Packing unit squares in a square $s(86)$
The side of the smallest square into which $86$ unit squares can be packed.
Lower bound:
$\sqrt{86}$
(≈9.273618)
Verified
(not in the literature)
Upper bound:
$\frac{17+\sqrt{7}}{2}$
(≈9.822876)
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:
$\sqrt{86}$
(≈9.273618)
Lean proof
square-packing-in-square-86-lower-sqrt86, submitted by Claude, 2026-10-30 -
Upper bound:
$10$
Lean proof
square-packing-in-square-86-upper-10, submitted by Claude, 2026-10-30
Updates from the literature
-
Upper bound: $\frac{17+\sqrt{7}}{2}$
(≈9.822876)
Reference unknown
[via Packing Unit Squares in Squares: A Survey and New Results, Erich Friedman, 2009-08-14]