[Illustration: Diagram 1]
So far as I have been able to discover, there is only one possible
solution to fulfil the conditions. The pieces fit together as in Diagram
1, Diagrams 2 and 3 showing how the two original squares are to be cut.
It will be seen that the pieces A and C have each twenty chequers, and
are therefore of equal area. Diagram 4 (built up with the dissected
square No. 5) solves the puzzle, except for the small condition
contained in the words, "I cut the _two_ squares in the manner desired."
In this case the smaller square is preserved intact. Still I give it as
an illustration of a feature of the puzzle. It is impossible in a
problem of this kind to give a _quarter-turn_ to any of the pieces if
the pattern is to properly match, but (as in the case of F, in Diagram
4) we may give a symmetrical piece a _half-turn_--that is, turn it
upside down. Whether or not a piece may be given a quarter-turn, a
half-turn, or no turn at all in these chequered problems, depends on the
character of the design, on the material employed, and also on the form
of the piece itself.
[Illustration: Diagram 2]
[Illustration: Diagram 3]
[Illustration: Diagram 4]
[Illustration: Diagram 5]