The following pictures show n dominoes (with short side 1) packed inside the smallest known tan (with short side s).
1.
2.
3.
s = 2√2 = 2.82842+
Trivial.
s = 1+2√2 = 3.82842+
Trivial.
s = 3√2 = 4.24264+
Trivial.
4.
5.
6.
s = 2+2√2 = 4.82842+
Found by Erich Friedman
in May 2026
s = 1+3√2 = 5.24264+
Found by Erich Friedman
in May 2026.
s = 4√2 = 5.65685+
Trivial
7.
8.
9.
s = 2+3√2 = 6.24264+
Found by Jonathan Viquerat
in May 2026.
s = 5+√2 = 6.41421+
Found by Erich Friedman
in May 2026.
s = 4+2√2 = 6.82842+
Found by Erich Friedman
in May 2026.
10.
11.
12.
s = 5√2 = 7.07106+
Trivial.
s = 6+√2 = 7.41421+
Found by Jonathan Viquerat
in May 2026.
s = 5+2√2 = 7.82842+
Found by Jonathan Viquerat
in May 2026.
13.
14.
15.
s = 8
Found by Erich Friedman
in May 2026.
s = 4+3√2 = 8.24264+
Found by Maurizio Morandi
in May 2026.
s = 6√2 = 8.48528+
Trivial.
16.
17.
18.
s = 6+2√2 = 8.82842+
Found by Erich Friedman
in May 2026.
s = 9
Found by Maurizio Morandi
in May 2026.
s = 5+3√2 = 9.24264+
Found by Maurizio Morandi
in May 2026.
19.
20.
s = 1+6√2 = 9.48528+
Found by Maurizio Morandi
in May 2026.
s = 7+2√2 = 9.82842+
Found by Jonathan Viquerat
in May 2026.