Consider all 3-digit numbers whose digits add up to exactly 3 (for example 120, 300, 111).
How many such 3-digit numbers are there in all?

The hundreds digit must be 1, 2 or 3 (it cannot be 0). If hundreds = 1, the other two digits sum to 2: 102, 111, 120 (3 numbers). If hundreds = 2, they sum to 1: 201, 210 (2 numbers). If hundreds = 3, they sum to 0: 300 (1 number). Total = 3 + 2 + 1 = 6.