"Of shreds and patches."—Hamlet, iii. 4.
The above represents a square of brocade. A lady wishes to cut it in four
pieces so that two pieces will form one perfectly square cushion top, and the
remaining two pieces another square cushion top. How is she to do it? Of course,
she can only cut along the lines that divide the twenty-five squares, and the
pattern must "match" properly without any irregularity whatever in the design of
the material. There is only one way of doing it. Can you find it?
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.
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.
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.
SQUARES OF BROCADE.
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."
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
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 12x12 and the other 5x5. She
proposes to join them together and make one square patchwork quilt, 13x13, but,
of course, she will not cut any of the material—merely cut the stitches where
necessary and join together again. What perplexes her is this. A friend assures
her that there need be no more than four pieces in all to join up for the new
quilt. Could you show her how this little needlework puzzle is to be solved in
so few pieces?
The diagram herewith represents two separate pieces of linoleum. The
chequered pattern is not repeated at the back, so that the pieces cannot be
turned over. The puzzle is to cut the two squares into four pieces so that they
shall fit together and form one perfect square 10×10, so that the pattern shall
and so that the larger piece shall have as small a portion as possible cut from
Can you cut this piece of linoleum into four pieces that will fit together
and form a perfect square? Of course the cuts may only be made along the