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  • Mrs =?UTF-8?B?UGVya2luc+KAmXM=?= quilt

    From David Entwistle@qnivq.ragjvfgyr@ogvagrearg.pbz to rec.puzzles on Fri Jan 16 09:43:08 2026
    From Newsgroup: rec.puzzles

    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.
    --
    David Entwistle
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  • From David Entwistle@qnivq.ragjvfgyr@ogvagrearg.pbz to rec.puzzles on Fri Jan 16 10:04:52 2026
    From Newsgroup: rec.puzzles

    On Fri, 16 Jan 2026 09:43:08 -0000 (UTC), David Entwistle wrote:

    Given a square grid if 13 x 13 smaller squares,

    Given a square grid of 13 x 13 smaller squares ...
    --
    David Entwistle
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  • From David Entwistle@qnivq.ragjvfgyr@ogvagrearg.pbz to rec.puzzles on Sat Jan 24 21:48:27 2026
    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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  • From richard@richard@cogsci.ed.ac.uk (Richard Tobin) to rec.puzzles on Sat Jan 24 23:25:41 2026
    From Newsgroup: rec.puzzles

    In article <10l3enb$14q4r$1@dont-email.me>,
    David Entwistle <qnivq.ragjvfgyr@ogvagrearg.pbz> wrote:

    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 sizes up to about 30x30 the solution can be found reasonably
    quickly with a brute-force program that tries successively smaller
    squares at the first free position and recurses.

    See also https://oeis.org/A005670

    That is a slightly different problem, in which the sides of the
    squares must have GCD 1.

    For the problem as stated, see https://oeis.org/A018835

    -- Richard
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  • From David Entwistle@qnivq.ragjvfgyr@ogvagrearg.pbz to rec.puzzles on Sun Jan 25 09:25:56 2026
    From Newsgroup: rec.puzzles

    On Sat, 24 Jan 2026 23:25:41 -0000 (UTC), Richard Tobin wrote:

    That is a slightly different problem, in which the sides of the squares
    must have GCD 1.

    For the problem as stated, see https://oeis.org/A018835

    Ah, yes. Thanks.
    --
    David Entwistle
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