# Amusements in Mathematics

any irregularity whatever in the design of the material. There is only one way of doing it.
Can you find it?
171.—THE BANNER PUZZLE.
A Lady had a square piece of bunting with two lions on it, of which the illustration is an
exactly reproduced reduction. She wished to cut the stuff into pieces that would fit
together and form two square banners with a lion on each banner. She discovered that this
could be done in as few as four pieces. How did she manage it? Of course, to cut the
British Lion would be an unpardonable offence, so you must be careful that no cut passes
through any portion of either of them. Ladies are informed that no allowance whatever
has to be made for "turnings," and no part of the material may be wasted. It is quite a
simple little dissection puzzle if rightly attacked. Remember that the banners have to be
perfect squares, though they need not be both of the same size.
172.—MRS. SMILEY'S CHRISTMAS PRESENT.
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.
173.—MRS. PERKINS'S QUILT.
It will be seen that in this case the square patchwork quilt is built up of 169 pieces. The
puzzle is to find the smallest possible number of square portions of which the quilt could
be composed and show how they might be joined together. Or, to put it the reverse way,
divide the quilt into as few square portions as possible by merely cutting the stitches.