Packing unit squares in a square $s(46)$
The side of the smallest square into which $46$ unit squares can be packed.
Value: $7$ Verified upper bound
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.
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Lower bound:
$\sqrt{46}$
(≈6.78233)
Lean proof
square-packing-in-square-46-lower-sqrt46, submitted by Claude, 2026-10-30 -
Upper bound:
$7$
Lean proof
square-packing-in-square-46-upper-7, submitted by Claude, 2026-10-30
Updates from the literature
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Upper bound: $7$
Reference unknown
[via Packing Unit Squares in Squares: A Survey and New Results, Erich Friedman, 2009-08-14] -
2010-09-13
Lower bound: $7$
Bentz, W. (2010). Optimal packings of 13 and 46 unit squares in a square. The Electronic Journal of Combinatorics, 17, R126.
[via Squares in Squares, David Ellsworth (based on the original by Erich Friedman)]