# SPSSs Order 37;

The first SPSS of this order was found by Willcocks, with a side of 1947 (see illustration). Willcocks claimed the year of discovery as 1947 [1], but this was questioned by Bouwkamp [2], Willcocks was asked it about didn't recall anything about this square (in 2012). [3]. Martin Gardner gave the year of discovery of 37:1947 as 1959 [4]. The order 37:1947 was based on Brook's order 38:3920, "by a slight modification of the method used" [1]. The first publication of the Brooks 38:2920 discovery was in 1950 by W.T. Tutte [5]. The next 2 SPSSs of this order were found by Ian Gambini in the late 1990s [6]. In 2013 Milla and Anderson found 282 and in the same year James Williams found 99746. In 2014 Brian Trial found 171.

It is estimated that there are approximately 1.8 x 10^7 SPSSs in order 37.

Listings; Bouwkampcodes spsso37.bkp.zip and tablecodes spsso37.txt.zip and postscript spsso37.ps.zip.

## References

- T. H. Willcocks, Some Squared Squares and Rectangles, Journal of Combinatorial Theory 3, 54-56 (1967) .
- C. J. Bouwkamp and A.J.W. Duijvestijn, Album of Simple Perfect Squared Squares of order 26, EDT Report 94-WSK-02 Eindhoven, July 1994, vi-vii.
- G. H. Morley, private correspondence 2013, 2014.
- Martin Gardner; The addendum (pp. 162-4) to Tutte's chapter in Martin Gardner's More Mathematical Puzzles and Diversions (1961) "The smallest published square that is both simple and perfect is a 38th-order square with a side of 4,920, discovered by R.L. Brooks. In 1959 this was bettered by T.H. Willcocks of Bristol, with a 37th-order square, 1,947 on the side."
- W. T. Tutte, Squaring the Square, Canad. J. Math. 2 (1950).
- I. Gambini, Thesis (1999) Quant aux carrés carrelés.