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?

83834, produced in half a second by the following awk program:

BEGIN {


  total = 0;


  for (A=0; A<=1000; A++)


  { for (B=A; B<=1000; B++)


    {


  	C = 1000-A-B;


	if (C>=B) total++


    }


  }


  print total


}

Posted by Federico Kereki on 2004-07-22 10:00:34