The initial formation of the trio is always as follows:

Genero, Benero and Zenero

After you pay your hard earned gil to play their game, they'll line up and one of them will say: "Which one is <Name>?"

Name, being their own name. - keep this in mind as you'll be tracking that guy.

There are different things that can happen in one shuffle:

For simplification, we'll just use 1, 2 and 3 to denote the current arrangement.

The possible patterns of movement are as follows:

1, 2, 3 -> 1, 3, 2 (if 1 stays in place, 2 and 3 swapped places)
1, 2, 3 -> 2, 1, 3 (if 1 swapped places with 2, 3 stays in place)
1, 2, 3 -> 2, 3, 1 (if 1 jumps to the end of the row, 2 and 3 move left one spot)
1, 2, 3 -> 3, 1, 2 (if 3 jumps to the front of the row, 1 and 2 move right one spot)

Note: 2 never stays in place, ever.

Now you're ready to face the challenge!

• A pen or pencil
  
• A sheet of paper

• Write the letters "G", "B" and "Z" leaving some space between them
  
• Pay the money to start the challenge and wait until the 3 guys line up
  
• Press your pen against the initial letter of the guy who said it. (Now you know why I chose those letters)
  
• Start the shuffle
  
• After 1 swap (read the basics) pause the game and draw a line between the previous position and the new position of the guy we're tracking.
  
• Repeat the previous step until they ask you "Which one is <Name>?" which by now you should be able to answer.

Keep in mind that as the game speeds up it may be hard keeping track of our target given that the game rocks a solid 30 FPS. If you have trouble with this method, Method 2 may be easier - however it takes a bit longer to do.

• A device which can record video in slo-motion, preferably over 20 seconds. I used an iPad mini for this.

Note: I have not tried using in-game capture software such as XSplit or OBS, but I'm guessing those could also work.

• Pay the money for the challenge and wait until the "Which one is <name>?" text appears.
  
• Align your camera so that you can see Genero, Benero and Zenero
  
• Start recording
  
• Wait 1 second (just to make sure you record the guy with the text prompt for tracking)
  
• Press X to start the shuffle
  
• Once they're done, wait for one or two seconds before Stopping the recording.
  
• Play-back the video and keep track of the guy who said 'Which one is <name>?" as that is the guy you're looking for.

I understand that Method 2 could be considered cheating, however, we're not altering the game in any way, just watching a slo-mo replay of their shuffle. If you consider this cheating, please feel free to ignore this Method.