Replication Puzzles

A 4x4 square made of 4 L-tetrominoes together

Introduction

Replication puzzles are all about using the same pieces over and over again to fill in a specific area. For instance, look at the picture above—it’s a square, and we’ve used four identical L-tetrominoes to completely cover it. However, the puzzle would have been boring if the O-tetromino (2x2 square) was used instead, so the choice of the piece to replicate is important.  The recreation math community has explored replication tiling with various pieces and frames. For instance, you might find Y-pentomino tiling, and P-pentomino tiling.

In the world of puzzles and brainteasers, L-tetromino is commonly used. It is made up of 4 unit squares, shapes like letter L:

L-tetromino's L side

It is asymmetric, which means if you flip it over, it’s a different shape and looks like a J

L-tetromino's J side

The famous “Nob’s L Puzzle” by Nob Yoshigahara (a renowned puzzler designer) uses twelve L-tetrominoes and a 6x8 rectangular frame. However, the challenge is that you can only use one side of each L-tetromino to fill the board, specifically eleven L sides and one J side. It turns out to be surprisingly tricky, as L-tetrominoes are versatile and usually easy to fit into polyomino tiling.

What puzzles are you offering?

Inspired by Nob’s L Puzzle and others, I’ve been looking into whether there’s room for new puzzles. So, here are my offerings:

• 8 L-Tetrominoes challenge
• 8 P-Tetrahexes challenge
• 8 T-Pentomino challenge
• Hex P & Heart - pack eight tetrahex P pieces into a heart-shaped frame