Consecutive Dominoes in Squares
The following pictures show n dominoes with short sides 1, 2, . . . n packed inside the smallest square (of side length s). All of these are probably optimal, except for possibly n=20.

1.

s = 2
Trivial. 		2.

s = 4
Trivial. 		3.

s = 6
Trivial. 		4.

s = 8
Trivial.
5.

s = 11
Found by Erich Friedman
in 1998. 		6.

s = 14
Found by Erich Friedman
in 1998. 		7.

s = 17
Found by Erich Friedman
in 1998. 		8.

s = 21
Found by Erich Friedman
in 1998.
9.

s = 24
Found by Erich Friedman
in 1998. 		10.

s = 28
Found by Erich Friedman
in 1998. 		11.

s = 32
Found by Erich Friedman
in 1998. 		12.

s = 37
Found by Erich Friedman
in 1998.
13.

s = 41
Found by Erich Friedman
in 1998. 		14.

s = 46
Found by Erich Friedman
in 2004. 		15.

s = 50
Found by Erich Friedman
in 2004. 		16.

s = 55
Found by Erich Friedman
in 2004.
17.

s = 60
Found by Erich Friedman
in 2004. 		18.

s = 66
Found by Erich Friedman
in 2004. 		19.

s = 71
Found by Erich Friedman
in 2004. 		20.

s = 76
Found by Maurizio Morandi
in 2014.
21.

s = 82
Found by Erich Friedman
in 2014. 		22.

s = 88
Found by Erich Friedman
in 2014. 		23.

s = 94
Found by Erich Friedman
in 2014. 		24.

s = 100
Found by Erich Friedman
in 2014.
25.

s = 106
Found by M. Sun and N. Sun
in June 2026. 		26.

s = 112
Found by Ryan Chi and d/dx
in September 2026. 		27.

s = 118
Found by Yanis Gomes
in November 2026. 		28.

s = 125
Found by Yanis Gomes
in November 2026.
29.

s = 132
Found by Matthew Sun
in June 2026. 		30.

s = 138
Found by Yanis Gomes
in November 2026. 		31.

s = 145
Found by Yanis Gomes
in November 2026. 		32.

s = 152
Found by Yanis Gomes
in November 2026.
33.

s = 159
Found by Yanis Gomes
in November 2026. 		34.

s = 166
Found by Yanis Gomes
in November 2026. 		35.

s = 174
Found by Matthew Sun
in June 2026. 		36.

s = 181
Found by Yanis Gomes
in November 2026.
37.

s = 188
Found by Yanis Gomes
in November 2026. 		38.

s = 196
Found by Yanis Gomes
in November 2026. 		39.

s = 204
Found by Rowan Jones
in October 2026. 		40.

s = 212
Found by Rowan Jones
in October 2026.
41.

s = 219
Found by Yanis Gomes
in November 2026. 		42.

s = 227
Found by Yanis Gomes
in November 2026. 		43.

s = 236
Found by Yanis Gomes
in November 2026. 		44.

s = 244
Found by Yanis Gomes
in November 2026.
45.

s = 252
Found by Yanis Gomes
in November 2026. 		46.
? 		47.

s = 269
Found by Yanis Gomes
in November 2026. 		48.

s = 277
Found by Yanis Gomes
in November 2026.
49.

s = 287
Found by Yanis Gomes
in November 2026. 		50.

s = 296
Found by Yanis Gomes
in November 2026.