Problem
COM-B1-M07-P008 Five Vertical Dominoes
#8
★★☆☆☆ Level 2 of 5
Can a \(6\times6\) board be tiled by dominoes so that exactly \(5\) dominoes are vertical?
Color the columns alternately.
Color the columns alternately in two colors. A horizontal domino covers one cell of each column color, while a vertical domino covers two cells of one column color. The board has \(18\) cells of each color. Horizontal dominoes keep the balance, so vertical dominoes must contribute equal numbers of cells of the two colors. Thus the number of vertical dominoes in the two types of columns must be equal. But their total is \(5\), impossible.
Important variation: color encodes direction.