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The 8×8 grid below has a 2×2 hole in the center. Fill the remaining 60 cells with the 12 pentominoes (F, I, L, N, P, T, U, V, W, X, Y, Z), each used exactly once. Pieces may be rot...
Can you find an octomino that can be dissected into two L tetrominoes in two essentially distinct ways? By essentially distinct, I mean the two dissections shouldn’t be related by...
Can you find an octomino that can be dissected into two L tetrominoes or into two skew tetrominoes (s or z)? Bonus: Can you find such an octomino that doesn't have any mirror or ro...
Inspired by these two questions on a grid, which is an example of a polyomino. For any polyomino — a connected set of unit squares glued edge-to-edge — construct, or prove impossi...
Rules Tile the 7×7 grid using the nine pentominoes shown below. Each pentomino is used exactly once and may be rotated or reflected. Two pentominoes are already placed as clues an...
Consider the following shape, which I call a hook: OO. O.O This is a four-cell polyplet, also known as a polyking or a pseudo-polyomino. Your job is to cover an N-by-M rectangle u...
One curious problem with pentominoes is the fencing problem. It consists of using the twelve pieces, joined side by side, to form a fence that encloses an empty field. The question...
Can you dissect the following figure into three congruent pieces in three different ways? Two pieces are congruent if they have the same area and "shape" - one can be transformed i...
We saw in a beautiful recent question by @Bubbler how to tile some rectangles with copies (including rotations and flips) of a hook, i.e., the four-celled polyplet shown below. Sa...
Can you dissect the following figure into two congruent pieces in three different ways? Two pieces are congruent if they have the same area and "shape" - one can be transformed int...
Can you tile an infinite square grid with L-trominoes such that there’s exactly one uncovered cell, a.k.a. the hole, and this hole can be moved anywhere in the grid by moving only...
I’m sure people here are familiar with Magna-Tiles or their variants. Here’s a simple version of it that I made. It’s a unit square with four unit length magnets along the four sid...
I'm sharing another puzzle idea. It's played on a grid. The goal is to draw rectangles using lines that connect the centers of some cells following the following rules: Rectangles...
Can you bisect the following figure into 2 congruent pieces in 2 different ways, and trisect it into 3 congruent pieces in 2 different ways? Two pieces are congruent if they have t...
I've posted tetromino nurikabes* before. They were all solvable. But that was before I became a moderator (mwah hah hah). No longer am I bound by the shackles of making puzzles wit...
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