Problem
COM-B1-M07-P013 Removed Diagonal
#13
★★★☆☆ Level 3 of 5
All cells on the main diagonal of a \(10\times10\) board are removed. Prove that the remaining region cannot be tiled by dominoes.
The cells \((i,i)\) have the same color.
In chessboard coloring, all cells on the main diagonal have the same color. The full \(10\times10\) board has equal color counts, and after removing \(10\) cells of one color the equality is broken. A domino always covers one cell of each color, so tiling is impossible.
Same method as smaller boards, but students must recognize the diagonal set.