Problem
COM-B1-M07-P007 One Diagonal
#7
★★☆☆☆ Level 2 of 5
All cells on the main diagonal of an \(8\times8\) board are removed. Can the remaining region be tiled by dominoes?
All cells on the main diagonal have the same color.
In chessboard coloring, cell \((i,i)\) always has the same color because \(i+i\) is even. Thus \(8\) cells of one color are removed. The full board had equal color counts, and after removal they are unequal. Dominoes cover colors equally, so tiling is impossible.
Good practice for recognizing hidden same-color sets.