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 My solution by John)

"Boo-yah" as they say.  My answer agrees with Richard's analytical solution.  Dude, if you're reading this, we're both right.  Two methods with the same solution.  The answer is 82834.

Posted by John on 2004-07-24 06:17:39