There are 40 ways to make sums of three distinct positive integers total 25. (1+2+22 is such a sum, but 1+12+12 and 1+2+3+19 are not.)

How many different ways can three distinct positive integers sum to 1000?

(In reply to re: My solution by John)

We seem to be the only ones who didn't use a computer to get our answers. Oskar gets the prize for best formula, though. From Oskar's formula we see that 82834=166x499 so that 82834 is the product of just the three primes 2, 83, and 499 -- how's that for a trivial fact? 

Posted by Richard on 2004-07-24 14:54:36