" with this, but also note that we just cleared one of the only two candidates for a blue cell that the "1" immediately to its right had; this means we can color its only remaining option. When we do this, we actually give a second blue hex to both empty "2" cells bordering the "1". We clear out the remaining orange cells bordering each of them; in the top-left corner, we reveal two empty "1" cells, both of which already have a blue hex. That means the cell in the top-left corner is also eliminated.

We now have enough information to solve those empty {3} cells in the top-center of the grid. With the first one, the first two hexes on its underside are already colored; when we color the third one, we also complete the sequence of three for the next one! Clear all of the other cells surrounding both of them! For that matter, clear the top cell in between the two zeroes revealed from this.


We can now finish this puzzle off. Continuing to the right, the "1" next to the second {3} already has its one blue cell, clearing the other two bordering it. The "3" revealed from this already has two blue cells, with two other possible candidates. However, if we look to the "1" right above it, we see that it has only one active hex that we can mark; it will be shared with the "3", and the final orange hex bordering it is now cleared. This reveals yet another "3". The "2" directly beneath it now has only one choice for a second blue hex, which will be shared with the "3" to give it a third blue hex. Now, clear the hex on its upper-right edge.

Finish the puzzle now from the far right side, bottom to top. Both empty "1" cells at the bottom of the next-to-last column have their required blue hexes, which lets us erase the bottom hex of the final column. This reveals another "1" which shares one of the blue hexes, so erase the cell above it. This reveals a "2" with only one obvious second blue hex to claim; marking it also gives a third blue hex to the "3" to the left, letting us erase its final hex. At this point, we're left with only two orange hexes, with two left to allocate; mark both to complete the puzzle.



Hexes Earned for Completing this Puzzle: 9

The previous puzzle isn't too difficult, but it's easy to make mistakes if you try to work too quickly without studying the relationships between the cells. Chapter 5 is revealed at this point if you would like to take a look at some of the more advanced puzzles coming up.


For now, though, here's the layout for the next challenge:



This is stylistically similar to Puzzle 4-2 in that the only information given to us is a bunch of empty cells with braced numbers; the layout itself, however, appears more complicated.

Many of the empty cells in this grid are positioned near edges, reducing the number of cells bordering them. One big exception is the {3} at the very top; it has the maximum of six hexes, so it's impossible to determine any of the cells it will claim.

It may be easiest, then, to start at the bottom. Start with the {3} in the very bottom-right corner; we know that we can mark the middle cell in the cluster surrounding it because, if we number the cells and count the possibilities for getting three consecutive blue cells, it will be part of all of them. Now, notice that we are also giving a cell to the {3} right above this one. Well, we still know that the center cell in its cluster will be colored, as well. Here's how this looks before we move on to how we actually solve those cells:

From this, we still don't necessarily know which cells the empty {3} cells will obtain to complete their sets of three; however, we do have more information concerning the ones they cannot have. Let's start with the upper {3} this time, since it now has two blue hexes. The fact that its final blue hex must be linked to them means either the cell above or the cell below must be the third one. Therefore, we can safely clear the one on its top-left edge. The "0" we reveal guides us to the answer; clear it, then mark the final remaining hex under the {3}.

Notice that we now have an identical situation with the {3} at the bottom; we have another obvious elimination of the orange hex on its bottom-right edge since it cannot possibly be linked to the two blue hexes surrounding it. We get another "0" from clearing it, which again makes the solution very easy.

Let's go back to where we just were, then; we revealed another "0" moments ago. We'll reveal a "1" by clearing the cell to its left, but it really doesn't tell us much. We'll need to work our way back to it later. Here's what we have so far, though:




Since we still can't do anything with the {3} at the top, it doesn't really matter whether we try to solve the left or the right side first. Let's go to the left side and see if we can join back up with where we left off. We have two more {3} cells on top, and two {2} cells on the bottom. Starting with the {3} closest to the left edge, we again know that the third cell in the surrounding cluster must be marked. This is shared with the {3} to the right, which interestingly only has four surrounding hexes. This means we can mark both center cells within its respective cluster.

Notice that when we mark the two center cells surrounding the second {3}, we also give a blue hex to the {2} directly below. We are now going to eliminate the two outermost hexes from the cluster surrounding the {2}; neither can be consecutive with the blue one we just gave it.




The "2" we just revealed towards the bottom of this group will help us solve the section. Note that it only has two choices for blue hexes. When we mark both, we solve it, the {2} to the left, and the {2} above! So now, we can erase the remaining cells surrounding each of these, as well as the one to the right of the "0" we also uncovered.

We can now solve the {3} on the right side of our pair; we've left it with only three active hexes. Marking the third also gives the {3} on the left a second blue hex. This allows us to treat it like the others in the bottom-right corner. The cell on its bottom-left edge cannot link up with the two blue ones; erase it, then use the "0" uncovered to finish it:


Well, we still can't solve the middle section, but we are a little closer. Let's tackle the upper-right section. The overall logic is similar to what we were just working with; the {3} near the corner has five surrounding hexes. We'll color the center one in the cluster again, also giving a blue hex to the {2} under the one we just marked. The {2} has a total of four hexes surrounding it; however, the position of the blue one tells us that only the cells to either side of it can possibly be marked blue. So we can safely eliminate the one on the bottom-right edge of the {2}, since it cannot link to the hex we just colored.

We reveal a "1" from this elimination; it has only one possible hex to claim, which will give a second consecutive blue hex both to the {2} and the {3}. Clear the final hex from the {2}; can you guess how we are going to solve the {3}?





We'll continue working this section to the left. Luckily, the {3} we just revealed only has three total active cells surrounding it. After marking them all, the {2} we uncovered a moment ago will have the two blue hexes it needs. Erase its remaining orange hex next. The "1" that this reveals also shares a blue hex with the empty hexes we just worked. Eliminate its adjacent orange hex, then follow the "0" that it reveals:

We're left with the central cluster. This is the hardest part of the puzzle, and this is where you are almost guaranteed to make a mistake at least the first or second attempt because the logic is a little more convoluted than what you are used to. I'll break this down to try and make it as straightforward as possible.

• We know that the {2} in the middle of the cluster has to have two blue cells in a row.
  
• We also know that with an unsolved empty "1" cell right next to it, one of the hexes shared between them has to be marked.
  
• This means that the two consecutive blue cells for the {2} have to be in a line extending from the shared blue hex we ultimately mark. See the next image for an illustration of this.

What we learn, then, is that the orange hex in the middle of the cluster surrounding the {2} cannot be colored. We eliminate it: This reveals a "2", and while it may not be readily apparent, this does give us an important new clue. That "1" on its bottom-right edge now has only a single option for its blue hex. When we color it, we also give the "1" directly above the lone blue hex it needs. We eliminate the orange hex attached to its bottom-left edge:



We've now reached the end. The "1" we just revealed shares the blue hex we just marked. When we clear the orange hex to its left, the final two hexes of the puzzle are colored to complete the requirements for the "1" and the {2}, and the puzzle is complete.



Hexes Earned for Completing this Puzzle: 14

The last puzzle actually isn't all that difficult until you finally reach the center section, since the solution is a little more difficult to flesh out than the rest of it. If you understand the logic to Puzzle 4-4, you're likely to do well with the more advanced puzzles coming up. For now, though, it's time for the final challenge of Chapter 4.

I ran through the next one once before deciding how to present it here; it's deceptively tricky. This is one where you can cruise along and then suddenly hit a roadblock as to how to proceed, so I'll try to address these areas in-depth.




What's this??? Empty cells with negative numbers?? Why is there no hint explaining this??

This is a mechanic that Hexcells does not take great pains to explain; however, if you remember from Chapter 3, anything with a negative integer has blue cells that are not all consecutive. This is true of negative integers inside of empty cells, as well. We'll take the -3- in the bottom-right corner as an example; yes, it will have three blue hexes surrounding it, but they won't all be linked together, meaning you'll have an empty hex between them. We'll examine the concept more as we work the puzzle, but it's no harder than dealing with non-consecutive blue hexes in rows or columns of cells.

In fact, let's go ahead and work that -3- to start with because it does illustrate an important concept. We can modify the counting scheme we have been using to this point to work this type of cell. Number the cells from 1 through 4 like we have been; just as there are different patterns of hexes we can use to get three which are consecutive, there are also patterns we can use to get three which are disjointed:

1, 2, and 4
1, 3, and 4

Any other sequence will cause the three hexes to be consecutive, which isn't what we want with a negative integer. What we learn, though, is that the first and fourth cells in the cluster have to be marked:



This brings up an important point: ANY -3- with only four consecutive active hexes will always have its endpoints marked. Learn to recognize this pattern. In fact, at the upper-right and left-center of the grid are two more -3- cells to which we can apply this logic. Don't even try it with the one at the top, though; with five active hexes, there are too many possible combinations to narrow them down yet. Mark the guaranteed blue hexes around the others, though, but be careful since we end up with a shared blue hex for the two on the right. Also, mark all of the hexes around the {5} at the bottom.

Alternatively, we could have solved the {5} at the bottom first; I chose to start with the -3- simply to illustrate the puzzle logic involved with them, and this was a great location in the grid to start with. The reason? Solving the {5} gives the -3- the third blue hex it needs now. We can clear its fourth cell to finish it.

We can't do much else in the middle of the grid right now, but we can look at one other thing. See the two nearby -2- cells near the top-center? They each have five hexes surrounding them. But look carefully; our work with the -3- cells a minute ago has given each of them a blue hex. While we cannot yet determine which other hexes they will capture, we do know to erase the orange hexes linked to the blue ones in their respective clusters:

If we now focus attention to the right edge of the grid, we can solve a big chunk of it now. Notice those two empty "2" cells on top of each other in the final column. Their only active hexes are the ones in the next column over. In order for each to get two blue cells, they will share the center cell, which is already marked, and then each claim one of the remaining cells. In other words, that whole column gets marked. This also gives each of the -3- cells we were working with a few minutes ago the third blue hexes they need, clearing their remaining orange hexes.

Let's look below now. The empty "4" cell right above the -3- we solved earlier has only one more choice for a blue cell that we can now color. For now, this is the last move we have in the middle of the grid; we can now focus on the far left side. Luckily, that "3" in the first column only has three hexes surrounding it to color. Notice that when we do this, the -3- nearby receives a third blue hex, letting us erase its final orange hex.

The "3" we just revealed from that elimination already has three blue hexes; clear the one above it. Then, go ahead and mark the second obvious blue hex the "2" we just revealed needs:






Now, remember that roadblock I mentioned in the puzzle introduction? Here it is. Look carefully around the entire grid. There is not another single obvious cell that we can color! Are we out of moves?

It may seem that way, and this is when you really have to look at the puzzle logic surrounding the indvidual cells on the grid. There are a couple of moves left that are not readily visible. Let's start near the bottom, with the -4- and the nearby "2" to its upper-left. The -4- has three blue hexes; the "2" has one, with three orange hexes around it to the right. We can use this to get rid of another cell. Can you figure out how?



Another empty "2" without any obvious cells to mark. Disappointing, but it still gets us a step closer. Maybe we'll have better luck at the top of the grid?



Use the details in that previous image to make your next move. In doing so, we'll give the two -2- cells on either side of the hex we just marked their second blue one, clearing two more:



Let's finish the top section from left to right. The -2- at the top of the fourth column has only one choice for a second blue hex. Mark it. The -3- two columns over now only has one final choice for its third hex; mark it, too. This blue hex is also shared with the -3- directly below it, giving it the third one it needs; eliminate the remaining orange hex to its right. Finally, the last orange hex in the section is colored to give the "3" right below it the last blue hex it needs:



It's time to finish this chapter. We'll work the remaining orange hexes from right to left. The one in the very center of the grid is the only remaining choice for the "3" beside it to get its third blue cell. This also gives that -4- we've been fighting with its fourth blue hex. Erase its final orange hex to reveal a "2". It pops up with two blue hexes already, so erase the one to its left. This clears one of the remaining choices for that -2- on the edge to get its second blue hex; mark the one below it and clear the final hex to solve the puzzle and the chapter!



Hexes Earned for Completing this Puzzle: 12

Congratulations on your progress so far. We are now 2/3 of the way through Hexcells. At this point, all of the game's puzzle patterns have been explained. What we will see for the rest of the game are simply variations on what we have already been taught; for example, Puzzle 5-5 introduces the concept of working diagonal lines, whereas we previously have only been given vertical columns to deal with. That puzzle will also formally demonstrate how to mark lines of cells to work with--though I find it useful in some of the other puzzles in this chapter, too...

One final note before we go on: As these final puzzles tend to be the longest and most complicated, many of them will need to be split into multiple parts. In such cases, a screenshot from the last completed step will be presented at the beginning of the second part for easier reference.




We don't get a lot to work with on this one. We have three column headers; three empty cells on the far left; and one blue cell given to us. That's it; we don't get anything else to fill in this whole big puzzle.

The very first thing we should do is eliminate the cells in the column headed with a "0". A few empty "0" cells will be revealed from this; just follow them until you get a "1", then stop since you can't solve it yet. We'll need to work this puzzle in a generally counterclockwise fashion, since most of the information is concentrated on the left side. Start with the "2"; it only borders two orange cells, so they will automatically be marked. This will give both empty "1" cells bordering the "2" a blue hex, as well, clearing two other cells:

We revealed two -2- cells with this; the one on the bottom is easiest to solve, since it only borders three active hexes. The first in its cluster is already colored; just skip a hex and color the third, then clear the middle one. When we do this, we reveal a "3"; it immediately has three blue hexes around it, clearing the two orange hexes to its right. Now, we can't immediately solve the -2- near the top yet; however, since we know that its second blue hex cannot touch the one it already has, we can at least clear the orange hex connected to the blue one.

We also can't do much with the -3- revealed at the end of the last step; however, since we have two consecutive blue hexes bordering it already, we at least know that the one next to them cannot be marked since we have to leave at least one empty cell between the blue ones.




The most obvious move we have now is to clear the two remaining orange cells from the "1" closer to the center of the section; it already has the blue cell it needs. The {3} revealed with this step will now be immediately solvable; color the only three active hexes surrounding it. Doing this will give the -2- on its upper-left edge a second blue hex, clearing the one directly above it. We now know which hex to give to the -3- we were working with a moment ago; once we mark it, it will also be shared with both the "2" we just revealed and the -2- on the left. This will clear the three remaining orange cells across the top of the section.

We're moving down the grid now, to the dueling empty "2" cells on the bottom edge of this big cluster; note that the one on the edge already has a blue cell, with only one other possible choice. Marking it gives a second, shared blue hex to both of them; clear the remaining orange cell below the other "2". The next several moves are pretty straightforward.


We've solved about 1/4 of the puzzle now, so we're making good progress. Notice that now, the "1" at the top of the empty column we cleared before (the one headed with a "0") has its blue hex. We can continue to the right by eliminating its remaining orange hex. The "0" this reveals lets us clear a few more cells.

Now, in the column to the right of the zeroes we just revealed, the "1" on the bottom has only one choice for a blue hex, which will naturally be shared with the "1" directly above it. Mark this cell, then clear the orange hex directly above it. In doing so, we'll eliminate a hex from beside the {2}, leaving it only two active cells to claim. One of them will be shared with the "2" we just revealed, and the two hexes to its right will now be cleared:

Let's now work with the {2} we revealed when we eliminated those last two cells; it shares the blue cell located below the "2" we just solved. So since the next blue cell it claims must be connected to this one, we just need to color the next hex over and clear the remaining orange hexes surrounding the {2}.

We can now solve the -2- directly above it; it now has only three consecutive active hexes, with an endpoint already marked. Mark the second endpoint, then erase the middle hex. Well, that's interesting; we get another -2-. Since it shares the two blue hexes of the one below, the three hexes along its top edge are now eliminated. Go ahead and follow the path created from the "0" we reveal from this, too.

Only a few more steps to clear this section now. The empty "3" cell at the bottom has a blue hex, with only two more possibilities; go ahead and mark them. This will give a second blue hex to the -2- above it, and we'll clear its remaining hex. Note that the "3" this reveals already has two hexes but also has two possible choices for its third. Look to the "1" above it for the solution; with only one cell to claim, marking it will also complete the "3". When we clear its final orange hex, we can advance to the right section of the puzzle:

I'm going to go ahead now and demonstrate a mechanic that will be vital in later puzzles, and which will be formally introduced in Puzzle 5-5. We still have two columns headed with a "2" that we have not yet solved; well, we can actually solve one of them. Click on the first "2", and you'll see a light white line drawn through all of the cells in that column:



Remember that the column header tells us the number of blue cells the column will contain; no more, no less. Our line just so happens to pass through two blue cells; this means we can go ahead and eliminate the two cells in the upper part of the column.

One other note about this mechanic. You can click on the column header a second time to remove the line, or right-click on it to dim it out altogether if you're sure you are done with the column. All of this is true for the headers outside of diagonal lines of cells, too; this will be demonstrated later.

We're just over halfway done; here's where we're at:



Returning to the right section of the puzzle, notice that we have a ring of four empty "1" cells; the two outer ones each have only one choice for a blue hex. When we mark both, this will clear away several other cells. Move next to the {2} revealed from this; it will only have two choices for the blue hexes it needs. When we color both, we will solve it, the "2" to its right, and the -2- to its left! Just clear away the two remaining orange hexes from the -2-.

Solving the rest of this section is pretty straightforward. The "4" we just revealed gets the remaining orange hexes surrounding it as there are only four active cells to start with. That also gives the nearby -2- the second blue hex it needs; clear its remaining orange hex. The "2" this reveals will then claim the final hex of the section to get its second blue one.

To continue now, we need to realize that the second column with a header of "2" has now been solved; when we marked the hexes surrounding the "4" a moment ago, we filled in the two cells that column needed. Eliminate the top cell to open the way forward.




Only one final section to solve. Take the triangle of empty "1" cells here in order; we know the one on the right has to capture that lone orange hex above it since no more are available. That hex is shared by the "1" at the top of this triangle; clear the two remaining orange cells to its left. This means that the final "1" at the bottom of the triangle will capture the remaining hex to its left.

Look next at the "3" we just revealed; we just gave it a blue hex, but only two more active hexes remain around it. We can go ahead and color both, also giving a blue hex to the "1" directly above the "3". Eliminate the orange hex still bordering its top-left edge.




We pretty much just continue with the same trains of logic now. From the "1" we just revealed at the very top of the puzzle, we see it has a blue hex directly below it. Clear the orange hex to its left. The "1" we reveal from this shares the same blue hex, and the two orange hexes below it are thus cleared.

We reveal another -3- now; it has two blue hexes which are adjacent to each other. It is surrounding by only four continuous active hexes. Remember that any -3- in this setup automatically has its endpoints marked. Go ahead and mark the second endpoint for this one, then erase the hex under it.

The blue hex we just filled is shared by both the "1" above it and the -3-; when we clear the orange hex on the bottom-left edge of the "1", we will reveal yet another "1" which shares that same blue hex. Clear the hex beneath it, then do the same thing with the next "1". For the "2" that this reveals, we see only one remaining choice to give it a second blue hex, and that will also give the "3" next to it a third blue hex. Clear the final orange cell in this cluster.



Now we just need to fill in the final cluster in the center of the puzzle. The "3" leading into this section already has three blue hexes, so we can eliminate the orange hex below it to clear the path. Honestly, if you understand everything up to this point, there is no reason why you can't solve the rest on your own. Don't worry; you won't be thrown any sudden curve balls at the end. Just do what you have been doing up to this point.



Whew! Puzzle 5-1 isn't so much a brain-teaser as it is a marathon. While there are a few reasonably tricky spots, the hardest part is simply getting the puzzle started. After you make your opening moves, the real challenge lies in your observation skills; there is so much to work through that it can be easy to miscount the number of remaining cells around a -3- or accidentally mark a second cell around an empty "1" cell because you missed the blue hex it already has. It's lengthy, but if you're alert and observant, it's honestly not extremely difficult.

Hexes Earned for Completing this Puzzle: 10

The next puzzle apparently gives us an ocean with a bunch of islands:




This is one of the more disjointed puzzles we will encounter. The vast number of column headers, each presenting their own conditons over the cells, doesn't help. Additionally, the few empty cells we get are on the right side; the only thing that we get on the left side of the grid is a single blue hex.

As far as the empty cells go, the only one we can truly do anything with is the -3- in the upper-right section. Where it only has four cells surrounding it, we know that the first and fourth ones in the cluster must be marked, and that only one of the middle cells can be. One thing that can help us, though: The first cell we mark is in a column headed by a -2-. While the orange hex above it would give the -3- a third blue, non-consecutive cell, it would be consecutive vertically, thus breaking the rules governing the whole column. We can solve the -3- just from this by erasing the cell directly above the first blue hex we mark, then coloring its remaining hex.

Working within that same cluster of cells, we revealed a "2" with that last step and can see it shares two of the blue hexes we just marked, allowing us to clear its other two orange hexes. The "0" we get helps finish out the cluster. Returning, then, to the highlighted -2- column, we can see that there is still an orange hex directly below the first blue one we marked around that -3- cell. We can safely clear it; remember, hexes across a gap within the same column of cells are still considered to be consecutive!

Concerning the next-to-last column of the puzzle, also headed by a -2-, we can erase its top cell for the same reason as the one we just erased: Because it lies across a gap from a blue cell we just marked. Interestingly, that gives us a "2", and there are only two cells bordering it. Mark both of them. Guess what? Doing this granted the first -2- column that we started with the second blue hex it needs. If you haven't clicked on the -2- to draw a line down the column, do it now; we're eliminating the cell at the bottom of the column.

We just uncovered a "0" on that bottom line. Follow it. You'll eventually reveal a "1" with an obvious choice of which hex to color; stop when you get that far. Now look at the final column; it needs five blue cells, and we just cleared one. Now count the number of remaining active cells; there are five, with two colored. Just color the three other cells to finish the column.


Look now just a few columns over, to the column headed by a "2"; it has only two orange hexes since we cleared out the rest from our earlier work. We can safely mark both of them. Let's look now at the next cluster down, which still has a number of orange hexes. This section may be the single hardest to complete because there are several variables in play:



I'll show how the solution presented in that previous image looks in relation to the puzzle shortly. For now, we want to clear the orange hex directly above the first hex of that section, in the column headed by the -3-; we have two consecutive blue hexes in the column now, so the next one cannot also be consecutive. That's going to give us a "2", which will make solving the remaining cells in the column easy.



That's about all we can do with the right side of the puzzle for right now. The other major piece of information given to us at the beginning is a free blue hex towards the left. Notice that it is in a column headed by a {2}; this means that either the cell above or below the blue hex will also be colored. We can thus eliminate the other cells in the column, and this will give us another trail of zeroes to follow. By the time we reveal the two empty "1" cells, there will be only one cell for them each to claim (and share)!

Let's go to the elongated grid right below this. See the empty "2"? Color the only two hexes it can capture. Note that the one on its right falls within a column headed by a "1"; so now, clear the other two hexes in the column.

In the third group down now, we have a "2" on its right edge, again with only two adjacent hexes; one is already colored. Once the other one is colored, we'll also give the column headed by the {2} the second consecutive hex it needs. Eliminate the column's last orange hex at the bottom.

On the bottom row now, we'll get another "0" to follow, which ultimately allows us to color two more cells. Let's now finish the other {2} column on this side by coloring the cell below the blue hex at the top (across the gap) and then erasing the cell below it. Finally, for the very first column, headed by a "2", we can see that both the top and bottom cells are colored, and we can clear the remaining cells.

We should now look to the column headed by a "1"; it begins in the fifth column from the left in the second cluster down. It has a blue hex already (at the very bottom), so the hex directly below the header can be erased. You know how to treat the "1" this reveals. To handle the pair of empty "1" cells revealed to the right, however, understand that the one on top only has one choice for a blue hex, and that it will be shared with the one below it. Can you solve the rest of this section on your own?

If you still need a bit more help there, remember that when you reach the wider section of that cluster, you actually get two hints as to which cell will be eliminated from the "3". The first is that the first column here is headed by a -2-, so the two blue hexes within it cannot be consecutive. The second is that the "1" on the right edge has only one choice for a blue cell, which will be shared by the "3".

We can now finish the bottom row, as well as the central column headed by a "5":



The last step is pretty straightforward. We do want to stay in the center column, though; we've now given the "1" we revealed moments ago the blue cell it needs, so we can clear the other two around it. This will actually allow us to solve this entire section:




The puzzle is now solved. Count the number of orange hexes left on the grid. Did you get six? Now, look at how many of the remaining hexes need to be marked in the puzzle. Did you get six again? Mark them all, and let's get out of here!



Hexes Earned for Completing this Puzzle: 16

The key to that last puzzle is to pay attention to not only the conditions set forth by the empty hexes, but also to those set forth by the column headers. You have to combine both sets of rules to avoid making mistakes.


We don't have any column or row headers this time around; everything is on the grid itself. We get quite a few empty cells, and a fairly generous spattering of blue cells is given to us:



Let's start with the zeroes. The one on top erases two cells, and the one just about halfway down the grid has six hexes to clear--something we haven't really seen since Puzzle 1-1! With all of those hexes erased, let's see if we can start working the grid from left to right. We're given a blue hex for the {2} on the far left; since the blue hex is at an endpoint, we just need to mark the next one beside it and then clear its remaining two hexes.

Note that clearing those last couple of cells also allows us to clear the bottom-left corner; we have left the "2" in the corner with only two obvious blue hexes to claim. We also uncovered a -3- just now; it has the normal chain of four consecutive hexes around it, with an endpoint already marked. Marking the second endpoint also gives a second blue hex to the "2" we revealed a moment ago right below it. This lets us clear the remaining orange hex beside the "2".

We don't yet have an obvious move to solve the "3" we just revealed or the -3- we've been dealing with, so let's turn our attention to the empty hexes we revealed around that middle "0". The "3" to the left of the "0" actually only has three active cells touching it, so we can color all of them. This does a couple of things: First, it gives the "2" directly below it a second blue cell; and secondly, it gives that -3- the third blue hex it needs. We can clear two more cells from this.

This now allows us to solve the "3" at the bottom of the grid by eliminating one of the two choices it had for a blue hex. Now, just color the other one. You may even notice that the "3" we just revealed under the "2" will claim the hex on the upper-right edge of the one we just colored to obtain its third blue hex.

If we continue along the bottom, the "1" on the upper-right edge of that "3" also shares the blue hex we just marked. Clear the orange hex on the bottom-right edge of the "1". The "2" that this reveals shares a blue hex with the "1"; either of the orange hexes to its right could give it a second blue cell. However, the "2" under this one only has one choice for its second blue hex. When it's marked, the upper "2" will share it, and the remaining orange cell to its right will be cleared.

You may have already noticed, but this puzzle is so far all about the relationships between the different cells. And that's what the entire puzzle is; it just gives you so many cells to work with that it can be easy to overlook something, which is when you are most likely to make a mistake. But we literally will just be continuing to open and work with new relationships as we reveal new empty hexes and fill in the blue ones.

So moving up just a little bit, we come to an empty -2- cell. No problem solving this one; it has the standard ring of three hexes, while the other three cells surrounding it are already eliminated. So we fill in the two endpoints and eliminate the middle cell in the ring. That will give the "2" to its left a second blue hex, as well. Go ahead and clear the remaining orange cell right above it. Another "2"; it will share the two blue hexes of the one below it, allowing us to eliminate the ring of three cells along its top edge.

Let's just finish these two columns; the {2} we just revealed at the top only has their two top cells to claim as blue hexes, anyway. Note that when we color them, the "3" on the bottom-right edge of the {2} will then have the three hexes it needs, so go ahead and erase the orange hex to its right.

Now, on the bottom-left edge of the {2} is a "1", which now has a blue hex. Erase the remaining orange hex on its bottom-left edge. This will reveal a {3} with a ring of four total cells rotating clockwise around the bottom edge. One of its blue hexes is at an endpoint, so we just need to mark the next one in sequence, then eliminate the final cell in the chain.

To finish this section, the "4" a couple of cells down now has its fourth blue hex. Clear the final orange hex from it. Since we don't have an obvious move to solve the "3" we just revealed, move up to the top; see how the "1" on the top edge has only one hex it can claim? This gives the "2" below it a second blue hex; when we clear its remaining orange hex, we reveal another "2", which will share the same two blue hexes and allow us to clear the orange hex in that corner. This leaves that "3" below with only one final choice for a blue hex; color it to solve this side of the puzzle.



If we now scan the center part of the grid, there aren't any more obvious moves we can make. So let's try to work from the right side back to the middle. Start with the -3- directly below the {2} near the far right edge. The -3- has our standard ring of four hexes, so mark the two outer ones as usual. Note that this gives a blue hex to the {2} at an endpoint; mark the next hex over and erase the third one from its ring.

Completing that {2} leaves the "1" on its upper-right edge with only one final choice for its blue hex. Marking it also gives the "2" we just revealed a second blue hex, and we can clear the orange hex on top of it. This links us to another {2} with a blue hex at an endpoint; mark the next cell over to give it a second consecutive blue hex, then erase its other two orange hexes.

We now unveil a "2" and a "1"; the "1" only has one choice for its blue hex. Again, marking it will also give the "2" a second blue hex. When we then clear the orange cells from the "2", we'll again find that we can clear additional cells by virtue of the new empty hexes sharing the same blue ones as those we've already completed. We'll ultimately erase a hex from the {5}, letting us solve it by marking all of its remaining hexes:

We uncovered another "3" on the top-left edge of the {5}; it has the three blue hexes it needs. Clear its remaining orange hex. We uncover yet another "2" which shares blue hexes we have already marked, letting us erase three more cells. However, we have no obvious choices for marking the blue hexes these new empty hexes need.

Move back up to the top, and we find another "1" with only one choice for its blue hex; as we have seen, this also gives the "2" right below it the second blue one it needs, letting us clear its final orange hex. The "2" we reveal also shares those blue hexes; clear the two orange cells to the left. The {3} this reveals is easy to solve since its existing blue hex is also at an endpoint. Mark the next two consecutive hexes from the blue one, then clear the fourth cell.

We're nearing the end of this somewhat lengthy puzzle. Here's where we left off:



We can move back down just a little bit now. From the {3} we just solved, go over one column to the right and then move down to the bottom "2" in the cluster. This specific "2" has only two active hexes surrounding it, meaning it will claim the remaining one on its bottom-left edge. This gives the "1" below a blue hex and lets us clear the two cells still surrounding it. The -2- we just revealed is just what we need; it has our usual ring of three hexes. Go ahead and solve it as we have the others.

Interestingly, we both reveal and solve a "4" at the same time! We just need to clear its remaining orange hexes now. We reveal another "4", which only has two choices for the last two blue hexes it needs. Mark them, then move up to the "2" which lies two cells above this "4"; clear the orange hex next to it, revealing yet another "4". This one already has four blue hexes. Clear the orange one on its bottom-right edge, and we can now solve that "3" at the bottom by filling in the final active hex on its bottom-right edge.

Move now to the "3" right above the one we just solved; it has only one remaining choice for its third blue hex. Marking it actually gives both the "2" on its bottom-right edge, as well as the -3- just up and to the right, the remaining hexes they need. When we clear the two orange hexes still adjacent to these cells, we find that the final orange hex in this corner must be marked to give these new empty hexes the final blue hex they each need.

We're almost done. Return to the column near the center that had the {3} we solved a little bit ago. The "2" a few cells down from it has two blue hexes, clearing two more. The -2- we reveal from this also has two blue cells; we can clear the two center cells from its cluster. This will give us a -3- and a normal "3". The -3- has the standard ring of four cells we've grown accustomed to; one of the outer cells is marked, so just mark the other one. When we do this, it also gives the "2" at the bottom a second blue cell, allowing us to clear the other orange cell above it.

Now, we need to mark the cell above the one we just erased, which will satisfy the requirements for both the normal "3" cells and the -3- in the vicinity. Go ahead now and clear the final remaining hex from the bottom row; it borders a "3" that has all the blue cells it needs.




And now for the finish. The orange hex furthest right of those remaining is sandwiched in between a pair of empty "2" cells and is the only remaining active hex in that column. The "2" below this orange hex already has the two blue ones it needs, so we need to erase the two hexes on its upper rim--including this cell.

These erasures give us a "2" and a "3". Start with the "2", as it has only one obvious blue hex to claim for its second one. Marking it gives the "2" above this one the second blue hex it needs, allowing us to clear the cell on its upper-left edge.

The "2" that we just uncovered shares its two hexes with the previous "2", letting us erase three more. The "2" that we uncover from this series of eliminations also pops up with the two blue hexes it needs. When we erase its two orange hexes, we leave the puzzle with only two final active hexes, and two blue hexes yet to be marked. Mark these final two hexes to finish the level.



Like Puzzle 5-1, this one does not have anything extraordinarily difficult about it; it's just long, and you again have to be careful with the new cells you reveal and determining how they fit in with the ones you have already solved. If you understand the puzzle structures we have seen many times up to this point, there isn't any reason why you can't solve this one without a mistake even on your own. But you do have to be careful, and you have to have good attention to detail.

Hexes Earned for Completing this Puzzle: 16

Once you have made it this far, the sixth and final chapter will unlock. If you would like to take a quick look at the toughest of the tough, feel free to do so. We're now 3/4 of the way done with Hexcells. Here's the layout for the next challenge:



A flower maybe? It kind of looks like the Fire Flower from the original Super Marior Bros. back in the 1980s to me. But anyway, we get a smattering of empty cells spread around the grid, and lots of numbered columns to impose additional requirements on how we need to fill in the blue hexes.

One thing that should jump out at you pretty quickly is that we have several zeroes in a triangle formation. Let's just start by following them. We'll actually be able to fill in a few blue hexes from this, too. The empty -2- cells both to the left and below the cluster of zeroes we revealed can be solved by the same method we have used previously:



There's one other move we can make from the center cluster: The "1" above the zeroes has only one choice for a blue cell, so we can go ahead and mark it.

One other thing I like to do is look at the individual columns to see if there are any I can go ahead and solve right away. Sometimes, you will get a column whose number of cells is equal to the number in the column header; or, you might have a pattern of cells whose solution is fairly obvious.

From the steps we have made, we can actually solve two columns. Count over to the third column from the right, which is headed by a "1". The column has only three total cells, with only one active. This means we can go ahead and color it. Now, move to the left three more columns, to the one headed by a -2-. There are only three active cells, all of which are in a straight line. We can go ahead and treat it similarly to the -2- cells we've been solving; mark the first and third cells, then eliminate the middle one.

The "1" revealed in solving that column will help us with the next series of moves. Notice that it shares one of the blue cells we just marked, letting us clear the orange hexes on either side of it. We'll get a -3- from this on the right side; it has the standard ring of four hexes around it. The first endpoint is already marked, so go ahead and mark the other.

To the left, we now have a line of three empty "1" cells. The two on the left only have an obvious choice for a blue hex, so mark it next. Afterward, we'll move to the left of the -2- we solved earlier; the "2" we revealed here shares the two blue hexes given to the -2-, letting us clear the cell to its left. We'll now find another "0" to follow:



Any time you are able to solve a decent amount of hexes on the grid, it can be a good idea to scan the column headers to see if those changes allow you to complete more whole columns of cells. In this case, we can actually solve two more. The central column is headed by a "4"; move three columns to the right, to the first one headed by a "2". It now contains only two active hexes, which need to be marked. Now, move three columns left of the central column This column is headed by a "1" and contains its single blue hex; we can now erase the final cell in the column.

Let's also look at the columns on the right side that are each headed with a -4-. Each of them has a total of five active hexes and will need a total of four blue ones, with at least one separated from the rest.

We can use a modification of the counting scheme we used previously to at least give us a few more blue cells. Let's number the cells from top to bottom, 1 through 5. In order to come up with a sequence of four blue hexes, with at least one separated from the rest, we have the following possibilities:

• Cells 1, 2, 3, and 5
  
• Cells 1, 2, 4, and 5
  
• Cells 1, 3, 4, and 5

From this, we know that the first and fifth cells in each column have to be marked:



This actually opens up some moves at the top of the puzzle. Notice the "2" in between the two blue hexes at the top of those columns; we now can clear the remaining two orange hexes along its bottom edge. And now, since we have reduced each column to just four active hexes apiece, we can solve them outright by marking the remaining cells in each. But this also opens up a whole series of steps.

We can start with the first -4- column; its lone remaining active hex is at the bottom. Go ahead and mark it. While we're down there, notice that the {2} not far to the left has two blue cells; clear the third, revealing an empty "3" cell. With the cells we've already marked, it pops up with the three blue hexes it needs; now, we can clear the orange hex above it.

Now, if you haven't done so already, go ahead and mark the other two hexes in the second -4- column. This will now let us solve the last column, governed by a "2." The empty "4" cell we revealed at the top when we solved the "2" is surrounded by only four active hexes. Marking the other two will also give the final column the two blue hexes it needs, and its final hex on the bottom can be cleared.

One last move for this series: Go back to the left of all of this, and you'll see that we can mark the top cell in the column headed by a "1". It's the only cell left for the -3- to claim, and it's also the only remaining cell in the column.





We can now try to solve the top-left corner. Notice that both the -4- and -3- cells each have five surrounding cells. Unfortunately, we can't do anything with the -3- yet. But we can at least start on the -4-; if we number the cells here as we did with the columns earlier, we get the same possibilities for cells that must be colored. So we'll mark the first and fifth cells surrounding it:



We can actually now solve the second column of the puzzle, headed with a "1"; we just gave that column the only blue cell it can have. Go ahead and erase the others in the column. Below the -3- in the top-left corner, we will reveal a "1", which will already have a blue cell. We can eliminate the orange hex to its left. This will also eliminate one of the only three cells in the first column, headed by a "2"; so now, go ahead and mark both remaining cells to both complete that column and solve the -3-.

We're about 2/3 of the way through this one now; here's the last step:



For our next move, we want to look to that "0" we uncovered on the bottom. While it doesn't take us too far, erasing its hexes does reduce the third column, which is headed by a "3", to just three active hexes. We can solve the column by marking the last two. Now, the "2" we revealed to the right of the zeroes has only two choices for blue hexes; go ahead and color them.

The next move isn't as obvious. We don't have any clear-cut moves for filling in blue hexes around any of the empty cells that are open now. This is another situation where we have to pay attention both to the conditions on the grid and the restrictions imposed by the column headers. Look to the empty "2" above the cluster of empty "1" cells on the bottom just left of center. Here's what we need to know:

• There are two orange hexes to its left.
  
• There is only one orange hex to its right.
  
• The two orange hexes on the left are also in a column headed by a "1"; they are also the only active hexes left in the column.

Since only one of those two hexes on the left can be marked because of the column restrictions, the one on the right is automatically colored. This cell is in a column headed by a "3", and it is the third blue hex the column needs. We can now erase the final cell from the bottom of that column.




Marking that last hex also did one other thing: It gave the "1" below the "2" a blue hex. We can now clear the orange hex to its left, which shows us which other hex the "2" will get and lets us complete that whole column.

Look now at the "1" at the bottom of the column we just completed, on the upper-left edge of that "0"; it must claim the hex to its left, which will also give the "2" above it the second blue hex it needs. The "4" that we uncover from clearing the orange hex between the blue ones already has four blue hexes, so the last hex in the section can be eliminated.

This brings us back to the column headed by the -3-; that last series now allows us to solve it. Go back up to the top-left corner. We need two of these remaining three cells at the top of the column to be colored. Well, the -4- up here already has three blue cells. Since two of the three cells each border the -4-, and only one of them can be colored, we know automatically that the bottom one must be marked. This gives a hex to the adjacent "1"; we now eliminate the middle orange hex and color the one on top to complete that section.

Only the center section remains; we'll again need to work on both the top and bottom sections at once in accordance with the column restrictions. See that great big {5} at the bottom-center? We're close to being able to solve it, but we aren't there yet. The "2" to its left, however, has only two choices for blue hexes; marking them will also feed the {5} two blue ones. But more importantly, we can now solve the whole column in which these blue hexes reside. The column is headed with a "3", and we already had one blue cell up above. Eliminate its remaining cells.

Let's see if we can solve the top section now. We've got two empty "2" cells at the top of the column we just solved. The bottom "2" already has two blue hexes; erase the other orange hex to its right. This clears one of the choices for the "2" on top of it and lets us mark the one remaining--also giving a second blue hex to the "2" we just uncovered and allowing us to clear the two orange hexes to its right. The final orange hex on top will now be colored to give a second blue hex to the "2" next to it.

We're almost done. In the center column, find the empty -2- / "2" pair in the very center of the puzzle. The "2" already has two blue cells, so clear the one below it. This reveals a "1"; notice how the empty "2" cell on its bottom-left edge now has only one choice for a second blue hex. Marking it gives a shared blue hex to it, the "2" directly below it, and the "1" we just revealed. We can erase the remaining orange hex on the bottom-right edge of the "1", as well as the cell directly below the blue one we just marked.

Luckily, the "1" revealed from this shares the blue hex we just marked, eliminating two more cells. We can now solve the {5} at the bottom. Mark the three hexes still left surrounding it. One of these is shared by the "1" a couple of cells to the right, letting us clear the remaining orange hex below it. The remaining orange cell above will be marked and given to the pair of empty "2" cells next to it, and the puzzle is complete.



Hexes Earned for Completing this Puzzle: 18

The complexity of the last puzzle lies in having to work on both the top and bottom sections at a time in several places. It underscores the importance of acknowledging the restrictions imposed by both the empty cells on the grid and by the headers of individual columns. It's essential that you be able to take both into consideration to understand what is or is not possible at any given time.

We are now at the end of Chapter 5; only one puzzle remains before we tackle the toughest ones that Hexcells has to offer...




Here, the game formally teaches us about managing lines of cells: "You can left click on outside numbers to activate a guide line and right click to mark them as complete." This is also the first puzzle that has us manipulate entire lines of cells that are not vertical columns. From this point forward, line management will be critical.

The X formation at the top of the puzzle is a good place to start. Go ahead and click on the row headers to see how this works with diagonal lines. As for solving them, remember what I said in the last puzzle: The number outside a row or column will sometimes be equal to the number of active cells within it. That's exactly what we have here; the rows are each marked by a "5", and each has only five active hexes:

Look carefully now at the remaining line headers, and you'll see some obvious moves:



Notice now that the column marked "1" in the bottom-right grid of the puzzle now has the hex it needs, so we just clear the other one. Back over on the bottom-left grid, you may now see that the diagonal line headed by a "3" can be solved:





Before moving on, that last step also demonstrated an important concept: That cells in multiple grids can be contained within the same row or column. Notice how in solving that last diagonal governed by the "3", we had to work with cells in both the second and third grids of the puzzle. I'll touch upon this idea again at the conclusion of the puzzle.

Continuing now, the puzzle is practically solved at this point. In the grid on the bottom-left, both the -2- column and the other diagonal line marked with a "1" have their required blue hexes, so we're going to eliminate their remaining orange hexes. This will unveil a {5}, which will need the final cell in that grid to get its fifth blue hex:



All of the blue cells the puzzle requires are now colored; we just need to eliminate the final orange hexes in the third grid to solve it.



There isn't much to say about this puzzle; for a chapter-closing puzzle, it's extremely easy if you understand how to manipulate lines of cells. Possibly the most important new idea we learn in this chapter is this: In puzzles containing multiple grids, the rules governing a particular line of cells can potentially impact the cells in more than one grid. Remember that these lines don't necessarily stop at the end of a grid; they keep going if the cells in another are along the same path! This is a big reason why using the line-marking mechanic is so important. As the puzzles get larger in the final chapter, it will be critical to understand which cells are governed by a particular row or column header. And with that, the final chapter of Hexcells begins...

Hexes Earned for Completing this Puzzle: 3

Welcome to the final chapter of Hexcells. At this point, all of the game's mechanics have been introduced and utilized. Only five puzzles stand in our way of puzzle mastery and the unlocking of all six achievements (we now have five; the final one is "Perfectionist," which is completion of every single puzzle without making a mistake). The final chapter will present the most complicated puzzles that the game has to offer. Will you be victorious, or will your brain be fried sunny-side-up from puzzle exhaustion?




So we start with a pair of barbells in an X formation. We get some row and column headers outside; our only empty cell inside is a "0" placed dead center. Let's just start there; by the way, I'm going to trust you to understand why I marked the blue cells I did after moving beyond the initial "0".




This is a good time to start looking at row and column headers. For the rest of this puzzle, I'm going to refer to the four large clusters of cells by number as follows:

Top-Left: Cluster 1
Top-Right: Cluster 2
Bottom-Left: Cluster 3
Bottom-Right: Cluster 4

I think this will help with parts of the description. The bottom diagonal row of Cluster 1 is headed by a "2", and we just gave it two blue hexes. It only eliminates one cell, but it's an important cell. Likewise, in Cluster 2, we have a diagonal governed by a {2}. While it may seem like we can't solve it, realize that the empty cell adjacent to it is a "1". What have we learned about lines and cells governed by a {2} and working with only three continuous hexes? That the middle one will always be marked. Go ahead and mark it, giving the empty "1" cell a blue hex. The second orange hex on top of the "1" will be eliminated, and we'll fiil in the last hex of that row.

The -2- we just revealed in Cluster 1 can be solved in the same manner used to solve any -2- cell with only three continuous active hexes around it. The "2" that this reveals lets us eliminate three more cells, since it shares the two hexes given to the -2- below it. We'll reveal a "4" on the right from this; it has only two obvious choices for its remaining blue hexes.


We can't quite solve this cluster yet, though if you wanted to, you could make some pretty educated guesses. But we want to make sure we're right. So let's start with the very first column. We know that only one cell in it can be marked; we also know from the arrangement of the cells surrounding the "3" in that corner that the column's lone blue hex must come from Cluster 1. Otherwise, it would not be possible for the "3" to claim three blue hexes. This means we can clear the bottom two cells from the column within Cluster 3.

We now get two empty "1" cells. The second column is headed by a "4"; in Cluster 1, there is only one more active cell that can be colored in this column, meaning that we have to mark two of the column's required cells in Cluster 3. There's only one way to do that without giving at least one of the empty "1" cells more than one blue hex:



We can use this to solve Cluster 1. Mark the remaining hex at the top of the second column to give it a fourth cell, which also gives the adjacent empty "2" cell the second blue hex it needs. Clear the remaining orange cell above the "2". Notice now that the diagonal line under which these hexes falls is headed by a "2"; this tells us which remaining hex the "3" will claim, since that row still needs a final blue hex with only one choice remaining:

Let's now see if we can solve Cluster 3; we're already off to a good start in that the "2" we revealed moments ago has the two blue cells it needs. If we clear the other two orange hexes, we get a -2-, but this one has four total hexes around it. No problem; it has one blue hex, and the next one it claims cannot touch that one. So we erase the next hex in its ring. The "2" this reveals has only one choice for a second blue hex, which when marked will allow us to complete the -2-.

Here's another mind-bender. To determine how to finish this cluster, we need to look just above Cluster 4, where there is a diagonal line header of "3", with one blue cell already filled. So we know that two of the three remaining hexes within that line will be colored; we also see that they each border at least one of the empty "2" cells here, both of which already have one blue hex. Similar to our previous scenario with the empty "1" cells on the left, there's only one way to mark two blue cells here without giving either "2" a third blue hex:

From this, solving Cluster 3 is easy:



Halfway there. There aren't any obvious moves remaining on the grid; remember what I said about reviewing the row and column headers? This is what we want to do now, starting with the central diagonal row headed by a "4" on the outside of Cluster 2. If we highlight the line and count carefully, we can see that it now has four blue hexes, meaning the rest can be cleared.

We can't quite solve the {3} revealed yet. Start at the right edge; the "2" has only two blue cells it can claim, which will also feed two to the adjacent "3". We can't solve either the "3" or the {3} immediately. However, from the pattern of cells around the {3}, we can see that the hex on top of it cannot be marked, since there's no way to connect it to the two blue hexes it will have at this point. Just erasing that cell sets up the solution to the whole cluster:

We still have nothing on the grid in Cluster 4; just to get it started, note that the second column from the right already has the two blue cells it requires; we need to erase its remaining cells from Cluster 4:





This is not an ideal setup! We have no obvious moves for any of the empty cells we just revealed. The logic for this took me quite some time to understand, but here it is in a nutshell:

• The top empty "2" cell is the key. The column to the left of these cells can only have one of the four remaining hexes marked.
  
• We know that one of them must be given to the top "2"; otherwise, there is no way for it to get two blue hexes (there is only one available hex to its right).
  
• Therefore, the two bottom hexes in the column headed by the "2" must be eliminated.
  
• The hex situated on the right in between the two empty "2" cells must be marked.
  
• Since the "1" under the empty "2" cells now only has one choice for a blue hex, the cell below the one we just marked must also be marked.
  
• This gives the "2" in the middle of the column a second blue hex; we must erase the other hex beside it, and the top cell of the column is now marked.

The puzzle is now basically solved. The top "1" in the third column from the right has a blue hex already; the two orange hexes next to it will be cleared. Note that again, the number of blue hexes shown in the "REMAINING" counter is equal to the number of remaining orange hexes on the grid; color them all to complete the puzzle.



Hexes Earned for Completing this Puzzle: 18

That last puzzle was just an appetizer to the main courses to follow in this chapter. Some of the logic is more complicated in 6-1, especially trying to solve Cluster 4. We're about to reveal the toughest puzzles that Hexcells can serve us. Here's the layout for Puzzle 6-2.




It looks like Swiss cheese to me. Well, yellow Swiss cheese, at least. We have precious little information here: A few column headers but absolutely zero empty cells and only a single blue hex just below the center.

That blue hex, as well as the {6} heading the column in which it is located, are actually the most important pieces of information we have; in fact, they're the only actionable information we have! The {6} at the top of course means that we must have six consecutive blue hexes in the column; the blue hex given to us will naturally be a part of that. So to start, we want to figure out the maximum reach that chain of blue hexes will have. Assuming that the blue hex is an endpoint, we want to measure both up and down to see just where the chain can end.

If we start from the blue hex and count downwards, we can create a chain of only five total hexes; naturally, any of them are candidates. So now, we'll count from the blue hex upwards; if we stop after counting to six, the two top hexes of the column are excluded:



The empty cells revealed here at least give us a starting point. Work the -2- in the normal way. Once you're done, notice that the blue hex to its left is in a column headed by a "1"; so now, that entire column can be eliminated! Once you've done that, do two more things: Eliminate the cells around the "0" you just revealed; then, eliminate the remaining cells surrounding the "2" revealed in the center column since it shares the blue hexes given to the -2-.



We've now eliminated several cells within the central column; this may just give us a way to isolate at least some of the cells that must be colored blue. We'll modify our counting scheme from before to come up with those cells that are 100% guaranteed to be in the chain of six:



There's one other isolation we can do here. Notice the "2" on the left side of the bottom two hexes of the column. Since there is only one hex on the left side of the "2," we know for a fact that at least one of those two hexes on its right will be colored, or else it cannot claim a second blue cell. If we assume that it's the top one (Cell 7 in the previous image) and then count up, then the top-most orange hex in the column cannot be part of the chain; we can now eliminate it:



We now have enough information to solve this column. Notice that the "2" we just revealed has only two choices for blue hexes; when we mark them, we will contribute one to the chain of six hexes. We now just need to color in the sixth blue hex at the end of the chain. Afterward, we can eliminate the column's final hex on the bottom, then solve the other two empty "2" cells in the next column to the left:



We now want to take the cells we have uncovered to this point and see what, if any, obvious relationships exist to either color or eliminate more cells in the puzzle. We've actually done the hardest part; now, it's all about creating and building upon the relationships among the remaining hexes. With so many cells to work with, the images presented will be your best guidance; I will elaborate here where necessary.



Basically, we just worked from bottom to top here, looking for empty cells either completed or with obvious cells to complete them. The most important rule whenever you are dealing with so many cells at a time is to try and isolate the empty hexes with the least number of surrounding active hexes, and try to solve them first.



Here again, we're building on the relationships already established, but remember to check the columns that still have headers above them to see if you can solve them, or at least add/subtract more cells.



One word of note: I still trust you to be able to identify the basic relationships among the cells. Even though many will be outlined in these steps, a minor cell relationship that I may skip over, intentional or not, is assumed to be clear enough to not be demonstrated verbatim.

With the steps we've completed until now, we can actually finish off the top-right section altogether:



We're almost done with the right half of the puzzle; let's see what we've missed:



To this point, what we've seen has been fairly straightforward. It's more complicated with the sheer number of cells we are dealing with, but it's nothing we haven't seen before. The dual {2} cells, however, present an interesting variation. If you count, they still only have the standard cluster of three surrounding cells; however, marking their respective central orange cells also gives two blue cells to the column headed with a "2," which makes the solution here not necessarily what you would expect!

This puzzle is long, but it isn't that bad after that tricky opening! Here's where we're at:



We have only the left half of the puzzle remaining. Well, and that last orange hex on the far right for which we have no current guidance. It will come, though.

Solving the left side is really no more complicated than solving the right; we're going to use the relationships of cells that we've already established and find their natural extensions. We'll start in the middle again:



This series of steps alone solved a major chunk of the puzzle. We're almost done. It looks like we may have to continue along the top half of the puzzle and work back towards the bottom-center near the end:



This basically cuts the rest of the puzzle in half. We can pretty much finish the bottom-left section now:



The last section bears some additional explanation. Initially, we just start from the middle and work back to the right. From the lone blue cell at the bottom of the column headed by the "1" that we just solved, begin with the empty "1" cell on its upper-right edge, then eliminate the next orange hex to the right to reveal another -2-. Having the normal ring of three hexes, it will be solved like the others. On the bottom, we find that solving the -2- gives a hex to the nearby "1," and we can clear its remaining orange hex:



But now, we are left with one final brain-teaser. If you glance at this cluster, there are no truly obvious moves we can make, so it's going to take a little bit deeper analysis of the empty cells and how they are positioned in relation to the remaining orange hexes.

The empty "3" cells here are basically arranged in a triangular formation. The "3" on the right has two blue cells on its right, with its only other active hexes on the left. The "3" on the left also has two blue cells, with three possible remaining hexes. Finally, the "3" on the bottom has only one blue hex, with three possible choices.

It's easy to make a choice that would allow for potentially four blue hexes around at least one of these. The problem is to isolate at least one hex that, logically, could not possibly be colored. Look at the "3" on the right again. Remember: Its only two remaining hexes are on its left edge. Those hexes are also shared by the "3" on the left. Which means that the orange hex directly below the "3" on the left cannot possibly be marked; otherwise, it becomes impossible to give the "3" on the right a blue hex without giving this one a fourth. So eliminate the hex directly below the "3" on the left. As this eliminates one of the possible choices for the "3" on the bottom of this triangle, we can fill in the other two orange hexes around it, and then the solution is revealed:



Bet you were wondering about those two final hexes on either side of the grid. Well, once again, we just refer to our friendly "REMAINING" counter in the top-right corner: Two blue hexes remain. We have two orange cells; mark both to complete this monster of a puzzle.



WOW!!! This is certainly the toughest puzzle Hexcells has thrown at us so far. There are only three puzzles left now. If you thought this one was hard, your brain hasn't even begun to sweat...

Hexes Earned for Completing this Puzzle: 18

It's the final countdown!!!! We are down to the final three puzzles in our Hexcells 100% no-mistake playthrough. The last puzzle was our biggest challenge so far, and it's not going to get easier before the end. Check out the structure for the next puzzle.




This might be my favorite puzzle, particularly from a design perspective. We have four concentric hexagons. We again are given no empty cells; this time, it seems like virtually every possible row or column has some kind of restriction placed upon it. Because there are gaps between all of the lines in this puzzle, line-marking is critical. Additionally, you'll want to keep checking the line headers for rows or columns you can complete entirely, adding or eliminating additional cells. Since many of the lines are short due to the concentric nature of the broader pattern, some may be completed rather quickly.

As always, take time to examine what you have before jumping right in. You should see that one of the rows has a "0"; highlight that line, then eliminate every cell along the marker:






I've also eliminated the cells surrounding the zeroes that will be revealed during this process. By the way, I'm going to number the rings for this puzzle in order from largest to smallest (or, if you prefer, outside to inside). So the outer-most ring will be Ring 1, and the small one in the very center will be Ring 4. You may notice that in Ring 3, we have a couple of empty "1" cells with only one adjacent orange hex apiece. So go ahead and mark those cells now.

Two other things to call attention to. At the bottom-right of the puzzle, in Ring 1, we have a row headed by a {4}; notice that in front of the empty hex we revealed in the beginning, there is only a line of three orange hexes. We can't make four continuous blue hexes with just three in a line; erase all three of these. For that matter, just follow the zeroes you will reveal, and you'll get another blue cell going up the final column of the puzzle.

The second item goes back to the blue hexes we just filled in for Ring 3. Notice that the left vertical column in the ring is headed by a "5". If we count the number of remaining active cells, including the blue one we just marked, there are only five in the column. Which means we can also mark the remaining active hexes and complete the column:



Returning now to Ring 1, we find that beyond the empty "1" cell in that diagonal row headed by a {4}, there are only five remaining orange hexes; since four consecutive hexes must be blue, we know that the middle three have to be colored. If we number them, we have to use either Cells 1 through 4, or Cells 2 through 5, to make a continuous row of four.

Returning to the final column of the puzzle now, we can see it's headed by a -2-. Since we already have one blue cell and know that the next one above it cannot be colored, we can go ahead and erase that one immediately. This reveals a "1"; let's see if we can finish the column:




Ring 1 is now just about halfway solved. Let's look around the puzzle some more and see if any other rows or columns can be solved. What about the one headed with an "8" two columns left of the center? It turns out that if you count the cells, there are only eight hexes in the whole column, meaning all must be colored. That's just as good as finding a zero!

This actually allows us to make another run along the bottom of Ring 1, this time going up the left side. This diagonal is also headed by a {4}. We now have two blue cells in the row, with an orange hex in between. Since the hexes must be continuous, we need to color that one to link them together. This leaves only two possible endpoints and allows us to clear the cells which fall outside of the chain. When we do this, the empty hexes revealed give us the solution:

So as not to get too far ahead, I didn't complete a few obvious moves with this, but I'm sure you can see where we're going next. Ring 1 can almost be completely solved now. Finishing up the first column, the -2- at the top isn't really relevant as the hexes on the grid show us which two cells need to be colored. We also can complete our other chain of four hexes at the bottom-right, as only one cell remains in the other {4} row.

One other thing to note: Both the second and next-to-last columns are headed by a "1"; each contain only two cells apiece; and each have zeroes as their second hexes. Guess which cells we're coloring next?





We can fill in a few more cells on the board now. We have some empty "2" cells in Rings 2 and 3; neither have more than two available cells to them, giving us six more to mark. We can also now eliminate a couple more, as well; if we look at the diagonals marked with numbers, we can see that one of them, headed by a "2" on the right side, already has two blue hexes, letting us clear the row's two remaining cells. This is going to reveal a "0" and a "2"; their positioning gives us a few more obvious moves:

Now, we can solve the central column. You have probably already noticed that big, glaring {6} at the top-center of the puzzle. With the last few cells we've filled in, we now have an endpoint for this chain of six blue cells. Notice the two blue hexes at the bottom, with the "2" at the very bottom. Mark the four cells above the pair we already have, and eliminate the top cell of the column:

We can solve many more lines now:



One very important note here: The lines in that last image must be worked in the exact order in which they are numbered; otherwise, you won't get all of the necessary cell eliminations to solve the last two columns worked in that sequence.

Those last steps also simultaneously solved two more diagonals marked on the left side of Ring 1; I've struck those out in the following images. We can now complete three more lines. Also on the left side of Ring 1 is a line headed by a "2", which has a blue hex and just one more active cell to mark. Directly below this, the diagonal headed by a "4" has its four blue hexes and additional cells to erase. Also, the diagonal marked with a "4" near the top-right of Ring 1 has the four blue hexes it needs, allowing us to erase several more:

Three more columns can now be solved; their number of remaining active cells is exactly equal to the remaining number of blue hexes they need (remember that "active" refers both to blue and orange hexes):





We have two last rows we can now immediately complete; again, work them in order:








Our final step involves that "1" at the top-center; it has the blue hex it needs. Clearing the one to the right of it sets up the final chain:



That completes Puzzle 6-3. The trick is in monitoring the rows and columns in addition to the conditions defined by the empty cells on the grid. Only two challenges remain...

Hexes Earned for Completing this Puzzle: 23

With the completion of the concentric hexagons of Puzzle 6-3, we have arrived at the ultimate, final challenges of Hexcells. If you have managed to complete everything up to this point, give yourself a huge pat on the back because it is not easy. Even writing this guide and reworking the puzzles, I stumbled onto things and discovered puzzle-solving tricks that I never figured out in my first playthrough. I had guessed (apparently correctly!) at parts of some of these puzzles without ever finding all of the 100% correct steps to follow. So just in writing this guide, I feel like I have become a better player. I hope you will feel the same way as we complete our journey through this game and this walkthrough together.

Behold!




And so we have the penultimate puzzle of Hexcells. The puzzle is every bit as challenging as it looks, but remember: No matter how tough one of these puzzles appears, solving it follows the exact same types of logic you have been using throughout this entire game. Don't worry; not a single thing which will be revealed in this puzzle is anything different from what you have already seen in these six chapters. The only thing that changes is the application of what you have learned, which may lead to thinking things through in a different way. The relationships between the various types of cells are all the same, as is the use of column and row headers to vary the conditions on the grid.

Due to the complexity of the puzzle solution, it will require multiple parts to explain in its entirety. Be sure to use the chapter links to return to a previous section as needed.

Here we go.

We'll need to jump around the puzzle at different times to reveal new sets of moves. Take a look around the puzzle. We have multiple grids this time. There are four smaller grids positioned in the cardinal compass directions around the central grid. The central grid is much larger, with one large section making up the center and smaller clusters positioned in each of the four corners. We have a decent number of empty cells given to us, as well as quite a few row and column headers. Finally, we are given four blue hexes around the outer edges of the puzzle. These serve no purpose other than to feed into the established conditions for the lines in which they fall.

As usual, let's start with the basics. If we look at the large central cluster, we'll find four zeroes in the corners. Let's go ahead and clear those few cells. We'll even get a couple more zeroes to help us out:





The easiest section of the puzzle to work is the small grid on the left side. In its bottom-right corner is a {2} surrounded by a ring of three cells. We know the middle one has to be colored, and doing so will feed a blue cell to the -2- above it. The dynamic here is interesting; that blue cell is now the center of a cluster of three active cells surrounding the -2-. Since we know that it's other blue cell cannot touch the one we just marked, those other two cells are eliminated. We can now easily determine which hexes will give the -2- and the {2} the ones they need.

The {4} in the center of the grid now only has four active cells around it. While we may not be able to immediately solve the {3} to its left after marking all four of them, we can pick out the ones which cannot complete the chain of three consecutive blue hexes it needs. When we erase those two cells, solving the "2" revealed will let us solve that side.

Finally, to complete this grid, note that the empty "2" cell in the top-right corner has only one choice for a second blue cell. The diagonal in which this cell falls is governed by a {2}; once it is marked, just color the next cell in the line to complete that grid and the diagonal, erasing the remaining cells within the line:



Completing that diagonal reveals another "0" in the main grid for us to follow. The "2" we'll reveal on its top-left edge can easily be solved, also giving a blue hex to the "1" under it and clearing the remaining orange hexes from the latter. This also gives a blue hex to the "1" above the "0", letting us clear the two remaining hexes along its top edge.

We can work along this bottom path now. The "2" on the top-right edge of the "0" has only two choices for blue hexes; marking both gives a blue hex to the "1" at the bottom of the grid, by the "0" we began with. We can't go much farther now, but we can at least eliminate the remaining orange hex bordering the "1".



Look now at the -2- four spaces above the "1" we just solved. We can solve it normally, since it just has the standard ring of three orange hexes. This does some of our work for us, but just to the left, above the "1" we worked a minute ago, is another "2" which now has the two blue cells it needs. This clears the other two around it. We can now clear the hexes above the empty "1" cells just revealed as they both have a blue hex. We can't go any farther for now, though.


Let's move to the top-center of the main grid now; see the {2}? We gave it a blue cell moments ago; we just need to mark the next consecutive cell over from that one, then clear the remaining orange hex. The "3" this reveals is in a position that only allows it three possible hexes to claim.

Just off to the right, we have both a cell and a column governed by a -2-. Each only have three cells; solve both of them as we normally would:







Notice that now, the empty "2" cells below the -2- cell we just solved already have two blue cells apiece; that's going to let us eliminate the remaining cells around them. The "1" that we'll reveal at the left side of this group will share a blue hex with the -2-, so we can clear the three remaining hexes around it.

We'll now find that the "2" located two cells below the -2- cell will have only one remaining choice for a second blue hex. It will be shared with the "1" two cells below, letting us clear the orange hex on its upper-left edge. This will reveal another "2"; to solve this one, notice that the "2" directly above only has one choice for a second blue cell itself, which will be shared with both of them. When its remaining orange cell is cleared, we reveal a "3" with only three obvious choices as to the hexes it will claim:



We revealed a -3- a few cells above the "3" we just solved. It has a standard ring of four active hexes, with the fourth already marked (counting from left to right). The first one in the ring can now be marked, giving the "2" below it a second blue hex. We can clear the remaining hex on its bottom-left edge but cannot solve the "4" revealed just yet.

Instead, move over to the left again; the "3" located below the -2- on that side has its three blue hexes. Clearing the orange hex on its bottom-right edge gives us a "2", which immediately has two blue hexes. Three more cells can now be cleared. Use the relationships this gives us to solve the section:

We're off to a strong start! Here's our current progress:



We're about 1/3 of the way done now. We haven't done anything that we weren't exposed to before; in fact, the last several sequences were just about relationships between different cells that we've been doing for awhile now!

There isn't too much more we can do on the grid without re-examining the line headers, but there are a few moves left. Continuing with the large central grid, we have another -2- over towards the right. It already has a corner blue hex in a ring of four surrounding it; we can eliminate the next hex over from that one, revealing a "1"; naturally, it will share the same blue hex, which lets us clear the next cell over in this ring. This means the -2- will claim its final remaining hex.

Solving the -2- in this manner also gives the "2" right above it a blue second hex, and that allows us to clear two more. Similar to the opposite corner on the left, we get a pair of empty "1" cells sharing the nearby blue hexes. So we'll again clear the cells above them:




This is a great time to start re-examining the line restrictions. Start with the diagonal marked with a "5" right near where we are. There are now only five active cells in the row, with the fifth remaining to be colored. Move now over to the small grid on the far right, where there is a diagonal guided by a {3}. This one is interesting. The work we've done gives us one line of three active cells in this grid, with another separate pair of active cells in the bottom grid. Guess which ones will be marked and which ones cleared?

The other two lines we can complete both originate in the top grid, in its lower-left and lower-right corners. They're pretty straightforward; they each already have three blue hexes, meaning we just need to erase those corner hexes in the top grid. Note that it doesn't matter in which order you work these lines, so their steps won't be numbered in this next image, in part to maximize the limited amount of space for the annotations.

We do get a few moves out of the top grid now. The empty "2" cells revealed on those corners each have only two hexes to claim, so we'll mark all four of those. Notice that on the left, the column is headed by a "4"; if we mark the column, we now see that four hexes are colored within the column, which lets us erase two more cells:



Work the -2- we just uncovered in the same manner as the others; this eliminates a hex around the {5}, and we fill in all of the other hexes around it. Alas, we can't solve the {4} just yet...

Since we have three blue hexes in the grid on the right, though, let's try to solve that one. Start at the right side and give the -3- the two obvious cells we know it gets. We give the -2- to the left a blue cell from this; eliminate the one below that blue cell, since we know the next blue hex is not consecutive. Now, just mark the final hex below the -3-.

Now, the trick to solving the -2- is in realizing that the column to the left is headed by a "3". The column has only four active cells; two are already blue, with the other two surrounding this -2-. So we know one of them must be marked, which clears the cell below the -2- as a candidate for a blue cell. When we erase this one, we can solve the entire rest of the grid:


The only other line we can clear now is to the left of the center grid. The line governed by a "4" here has only four active hexes, with three already marked, meaning the fourth needs to be colored. Extending now to the bottom-right of the center grid, we can see that both of those empty "1" cells already have a blue hex. When we clear their remaining hexes, we get another "0" to follow. Though it only clears two more cells this time, we are set up for the next sequence. Notice how the grid kind of "bends" downward from where we just were; the "1" on this edge has only one choice for a blue hex. When it's filled, we can clear additional hexes and work towards the right side:

Let's work the -2- and -3- we just revealed. Solve the -2- as we have grown accustomed to doing. This feeds a second cell to the -3-. Here's the trick to solving it: The column to its left is headed by a "7". There are now only seven active cells in the column. When we fill in the remaining hexes, the -3- will get its third blue hex, erasing the last orange hex below it:


Go ahead and fill in the remaining hexes surrounding the "5" we just revealed. Again, we can't solve the nearby "4" yet! That's okay; for now, return to the top grid. Notice the diagonal wiith a "6" pointing to the grid on the right. That row now has six blue hexes, letting us clear a few more.

Notice how this gives us new information in the top-right of the center grid. The newly-revealed "3" on the bottom-right edge has only three cells to claim. We just gave a blue cell to the "1" farthest left of here when we solved the column governed by the "7", letting us clear a cell from the "3" in the middle of this group. The "4" here now gets the two remaining cells around it, also completing that middle "3".

We're very nearly finished, but we still don't have enough information on the grid itself yet. Remember that it's always a good idea to recheck your line headers periodically to see if any new lines can be completed. We do have one more. Starting from the upper-left corner of the puzzle, we have a line headed by a "5"; this one now contains five blue hexes, clearing a lot more cells:


That last step is going to let us complete one more line, this time from the bottom-right corner; this diagonal, headed by a "7", now only has seven active cells. Fill in everything that's left:






Let's try to solve the top-left corner now. Starting with the column governed by a "7", notice that both of the empty "3" cells at the bottom of this cluster have only three hexes to choose from; all of them will thus be marked. Similarly, the empty "2" cells at the top-left each have only two to choose from.

This step completes the column headed by a "3" on the right side of this cluster; we just gave it the third blue hex it needs, letting us clear the others from the column. Can you guess how we're going to solve the top-left cluster now?

We are almost at the end of Puzzle 6-4. Here's the recap:



Let's now try solving the bottom-right cluster of the central grid. We only have the {2} and the "4" left to work out. Our biggest hint comes from the fact that the fourth cell around the {2} can't be marked simply because of the position of the blue cell in its possession:




We should now be able to make substantial progress in the bottom-left cluster of the center grid. Work from right to left; the "2" here has only two cells it can claim. Marking both gives a blue hex to the "1" right below it. The -2- revealed from eliminating its remaining orange hex will again be solved like so many others. However, to solve the "3" here, we need to complete one more diagonal:


The {4} we just revealed can be immediately completed, also setting up completion of the "3" just above and to its right; consequently, that will also finish the column headed by a "7" in this part of the puzzle. Once you get this far, just pay attention to the shared blue hexes, and you won't have much trouble finishing this section:



The end is now in sight. Let's recheck the remaining line headers one more time. The column governed by the "6" at the top-right of the central grid now has six blue hexes and can be completed by simply erasing the rest. Start now with the empty "2" cell just revealed, and we can complete that cluster, as well; consequently, this also completes the line headed by an "8" starting from the bottom-left corner of the puzzle.

The bottom grid has the largest cluster of remaining hexes. From the left side, notice that the "2" in its top-left corner has only one choice for a second blue hex. Marking it will also give the "1" below it the blue hex it needs, and also the "2" on the right the second blue hex it needs. This clears two more cells. The {2} this reveals is easily solved; just give it a second consecutive blue hex. When we clear its remaining orange hex, we reveal a {3} to solve in the same manner:

We can finish this grid if we're careful. The "2" on the upper-right edge of the {3} we just solved has only one choice for a second blue hex; it is shared with both of the other empty "2" cells in that corner. Clear the cell directly below the "2" on the edge. The "1" shares the blue hex we just marked; and the "2" revealed from clearing its remaining hex will share two blue cells we've already marked, as well.

And now, the final steps. We have yet to solve the {4} and "4" at the top. The final line headers tell us how to complete the puzzle. Start with the column headed by the "5"; it now contains only five active hexes, with the two on top still needing to be colored. Note that this also solves the adjacent diagonal governed by a "7". We don't need the line headers anymore; the {4} cell now has its four blue hexes. Clear the last one surrounding it and mark the final orange hex of the puzzle to WIN!!!!!!!!!



And there you have it. The toughest puzzle in Hexcells so far is finished. After that insanely intricate and complicated solution, what could the final puzzle in the game possibly give us to top it...?

Hexes Earned for Completing this Puzzle: 25

This is it. We have now reached the end of Hexcells and our 100% no-mistake playthrough of the game. As we conclude this journey through one of the most innovative puzzle games in recent memory, I do want to thank you for letting me be your guide to not only completing the game, but also to (hopefully) better understanding the puzzles themselves and just why the solutions presented work as they do. I'll have some closing thoughts after we conclude the final challenge. Here it is:




:-) I'll bet you were as surprised as I was the first time this puzzle came up. The final "puzzle" isn't a puzzle at all. From what I gather, it is designed as more of a "thank you" from the developer for playing through the game. It really is a clever way to end the game, and it certainly concludes Hexcells on a high note for everyone who has made it this far. The note that the game provides is truthful: "They're all blue hexes, honest. :)" If you're like me at all, though, you'll probably want to count everything up before marking them all. So here's a formal tally:

Total Number of Blue Hexes (from the "REMAINING" counter): 57

"F" Hexes: 9
"I" Hexes: 5
"N" Hexes: 15
"I" Hexes: 5
"S" Hexes: 11
"H" Hexes: 12

Total Hexes for the Puzzle: 9 + 5 + 15 + 5 + 11 + 12 = 57

And there's your confirmation that the entire puzzle consists of only blue hexes. Happy marking!!!



Hexes Earned for Completing this Puzzle: 1; Could it really be any more than this? :-)

Well done if you have managed to complete the puzzles in Hexcells without making a mistake, with or without using this or any other walkthrough. I truly enjoy the nature of the puzzles in this game, as well as the mostly gentle steps up in difficulty throughout. The developer really did an amazing job in presenting new mechanics as the game progresses, as well as creating an atmosphere that is devoid of any real pressure. There is absolutely no time limit to anything; if it takes you two hours to get through a hard puzzle, it's fine! There is never any pressure to rush through a puzzle. And, most importantly, unlike a lot of other puzzlers I've played through in recent memory, there actually is a way to get through them without making a mistake. As I said before, I missed some of these steps in my first playthrough; however, this guide illustrates that you never have to take a guess. There's always a move available to you, even if it takes a long time to find it.

This is my first-ever guide for Steam. In writing it, I tried to determine the most logical solutions to each puzzle, but these are not the only approaches that should work. Part of the fun of any puzzle game is to find your own way to complete it within the rules it gives you. You may have marked out cells or lines far ahead of what I did in the walkthrough, and that's perfectly okay! In fact, it would be interesting to see similar walkthroughs that demonstrate entirely different approaches to some of the puzzles, particularly 6-4. Full disclosure: I scrapped one attempt at writing out 6-4 because I didn't like the direction I was going. It would have worked in the end but might have been even clunkier than the final version. However, I'm not going to revise it for the official walkthrough outside of the normal proofreading and clarification; it's important to show even the long way of doing things and not make the guide "perfect" in that respect to encourage multiple approaches to the solution.

I really have enjoyed crafting this guide, and I hope that most of you viewing it like it and appreciate the work that went into it with taking the screenshots, annotating them, and trying to write out the puzzles to the best of my ability. Feel free to comment on what works and what doesn't. Also, if anyone wants to contribute steps for alternate solutions to any of the puzzles, please do! I may just feature the best ones as appendices to my "official" guide. Just write out the information in as much detail as you can so I can replicate your solution in-game, and I'll help out with any proofreading or issues with clarity.

So once again, thank you for reading my guide, and I hope it has helped you. Remember: Perfection comes not from mastering everything you do the first time. Perfection comes from learning from your mistakes and growing from them. In Hexcells, there is no true punishment for mistakes; learn from them, then return and conquer them later. Take care, everyone.

Thanks to user Rettima for posting this question in the comments! The question was if there is a way to determine which puzzles have not yet been perfected for earning all possible hexes and unlocking the "Perfectionist" achievement.

I have to give credit to this Steam Community discussion for the answer:

http://steamproxy.net/app/265890/discussions/0/619574421563043505/

It turns out that whenever a puzzle is completed, its selection button in the puzzle index will be colored blue. The difference, however, is in the button's overall appearance. Take the following screenshot:



Here, you can see all three types of icons a particular puzzle's selection button might exhibit. The orange ones, of course, are puzzles that have not yet been completed. Notice, however, that the buttons for both 1-1 and 1-4 are the same, as are those for 1-2 and 1-3. The buttons for 1-2 and 1-3 are blue, but they're flat, much like the orange buttons for those not yet completed on this save file. These puzzles have not been perfected.

By contrast, the buttons for 1-1 and 1-4 sport more of a 3-D appearance, and they have special lighting effects across them. These puzzles have been perfected. The difference is a little subtle, but it is visible if you look closely. So if you go through your save file and notice that the buttons for some of the completed puzzles have a flat, uniform blue appearance to them, these are the ones to play again to achieve perfection.

This same rule also applies to the puzzle indices for both Hexcells Plus and Hexcells Infinite.


Saturday, November 1st, 2014: Version 1.0 Published

Saturday, May 2nd, 2015: Version 1.0.1 Release:

• Corrected a silly error in a screenshot for Puzzle 1-2. :-P
  
• Corrected some very minor typos in the solution to Puzzle 6-4.

After the Hexcells Plus guide is complete--possibly within the next 10 days--all three guides will undergo a final round of revisions. As always, please let me know if you find anything particularly egregious that needs to be fixed right away.

Monday, May 11th, 2015: Version 2.0 Final Release:

I think I can safely declare the Version 2.0 revisions to be complete. The guide still is not "flawless," but I believe the changes I have made are meaningful and bring more polish to it. The flaws that I have identified are so minor that I do not believe they detract from the clarity of the solutions. A few puzzles had entire steps rewritten, and one was redone almost completely from scratch! Please let me know if these changes make a difference, and if you believe there is still something major that needs to be revised, and I will certainly take a look at it. In the meantime, here's the change log:

Rewrote parts of the game introduction, expanding substantially on unlocking of additional puzzles, earning hexes for completion of a puzzle, and unlocking achievements.

Puzzle 1-2: Expanded slightly the discussion on "shared hexes."

Solution rewrites in the following puzzles:

• Chapter 2: Puzzles 2-3 and 2-4
  
• Chapter 3: Puzzles 3-2 and 3-3 (almost a complete rewrite of 3-3!)
  
• Chapter 4: Puzzles 4-3 and 4-5
  
• Chapter 5: Puzzle 5-3

Screenshot edits/redos in the following puzzles:

• Puzzles 1-2 through 1-6
  
• All of Chapter 2
  
• All of Chapter 3
  
• Puzzles 4-1, 4-3, 4-4, and 4-5
  
• Puzzles 5-3 and 5-4
  
• Puzzle 6-4

Screenshot edits range from rewriting annotations to complete redos more in line with the Hexcells Infinite guide.

Made minor changes to formatting; all puzzle solutions have minor rewording and grammatical changes. However, compared to the ones listed above, the other puzzle solutions are not changed very much and only have minor edits for clarity.

Also added an appendix on how to tell which puzzles are perfected and which are not from the puzzle index.

Monday, December 7th, 2015: Version 2.5 Release:

When I first wrote all of the Hexcells guides, I wasn't fully aware of just how Steam's image display options worked. Unfortunately, having Steam load all images at once caused some major issues with the Steam client, including crashing of the Web rendering engine. To try and remedy this, I have retooled the image code. Even before finishing this, I received positive reports of improved page-loading. This will eventually be rolled out across all three guides.

All puzzles have now had their image coding retooled (except for 6-5, which only has two images to start with). Some images will still initially display at full-size, but I tried to be strategic here. For many, you'll need to click a thumbnail to open the original size. I've also cleaned up paragraph spacing to avoid any layout problems.

I've also slightly edited many solutions and reworked a few images and annotations. Nothing required a total rewrite; these were mainly for clarity, though I did fix a significant problem in the solution to Puzzle 6-4.

Unless I happen to find or am notified of a major omission or error in a solution, these are slated to be the final changes to this guide. Again, please let me know if you find anything. I would also love to know if these changes help you in any way compared to the first release. Happy gaming!!