Jagged Square Puzzles

thingiverse

Jagged or skewed squares, particularly one made of 61 small squares with the central square missing, are part of pentomino puzzle history. Tiling the 60 square version with 12 pentominos was proved impossible in the 1980's. Here is a small jagged square box composed of 25 small squares and a second box, with the middle square missing, composed of 24 small squares. The 25 square version can be tiled by 5 pentominos, (F, N, P, W, and X), and the 24 square version by 4 hexominos, (A, B, C, and D). Both are presented as puzzles; the hexomino one is trivial; the pentomino one a bit harder. Many additional sets of pieces that tile the small jagged square boxes can be created with combinations of the 5 pentominos, the 4 hexominos and a single "T" tetromino. The F, N, P, and W pentomino's can be replaced in turn by the "T" tetromino to make four sets of pieces that tile the jagged square box with 24 small squares. One can also take the 4 hexominos in turn, combine them with the "T" tetromino and see if the combination can replace two of the pentominos in the tiling of the jagged square box with 25 small squares. Twelve such sets of pieces can be found. Solutions to all of these puzzles are given below.