[Illustration]
The Pierrot in the illustration is standing in a posture that represents
the sign of multiplication. He is indicating the peculiar fact that 15
multiplied by 93 produces exactly the same figures (1,395), differently
arranged. The puzzle is to take any four digits you like (all different)
and similarly arrange them so that the number formed on one side of the
Pierrot when multiplied by the number on the other side shall produce
the same figures. There are very few ways of doing it, and I shall give
all the cases possible. Can you find them all? You are allowed to put
two figures on each side of the Pierrot as in the example shown, or to
place a single figure on one side and three figures on the other. If we
only used three digits instead of four, the only possible ways are
these: 3 multiplied by 51 equals 153, and 6 multiplied by 21 equals 126.