If every rectangular tile has at least one side of integer length, must the tiled rectangle also have at least one integer-length side? — Tiling, or tessellation, problems ask if/how a surface can be completely covered by non-overlapping tiles. The study of tilings has yielded many important results, both in pure math and for real-world applications. Examples include the Four Color Theorem, the characterization of tiling patterns with group theory, algorithms in unsupervised machine…