Problem
COM-B1-M12-P017 Set 5. Trominoes
#17
★★★☆☆ Level 3 of 5
The cell \((1,1)\) is removed from a \(5\times5\) board. Can the remaining region be tiled by straight \(1\times3\) trominoes?
Color by \(i+j\pmod3\).
Under coloring by \(i+j\pmod3\), each tromino covers all three colors. On a \(5\times5\) board the counts are \(9,8,8\), and after removing \((1,1)\) they do not become equal. Hence no tiling exists.
Three-coloring.