Problem
COM-B1-M07-P003 One Uncovered Cell
#3
★☆☆☆☆ Level 1 of 5
A \(7\times7\) board is covered by dominoes with one cell left uncovered. Prove that this cell has the same color as the corner cells.
Count the colors on an odd board.
On a \(7\times7\) board, the corner color occurs \(25\) times and the other color \(24\) times. Dominoes cover equal numbers of the two colors. Hence the remaining cell must have the color that occurred one more time, the corner color.
Shows that coloring can give a necessary position, not only impossibility.