Mrs. Perkins' Quilt

The Dissection of a Square of side $n$ into a number $S_n$ of smaller squares. Unlike a Perfect Square Dissection, however, the smaller Squares need not be all different sizes. In addition, only prime dissections are considered so that patterns which can be dissected on lower order Squares are not permitted. The smallest number of Relatively Prime dissections of an $n\times n$ quilt for $n=1$, 2, ..., are 1, 4, 6, 7, 8, 9, 9, 10, 10, 11, 11, 11, 11, 12, ... (Sloane's A005670).

See also Perfect Square Dissection

References

Conway, J. H. ``Mrs. Perkins's Quilt.'' Proc. Cambridge Phil. Soc. 60, 363-368, 1964.

Dudeney, H. E. Problem 173 in Amusements in Mathematics. New York: Dover, 1917.

Dudeney, H. E. Problem 177 in 536 Puzzles & Curious Problems. New York: Scribner, 1967.

Gardner, M. ``Mrs. Perkins' Quilt and Other Square-Packing Problems.'' Ch. 11 in Mathematical Carnival: A New Round-Up of Tantalizers and Puzzles from Scientific American. New York: Vintage, 1977.

Sloane, N. J. A. Sequence A005670/M3267 in ``An On-Line Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.

Trustrum, G. B. ``Mrs. Perkins's Quilt.'' Proc. Cambridge Phil. Soc. 61, 7-11, 1965.