Problem
COM-B1-M07-P012 Odd Rectangle
#12
★★☆☆☆ Level 2 of 5
Let \(m\) and \(n\) be odd. An \(m\times n\) rectangle is covered by dominoes except for one cell. Prove that the uncovered cell has the color that occurs one more time on the board.
In an odd rectangle, the color counts differ by one.
Since \(mn\) is odd, one color occurs one more time in chessboard coloring. Dominoes cover one cell of each color. Hence after all domino-covered cells are removed, the remaining cell must have the majority color.
Builds a general statement instead of memorizing separate boards.