mathschallenge.net

Problem

There are exactly three different pairs of positive integers that add to make six.

1 + 5 = 6
2 + 4 = 6
3 + 3 = 6

How many different pairs of positive integers add to make one-thousand?

Solution

By writing the sums as: 1 + 999, 2 + 998, 3 + 997, ... , 499 + 501, 500 + 500. It is clear that the number of different pairs is five hundred.

How many different triplets of positive integers add to make one-thousand?