Klarner's Theorem

An $a\times b$ Rectangle can be packed with $1\times n$ strips Iff $n\vert a$ or $n\vert b$.

See also Box-Packing Theorem, Conway Puzzle, de Bruijn's Theorem, Slothouber-Graatsma Puzzle

References

Honsberger, R. Mathematical Gems II. Washington, DC: Math. Assoc. Amer., p. 88, 1976.