# The Pierrot Puzzle

### Question on Special Products

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 you shall give all the cases possible. Can you find them all?

Remember 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.

Leave your answers below as comments.

I have found following multiplication which match your requirements.

41 x 35 = 1435

21 x 87 = 1287

81 x 27 = 2187

I am searching for more.

Well, is there any way how you could figure this out?

Or is it by trial and error?

Well, is there any way how you could figure this out?

Or is it by trial and error?