Problem
COM-B1-M07-P017 A Monomino on a \(9\times9\) Board
#17
★★★☆☆ Level 3 of 5
A \(9\times9\) board is tiled by dominoes and one monomino. Prove that the monomino lies on a square of the same color as the corners.
Dominoes cover colors equally.
On a \(9\times9\) board, the corner color occurs \(41\) times and the other color \(40\) times. All dominoes together cover equal numbers of the two colors. The one remaining cell, covered by the monomino, must have the majority color, the corner color.
Important type: determine the location of an exceptional cell.