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(Patchwork Puzzles)
Mrs. Smiley's expression of pleasure was sincere when her six
granddaughters sent to her, as a Christmas present, a very pretty
patchwork quilt, which they had made with their own hands. It was
constructed of square pieces of silk material, all of one size, and as
they made a large quilt with fourteen of these little squares on each
side, it is obvious that just 196 pieces had been stitched into it. Now,
the six granddaughters each contributed a part of the work in the form
of a perfect square (all six portions being different in size), but in
order to join them up to form the square quilt it was necessary that the
work of one girl should be unpicked into three separate pieces. Can you
show how the joins might have been made? Of course, no portion can be
turned over.


The first step is to find six different square numbers that sum to 196.
For example, 1 + 4 + 25 + 36 + 49 + 81 = 196; 1 + 4 + 9 + 25 + 36 + 121
= 196; 1 + 9 + 16 + 25 + 64 + 81 = 196. The rest calls for individual
judgment and ingenuity, and no definite rules can be given for
procedure. The annexed diagrams will show solutions for the first two
cases stated. Of course the three pieces marked A and those marked B
will fit together and form a square in each case. The assembling of the
parts may be slightly varied, and the reader may be interested in
finding a solution for the third set of squares I have given.

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