Problem
COM-B1-M11-P019 Corner of \(5\times5\)
#19
★★★☆☆ Level 3 of 5
The corner cell \((1,1)\) is removed from a \(5\times5\) board. Can the remaining region be tiled by straight \(1\times3\) trominoes?
Color cells by \(i+j\pmod3\).
Under coloring by \(i+j\pmod3\), every straight tromino covers one cell of each color. On the \(5\times5\) board the color counts are \(9,8,8\). The cell \((1,1)\) has one of the colors occurring \(8\) times, so after removal the counts are not equal. No tiling exists.
Mixed task requiring three-coloring, not chessboard coloring.