Smallest Squared Squares

TL;DR

This paper classifies all small squared squares with side lengths up to 17x17 under a specific non-sharing border constraint, identifying exactly two such configurations and their mirrored versions.

Contribution

It provides a complete enumeration and proof of the only two squared squares satisfying the given conditions up to size 17x17.

Findings

Exactly two squared squares up to 17x17 meet the criteria.

The paper includes explicit constructions of these squares.

Mirrored versions are also considered and included.

Abstract

In this paper we have a look at squared squares with small integer sidelengths, where the only restriction is that any two subsquares of the same size are not allowed to share a full border. We prove that there are exactly two such squared squares (and their mirrored versions) up to and including size 17x17. They are shown in Figure 1 (page 2).