Jagged Square Puzzles

thingiverse

Jagged or skewed squares, particularly one made of 61 small squares with a missing central square, hold an important place in pentomino puzzle history. Tiling the 60 square version with just 12 pentominos was proved impossible back in the 1980s. A small jagged square box composed of 25 small squares and another, with its middle square missing, made up of 24 small squares, are presented here as puzzles. The 25 square version can be easily tiled by combining 5 specific pentominos - F, N, P, W, and X - while the 24 square version requires just 4 hexominos - A, B, C, and D. Additional sets of pieces that can tile these small jagged square boxes can be created using various combinations of these pentominos, hexominos, and a single "T" tetromino. By replacing each of the F, N, P, and W pentominoes with the "T" tetromino, four new sets of pieces that can tile the jagged square box with 24 small squares are formed. Furthermore, one can also try combining the 4 hexominos with the "T" tetromino to see if they can replace two of the pentominos in tiling the 25 small square jagged box. A total of twelve such sets of pieces were found through this method. Solutions to all these puzzles are provided below.