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.

[Illustration]

173.--MRS. PERKINS'S QUILT.

[Illustration]

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.

174.--THE SQUARES OF BROCADE.

[Illustration]

I happened to be paying a call at the house of a lady, when I took up
from a table two lovely squares of brocade. They were beautiful
specimens of Eastern workmanship--both of the same design, a delicate
chequered pattern.

"Are they not exquisite?" said my friend. "They were brought to me by a
cousin who has just returned from India. Now, I want you to give me a
little assistance. You see, I have decided to join them together so as
to make one large square cushion-cover. How should I do this so as to
mutilate the material as little as possible? Of course I propose to make
my cuts only along the lines that divide the little chequers."

[Illustration]

I cut the two squares in the manner desired into four pieces that would
fit together and form another larger square, taking care that the
pattern should match properly, and when I had finished I noticed that
two of the pieces were of exactly the same area; that is, each of the
two contained the same number of chequers. Can you show how the cuts
were made in accordance with these conditions?

175--ANOTHER PATCHWORK PUZZLE.

[Illustration]

A lady was presented, by two of her girl friends, with the pretty pieces
of silk patchwork shown in our illustration. It will be seen that both
pieces are made up of squares all of the same size--one 12 x 12