## Sum Of Three

#### Problem

Three different positive integers add to make sixteen. The two smallest numbers add to make the biggest number. How many different solutions can you find?

#### Solution

Let the integers be `a`, `b` and `c` such that `a` `b` `c`.

Therefore `a` + `b` + `c` = 16.

But `a` + `b` = `c`, so `c` + `c` = 2`c` = 16, hence `c` = 8.

So solutions are: (1,7,8), (2,6,8) and (3,5,8)

Problem ID: 25 (Dec 2000) Difficulty: 1 Star