THE SQUARES OF BROCADE.
(
Patchwork Puzzles)
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 conditions?
175--ANOTHER PATCHWORK PUZZLE.
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 and the
other 5 x 5. She proposes to join them together and make one square
patchwork quilt, 13 x 13, 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?
Answer:
[Illustration: Diagram 1]
So far as I have been able to discover, there is only one possible
solution to fulfil the conditions. The pieces fit together as in Diagram
1, Diagrams 2 and 3 showing how the two original squares are to be cut.
It will be seen that the pieces A and C have each twenty chequers, and
are therefore of equal area. Diagram 4 (built up with the dissected
square No. 5) solves the puzzle, except for the small condition
contained in the words, "I cut the _two_ squares in the manner desired."
In this case the smaller square is preserved intact. Still I give it as
an illustration of a feature of the puzzle. It is impossible in a
problem of this kind to give a _quarter-turn_ to any of the pieces if
the pattern is to properly match, but (as in the case of F, in Diagram
4) we may give a symmetrical piece a _half-turn_--that is, turn it
upside down. Whether or not a piece may be given a quarter-turn, a
half-turn, or no turn at all in these chequered problems, depends on the
character of the design, on the material employed, and also on the form
of the piece itself.
[Illustration: Diagram 2]
[Illustration: Diagram 3]
[Illustration: Diagram 4]
[Illustration: Diagram 5]
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