THE PIERROT'S PUZZLE

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`.