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Different Sums (Posted on 2004-07-22) Difficulty: 3 of 5
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?

See The Solution Submitted by Brian Smith    
Rating: 3.2500 (4 votes)

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Solution With a little help from awk | Comment 1 of 17
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
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