Problem
COM-B1-M07-P009 A Cell Next to a Corner
#9
★★☆☆☆ Level 2 of 5
The cell \((1,2)\) is removed from a \(7\times7\) board. Can the remaining region be tiled by straight \(1\times3\) trominoes?
Use coloring by \(i+j\pmod3\).
Under the coloring \((i,j)\mapsto i+j\pmod3\), every straight tromino covers one cell of each color. On a \(7\times7\) board, colors \(0,1,2\) occur \(16,16,17\) times. The cell \((1,2)\) has color \(0\), so after removal the counts are \(15,16,17\). They are not equal, so the remaining region cannot be tiled by straight trominoes.
Standard use of three-coloring after the area check.