# Solution

(related to Problem: Mrs. Hobson's Hearthrug)

As I gave full measurements of the mutilated rug, it was quite an easy matter to find the precise dimensions of the square. The two pieces cut off would, if placed together, make an oblong piece $12\times6,$ giving an area of $72$ (inches or yards, as we please), and as the original complete rug measured $36\times27,$ 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 $30\times30$ 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.

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### References

#### Project Gutenberg

1. Dudeney, H. E.: "Amusements in Mathematics", The Authors' Club, 1917

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