The following pictures show n dominoes (with short side 1) packed inside the smallest known square (with side s).
1.-2.
3.-4.
3.
s = 2
Trivial.
s = 3
Trivial.
s = 2+5√2/4 = 3.76776+
Found by Jonathan Viquerat
in May 2026.
6.-8.
9.
10.-12.
s = 4
Trivial.
s = 4.86812+
Found by Jonathan Viquerat
in May 2026.
s = 5
Trivial.
13.
14.
15.-18.
s = 5+1/√2 = 5.70710+
Found by Jonathan Viquerat
in May 2026.
s = 5.89758+
Found by Jonathan Viquerat
in May 2026.
s = 6
Trivial.
19.
20.-24.
s = 6.81192+
Found by Jonathan Viquerat
in May 2026.
s = 7
Trivial.