Problem
COM-B1-M06-P015 Board Without Corners
#15
★★★☆☆ Level 3 of 5
Can an \(8\) by \(8\) board be tiled with dominoes if two opposite corner cells are removed?
In chessboard coloring, opposite corners have the same color.
The original board has \(32\) black and \(32\) white cells. Opposite corners have the same color, so after removal there are \(30\) cells of one color and \(32\) of the other. Each domino covers one black and one white cell, so tiling is impossible.
Classic coloring invariant.