From Newsgroup: rec.puzzles
On Fri, 16 Jan 2026 09:43:08 -0000 (UTC), David Entwistle wrote:
Often attributed to Dudeney and sometimes referred to as 'Mrs Perkins
quilt' problem, this problem appears as 343. SQUARE OF SQUARES in
Dudeney's book: `536 Puzzles and Curious Problems`...
Given a square grid if 13 x 13 smaller squares, what is the smallest
number of square pieces into which the diagram can be dissected?
For example, we could could cut away the border, on two sides, leaving
one 12 x 12 square and then cut the border into 25 little squares,
giving a total of 26 squares in all. This is not an optimal solution.
Feel free to try to find solutions for other values of n x n squares.
SOLUTION
OLUTION
LUTION
UTION
TION
ION
ON
N
I tried for days and couldn't find a solution with fewer than 12 squares,
nor write a program to find a solution, but there clearly is one, and here
it is:
https://pasteboard.co/gxe47kMj0Qan.png
The given solution, from the book, states:
There is, we believe, only one solution to this puzzle, here shown. The
fewest pieces must be 11, the portions must be the sizes given, the
largest three pieces must be arranged as shown, and the remaining group of eight squares may be "reflected" but cannot be differently arranged.
For a discussion of the general problem, still unsolved, of dividing a
square lattice of any size, along lattice lines, into the minimum number
of smaller squares see J. H. Conway, "Mrs Perkin's Quilt," Proceedings of
the Cambridge Philosophical society, Vol. 60, 1964, pp. 363-368; G. B. Trustrum's paper of the same title, in the same journal, Vol. 61, 1965,
pages 7-11; and my (Martin Gardner's) Scientific American column for
September 1966. The corresponding problem on a triangular lattice has not,
to my knowledge, been yet investigated.
Gardner goes on to discuss the history of the problem.
See also
https://oeis.org/A005670
--
David Entwistle
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