Button Game: Rules

1. Create a board of 36 (6 x 6) cells (buttons). To start the game, initialize the value of each cell to be 0.
2. Pick a pair of random numbers, x,y, each in the range of [1,6].
3. Increment the value of cell C_x,y by 1.
   • If x-1 >= 1 then increment C_x-1,y by 1.
   • If x+1 <= 6 then increment C_x+1,y by 1.
   • If y-1 >= 1 then increment C_x,y-1 by 1.
   • If y+1 <= 6 then increment C_x,y+1 by 1.
4. If the value of any cell exceeds a value of 3, then set its value to 0. That is, repeated incrementing of a cell progresses as follows 0,1,2,3,0,1,...
5. Repeat steps 2 and 4 for as many times as you would like -- fewer times makes the game easy, and more makes it hard.

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6. To play the game, the user may click on any cell (button), C_x,y. Decrement that cell's value by 1.
   • If x-1 >= 1 then decrement C_x-1,y by 1.
   • If x+1 <= 6 then decrement C_x+1,y by 1.
   • If y-1 >= 1 then decrement C_x,y-1 by 1.
   • If y+1 <= 6 then decrement C_x,y+1 by 1.
7. If the value of any cell falls below a value of 0, then set its value to 3. That is, repeated decrementing of a cell progresses as follows 3,2,1,0,3,2,...
8. If all of the cell's values are 0, then the game is over. Otherwise, the user can choose another cell.