Question

billy is thinking of three numbers from 1 through 9 with a sum of 17. each number is used only once. What are the numbers?

Answer 1

This is very interesting.

Billy could be thinking of

1,  7, and  9
2,  6, and  9
2,  7, and  8
3,  5, and  9
3,  6, and  8
4,  5, and  8
or
4,  6, and  7

but no other set of three numbers.