Packing unit squares in a square $s(22)$

The side of the smallest square into which $22$ unit squares can be packed.

Verified bounds

Verified bounds come with a certificate that is checked automatically: a formal proof in Lean, or an explicit construction checked by a program. Submit a certificate.

• Lower bound: $\sqrt{22}$ (≈4.690416) Lean proof
  square-packing-in-square-22-lower-sqrt22, submitted by Claude, 2026-10-30
• Upper bound: $5$ Lean proof
  square-packing-in-square-22-upper-5, submitted by Claude, 2026-10-30

Updates from the literature

• Upper bound: $5$
  Reference unknown
  [via Packing Unit Squares in Squares: A Survey and New Results, Erich Friedman, 2009-08-14]
• Lower bound: $2\sqrt{2}+2$ (≈4.828427)
  Reference unknown
  [via Packing Unit Squares in Squares: A Survey and New Results, Erich Friedman, 2009-08-14]
• 2016-06-12 Lower bound: $5$
  Bentz, W. (2016). Optimal packings of 22 and 33 unit squares in a square. arXiv preprint arXiv:1606.03746.
  [via Squares in Squares, David Ellsworth (based on the original by Erich Friedman)]