Why is it not possible to cover the chess board with 3X1 dominoes if one of the corner squares is missing (e.g. the top right square)?
Asked
Active
Viewed 2,033 times
0
-
1Try colouring the board, instead of two colours, with three colours $abcabcab$ – Empy2 Sep 12 '15 at 15:39
1 Answers
1
Color the board in vertical stripes of red, blue, and yellow squares. There are three full columns of red squares, so $24$. There are $23$ blue squares, because one is removed. There are $16$ yellow squares. Each tromino covers either three squares or one of each. The quantity $red + yellow -2blue \bmod 3$ doesn't change as we place trominos, but it starts out $2$ and ends $0$.
Ross Millikan
- 383,099