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 have been proved optimal.


1.            2.            3.
s = 2
Trivial.
s = 4
Trivial.
s = 6
Trivial.


4.            5.            6.
s = 8
Trivial.
s = 11
Found by Erich Friedman in 1998.
s = 14
Found by Erich Friedman in 1998.

7.            8.            9.
s = 17
Found by Erich Friedman in 1998.
s = 21
Found by Erich Friedman in 1998.
s = 24
Found by Erich Friedman in 1998.

10.            11.            12.
s = 28
Found by Erich Friedman in 1998.
s = 32
Found by Erich Friedman in 1998.
s = 37
Found by Erich Friedman in 1998.

13.            14.            15.
s = 41
Found by Erich Friedman in 1998.
s = 46
Found by Erich Friedman in January, 2004.
s = 50
Found by Erich Friedman in January, 2004.

16.            17.            18.
s = 55
Found by Erich Friedman in January, 2004.
s = 60
Found by Erich Friedman in January, 2004.
s = 66
Found by Erich Friedman in January, 2004.

19.
s = 71
Found by Erich Friedman in January, 2004.

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