Knight's-Move Cell Shifts for Polyominoes

Introduction

Two figures can be tiled with copies of the same polyomino. The figures differ in only one cell. Can the different cells lie a knight's move apart? Thanks to Jenard Cabilao for suggesting this problem.

Here I show minimal known solutions for polyominoes of orders 3, 5, and 7. Cell shifts for polyominoes of even order must preserve parity, so they cannot be a knight's move apart.

If you can solve any of the unsolved cases, please let me know.

Trominoes

Impossible

Pentominoes

Impossible

Birotary Variants

Heptominoes

Impossible

Unsolved

Birotary Variants

Unsolved Cases

Last revised 2014-02-14.


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Col. George Sicherman [ HOME | MAIL ]