MRS. HOBSON'S HEARTHRUG.
(
Various Dissection Puzzles)
Mrs. Hobson's boy had an accident when playing with the fire, and burnt
two of the corners of a pretty hearthrug. The damaged corners have been
cut away, and it now has the appearance and proportions shown in my
diagram. How is Mrs. Hobson to cut the rug into the fewest possible
pieces that will fit together and form a perfectly square rug? It will
be seen that the rug is in the proportions 36 x 27 (it does not matter
whether we say inches or yards), and each piece cut away measured 12 and
6 on the outside.
Answer:
As I gave full measurements of the mutilated rug, it was quite an easy
matter to find the precise dimensions for the square. The two pieces cut
off would, if placed together, make an oblong piece 12 x 6, giving an
area of 72 (inches or yards, as we please), and as the original complete
rug measured 36 x 27, it had an area of 972. If, therefore, we deduct
the pieces that have been cut away, we find that our new rug will
contain 972 less 72, or 900; and as 900 is the square of 30, we know
that the new rug must measure 30 x 30 to be a perfect square. This is a
great help towards the solution, because we may safely conclude that the
two horizontal sides measuring 30 each may be left intact.
There is a very easy way of solving the puzzle in four pieces, and also
a way in three pieces that can scarcely be called difficult, but the
correct answer is in only two pieces.
It will be seen that if, after the cuts are made, we insert the teeth of
the piece B one tooth lower down, the two portions will fit together and
form a square.
Informational
