As I gave full measurements of the mutilated rug,
it was quite an easy matter to find the precise dimensions for the
The two pieces cut off would, if placed together,
make an oblong piece 12x6, giving an area of 72 (inches or yards, as we
please), and as the original complete rug measured 36x27, 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 30x30 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
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.