Sudoku color pairs

Posted by Dan on Mar 30th, 2008
2008
Mar 30

Here is a particular color sudoku, displayed two colors at a time. There are 9 ways to choose the first color, and 8 ways to choose the second color. 9 times 8 is 72, but this counts every pattern twice, since either color can be chosen first. So we really have 36 different combinations of two colors.

For sudokus in general, there are 46,656 ways to arrange the first color, and 17,972 ways to arrange the second color without overlapping the first color. 46,656 times 17,972 is 838,501,632, and adjust for double-counting, we get 419,250,816 possible patterns of two colors.