(related to Problem: Linoleum Cutting)
There is only one solution that will enable us to retain the larger of the two pieces with as little as possible cut from it. Fig. $1$ in the following diagram shows how the smaller piece is to be cut, and Fig. $2$ how we should dissect the larger piece, while in Fig. $3$ we have the new square $10 \times 10$ formed by the four pieces with all the chequers properly matched. It will be seen that the piece $D$ contains fifty-two chequers, and this is the largest piece that it is possible to preserve under the conditions.
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