A (normal) magic square, containing 9 distinct positive integers, could be made as follows:

2 9 4

7 5 3

6 1 8

Note all rows/columns/diagonals

*sum* to 15.

Can you find the "smallest" *multiplication* magic square using 9 distinct positive integers where the *product* of all rows/columns/diagonals are equal?

(One *multiplication* magic square is smaller than another if its *magic product* is less than the other's.)

At least I think this is the "smallest"...

2 36 3

9 6 4

12 1 18

All rows, columns, and diagonals multiply to 216.

I did have a little help from the computer but only to find numbers that had at least 8 unique sets of 3 factors. (there's a bunch of them!)

*Edited on ***July 16, 2004, 11:04 am**