I stumbled on hmlee's algorithm chart quite by chance. A lot of good questions in there.

Question 53 caught my eye as a mathematician.

Q53: Say you have three integers between 0 - 9. You have the equation: A! + B! + C! = ABC (where ABS is a three digit numbers, not A * B * C). Find A, B, and C that satisfies this equation.

Interesting. But I'd like to modify the question a little.

Q53': Say you have three integers between 0 - 9. You have the equation: A! + B! + C! =

A * B * C.

Find A, B, and C that satisfies this equation.

Astute readers will notice that A, B, and C are interchangeable. Nonetheless there is a unique solution (modulo swapping A, B, and C.)

I'm much less interested in the answer to this question (I know the answer) than I am in the quality of the program used to find the answer. (I tried finding the answer by hunt-and-peck, then gave up and wrote a program - I find the program to be more interesting than the answer.) Try to find the solution as efficiently as possible (without cheating.)

I'll post my program later.

If you see a fact, try to see it as intuitively as possible.

I *suspect* that the following even more general problem has the same unique solution, which would be very interesting indeed. This is the kind of thing where programs fail, and the mathematical mind becomes necessary again:

Q53'': Say you have three integers

that are >= 0. You have the equation: A! + B! + C! = A * B * C.

Find A, B, and C that satisfies this equation.