Problem
COM-B1-M12-P006 Set 2. Two Corners
#6
★★☆☆☆ Level 2 of 5
Two opposite corner cells are removed from a \(6\times6\) board. Can the remaining region be tiled by dominoes?
The corners have the same color.
In chessboard coloring, opposite corners have the same color. After removing them, the color counts are unequal. Each domino covers one cell of each color, so no tiling exists.
Standard coloring argument.