Use all the digits 1 to 9 create three 3-digit numbers, which, when multiplied together creates the highest value possible.

(In reply to How to do! by Juggler)

I agree that the product of n positive numbers whose sum is fixed is maximized when the numbers are equal.  That can be shown by elementary calculus. 

However, the condition of this problem is not equivalent to the condition of a fixed sum.  So while the intuition is good, I believe a computer verification is necessary to prove optimality.

Posted by David Shin on 2004-09-18 13:56:45