Solution to Problem 6
Solution by Mike ArsenaultAll you have to do is randomly choose the colours of the first row andthen the colours of the second row can be determined. This is because,after the first row is chosen, each square on the first row will haveall it's neighbours set except one, and that is the one immediatelybelow it in the second row. So that block in the second row just has tobe set to either Black or White, depending on how many Black neigboursthe cell above it (in row 1) already has.This process is then repeated for row 3, now that all of row 2 and row 1has been determined. Then repeat for rows 4, 5, and 6.
I guess since the colours of all the blocks in the first row can berandomly chosen and these choices determine what the rest of the tablelooks like, there are 2 ^ 6 = 64 possible combinations of a 6x6checkboard that can meet the criteria.
Some of them are:
WBBWBB WBWWBB BWWWWBWWWBWW WBWWWW BWBBWBBWBBBW WWWBWW WBWWBWBBWWWW BWWBWB BBBBBBBWBWWB BWWWBB WWBBWWWWBWWB WWBBWB WBBBBW
[Editorial note: Does this work for any size of board?]
Also solved by Brian Gregory.
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