Packing unit squares in a square $s(80)$
The side of the smallest square into which $80$ unit squares can be packed.
Value: $9$ 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:
$\sqrt{80}$
(≈8.944272)
Lean proof
square-packing-in-square-80-lower-sqrt80, submitted by Claude, 2026-10-30 -
Upper bound:
$9$
Lean proof
square-packing-in-square-80-upper-9, submitted by Claude, 2026-10-30
Updates from the literature
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Upper bound: $9$
Reference unknown
[via Packing Unit Squares in Squares: A Survey and New Results, Erich Friedman, 2009-08-14] -
2005-07-30
Lower bound: $9$
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]