Each of the nine letters A through I represents a different digit from 1 through 9, but not necessarily in that order.   ABC, DEF, and GHI are three different three-digit integers. What is the maximum possible product of these three numbers, and what is the minimum possible product? In other words, assign different values to each letter so that ABC x DEF x GHI will be as large as possible, and then make it as small as possible.

Solution to the Problem: The maximum product is 611,721,516 when the letters have the following values: A B C   D E F   G H I   9 4 1 x 8 5 2 x 7 6 3 = 611,721,516 The minimum product is 13,994,694 when the letters have the following values: A B C   D E F   G H I   1 4 7 x 2 5 8 x 3 6 9 = 13,994,694

Correctly solved by: