ForumArcade ► Four Colors
A quick Sunday afternoon hack... Prove an instance of the four color theorem by construction.

Click a region to change its color. White is considered uncolored. You win when all regions have a color and no two adjacent regions have the same color.
  
I think I beat it. I am not sure. Is there a win condition or do you just have to figure out if you won?
  
When you win it automatically resets. If it didn't reset, there should be two matching adjacent colors somewhere!
  
kjldslfsdflsad i cant find it
  
it was two cyans touching in one square
  
Yeet i am getting better at this
  
Nicely done! 😄
  
I am addicted.
  
Is it possible to beat the game without using purple?
  
This is actually a very calming little game. It reminds me a bit of I Love Hue (a color matching app game).
  
Is it possible to beat the game without using purple?


It is theoretically possible, but I think very unlikely
  
Glad you guys like it! 😄

It's even possible to color some maps with just two colors, for example if the map is shaped like a checkerboard. I concur that 2- or even 3-colorable maps are probably really rare. I've never solved one of these puzzles using just three colors, though maybe it's been possible before and I just didn't notice (since wasting colors is free).
  
is it possible for the random generation to make a complete checkerboard?

also wouldn't any tessellation work for 2 colors too?
  
I think so, yes. The map generation algorithm starts with a grid of 3,072 tiny regions and merges the smallest one into a random neighboring region until it gets down to 40 regions. You can imagine a generated map where the regions happen to form an 8 x 5 stretched checkerboard.

And I don't think so. For instance a regular hexagonal tiling requires three colors.
  
true, I didnt think of hexagons.
  
I too have become addicted. It does remind me of I Love Hue, which I enjoy.
  
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