The number of simple and compound perfect squared squares of various orders is known to be as follows:
Order | Simple | Compound |
---|---|---|
<21 | 0 | 0 |
21 | 1 [Duijvestijn, 1978] | 0 |
22 | 8 [Duijvestijn, 1993] | 0 |
23 | 12 [Duijvestijn, 1993] | 0 |
24 | 26 [Duijvestijn, 1993] | 1 [Willcocks, 1951; Duijvestijn, Federico and Leeuw, 1982] |
25 | 160 [Duijvestijn, 1994] | >=1 |
26 | 441 [Duijvestijn, 1996] | >=2 |
27 | >=227 [Bouwkamp, 1998] | >=2 |
Here, the compound perfect squared squares obtained by changing the orientation of the squared rectangle inside the squared square are not counted as different. If I have a list of the squares' Bouwkamp codes, there is a link to it above.
Thanks to Stuart Anderson for providing squared squares of order 25 and 27.
[Willcocks, 1951]: A note on some perfect squared squares, Canadian J. Math., 3, (1951), 304-308.
David Moews ( dmoews@fastmail.fm )
Last updated 20-IX-2004