Packing unit squares in a square $s(17)$
The side of the smallest square into which $17$ unit squares can be packed.
Lower bound:
$\frac{40\sqrt{2}+19}{17}$
(≈4.445208)
Upper bound:
${\approx}4.6755$
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:
$\sqrt{17}$
(≈4.123106)
Lean proof
square-packing-in-square-17-lower-sqrt17, submitted by Claude, 2026-10-30 -
Upper bound:
$5$
Lean proof
square-packing-in-square-17-upper-5, submitted by Claude, 2026-10-30
Updates from the literature
-
Upper bound: ${\approx}4.6755$
Reference unknown
[via Packing Unit Squares in Squares: A Survey and New Results, Erich Friedman, 2009-08-14] -
Lower bound: $\frac{40\sqrt{2}+19}{17}$
(≈4.445208)
Reference unknown
[via Packing Unit Squares in Squares: A Survey and New Results, Erich Friedman, 2009-08-14]