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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀   Osaka, Japan
 
 
⠘⣻⠟⢠⣿⡆⠀⠀⣏⣹⢤⡞⢹⡆⣾⠛⠗⢸⠋⠓⢸⣇⣾⡇⣿⣼⠋⢷⠀⠀ ⠾⠷⠶⠾⠛⠿⠀⠀⠏⠀⠈⠷⠾⠃⠻⠶⠗⠘⠶⠖⠸⠟⠸⠇⠿⠹⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡻⠕⠅⠁⣀⣤⣤⣄⣀⠈⠄⠁⠄⠁⣿⡮⠄⠁⠄⠄⡠⠶⠶⠦⡀⠈⣽⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠄⠁⠄⠔⠒⠭⠭⠥⠥⠓⠄⢀⣴⣿⣿⡄⠁⠠⣤⠉⠉⣭⠝⠈⢐⣽⣕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡢⢄⡰⡢⡙⠄⠠⠛⠁⢀⢔⣵⣿⣿⣿⣿⣧⣄⡈⠁⠈⠁⠉⡹⣽⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣬⣭⡭⠔⣠⣪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣵⡒⠫⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⣛⣥⣶⣿⠟⢁⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡙⣿⣿⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡫⠁⢀⠑⠓⠫⢝⢟⣿⣿⣿⣿⡻⠊⢉⣄⠈⠪⡫⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢟⠁⣰⣿⣿⣢⢤⣀⡀⠈⠉⠉⢀⠠⠪⢝⡻⣷⡀⠊⡪⡻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡫⢟⣿⣿⣿⣿⡊⢠⣿⣿⡫⠚⣊⣡⠶⢦⣤⣤⠶⠞⡛⠳⣌⠫⡻⡀⠈⡺⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⡪⡫⢟⡿⣕⠁⡫⠝⠊⡴⠋⠁⠁⠐⠁⠂⠈⠐⠈⠈⠐⠐⠳⠄⠹⣇⠪⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠊⠕⡪⢕⢀⠞⠁⠄⣁⢀⢀⣀⣤⣤⣠⣀⣤⣴⣶⣶⣶⡆⠄⠆⢷⠕⡪
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠄⠁⠄⠁⠄⡎⠄⠁⢬⣮⣕⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡫⡪⡵⠄⠁⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠁⠄⠁⠄⡣⠄⠁⣷⣯⣵⣢⠄⠄⠉⠉⠉⠉⠉⠉⣠⣬⣟⡕⠄⠁⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣋⣹⠀⠀⢸⣉⡷⠸⣆⡟⢠⡏⠑⠀⣾⠉⠂⢸⣇⠟⠀⡇⡴⡇⢸⢀⢾⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠸⠀⠀⠸⠀⠀⠠⠜⠀⠘⠧⠴⠂⠻⠤⠖⠸⠏⠧⠀⠟⠁⠇⠸⠏⠸⠇⠀
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Naposledy hráno 27. zář.
5,5 hodin celkem
Naposledy hráno 26. zář.
apoper114dolce před 5 hodinami 
   :mind_rose::anywayredspring:    :heartred:    :anywayredspring::mind_rose:
:anywayredspring::ai_flare::atomical::mind_rose:    :mind_rose::atomical::ai_flare::anywayredspring:
:mind_rose::atomical::shinealight::atomical::anywayredspring::atomical::shinealight::atomical::mind_rose:
:atomical::anywayredspring::atomical::ai_flare::atomical::ai_flare::atomical::anywayredspring::atomical:
:atomical:   :mind_rose::atomical::shinealight::atomical::mind_rose:   :atomical:
:heartred:   :atomical::anywayredspring::atomical::anywayredspring::atomical:    :heartred:
      :atomical:   :mind_rose:   :atomical:
       :heartred:   :atomical:    :heartred:
            :atomical:
             :heartred:
apoper114dolce 22. zář. v 2.37 
Problem: Prove that the sum of the first n positive integers can be expressed as:

n(n+1)/2

Prove:

1 + 2 + 3 + ... + n = n(n+1)/2
apoper114dolce 20. zář. v 2.44 
⠀⠀⠀⠀:bombgd::bombgd::bombgd::bombgd:
⠀⠀⠀⠀:bombgd::starsky::invade::bombgd:
⠀⠀⠀⠀:bombgd::invade::starsky::bombgd:
⠀⠀⠀⠀:bombgd::starsky::invade::bombgd:
:bombgd::bombgd::bombgd::invade::starsky::bombgd::bombgd::bombgd:
:bombgd::starsky::invade::starsky::invade::starsky::invade::bombgd:
:bombgd::invade::starsky::invade::starsky::invade::starsky::bombgd:
:bombgd::bombgd::bombgd::starsky::invade::bombgd::bombgd::bombgd:
⠀⠀⠀⠀:bombgd::invade::starsky::bombgd:
⠀⠀⠀⠀:bombgd::bombgd::bombgd::bombgd:
apoper114dolce 14. zář. v 4.44 
⠀⠀ :fireflies::dealstars::fireflies:⠀⠀⠀⠀⠀⠀:fireflies::dealstars::fireflies:
:fireflies::dealstars::Y_H::Y_H::dealstars:⠀⠀::dealstars::Y_H::Y_H::dealstars::fireflies:
:dealstars::Y_H::glare::glare::Y_H::fireflies::Y_H::glare::glare::Y_H::dealstars:
:fireflies::Y_H::glare::glare::glare::Y_H::glare::glare::glare::Y_H::fireflies:
⠀⠀ :dealstars::Y_H::glare::glare::glare::glare::glare::Y_H::dealstars:
⠀⠀⠀⠀ :fireflies::Y_H::glare::glare::glare::Y_H::fireflies:
⠀⠀⠀⠀⠀⠀ :dealstars::Y_H::glare::Y_H::dealstars:
⠀⠀⠀⠀⠀⠀⠀⠀ :fireflies::Y_H::fireflies:
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ :dealstars:
apoper114dolce 12. zář. v 18.47 
:heart_blue::rarebutterfly::rarebutterfly::heart_blue::butterfly::heart_blue::heart_blue:
:rarebutterfly::heart_blue::heart_blue::rarebutterfly::heart_blue::heart_blue::butterfly:
:rarebutterfly::heart_blue::heart_blue::heart_blue::heart_blue::heart_blue::butterfly:
:heart_blue::rarebutterfly::heart_blue::heart_blue::heart_blue::butterfly::heart_blue:
:heart_blue::heart_blue::rarebutterfly::heart_blue::butterfly::heart_blue::heart_blue:
:heart_blue::heart_blue::heart_blue::butterfly::heart_blue::heart_blue::heart_blue:
apoper114dolce 6. zář. v 22.14 
⠀⠀ :heartred::heptagramred::heartred:⠀⠀⠀⠀⠀⠀:heartred::heptagramred::heartred:
:heptagramred::lifeheart::redjewel::lifeheart::heptagramred:⠀⠀:heptagramred::lifeheart::redjewel::lifeheart::heptagramred:
:heartred::redjewel:⠀⠀⠀⠀:redjewel::heartred::redjewel:⠀⠀⠀⠀:redjewel::heartred:
:heptagramred::lifeheart:⠀⠀⠀⠀⠀⠀:lifeheart:⠀⠀⠀⠀⠀⠀:lifeheart::heptagramred:
⠀⠀:heartred::redjewel:⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀:redjewel::heartred:
⠀⠀⠀⠀:heptagramred::lifeheart:⠀⠀⠀⠀⠀⠀:lifeheart::heptagramred:
⠀⠀⠀⠀⠀⠀:heartred::redjewel:⠀⠀:redjewel::heartred:
⠀⠀⠀⠀⠀⠀⠀⠀:heptagramred::lifeheart::heptagramred:
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀:heartred:
⠀  :LilyHeart: 𝐇𝐚𝐯𝐞 𝐚 𝐥𝐨𝐯𝐞𝐥𝐲 𝐝𝐚𝐲 :LilyHeart: