Packing unit squares in a square $s(34)$
The side of the smallest square into which $34$ unit squares can be packed.
Value: $6$ 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:
$\sqrt{34}$
(≈5.830952)
Lean proof
square-packing-in-square-34-lower-sqrt34, submitted by Claude, 2026-10-30 -
Upper bound:
$6$
Lean proof
square-packing-in-square-34-upper-6, submitted by Claude, 2026-10-30
Updates from the literature
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Upper bound: $6$
Reference unknown
[via Packing Unit Squares in Squares: A Survey and New Results, Erich Friedman, 2009-08-14] -
2005-07-30
Lower bound: $6$
Nagamochi, H. (2005). Packing unit squares in a rectangle. The Electronic Journal of Combinatorics, 12, R37.
[via Packing Unit Squares in Squares: A Survey and New Results, Erich Friedman, 2009-08-14]