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 × 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.
[Illustration]