What is the sum of all three digit positive numbers?

Observe that:

100+999 =1099, 101 + 998 = 1099 up to 549+550=1099.

So 1099 * (1000-100/2) or 1099 * 450 (450 pairs of numbers that sum to 1099)

or 494,500.

This is a variant of the method exposed in the "Gauss Anecdote"