# How many possible sets of three odd numbers are there whose sum is even?

Jan 15, 2017

None

#### Explanation:

The sum of any three odd numbers will be odd.

Any odd number is expressible in the form $2 k + 1$ for some integer $k$.

So the sum of $3$ odd numbers will take the form:

$\left(2 {k}_{1} + 1\right) + \left(2 {k}_{2} + 1\right) + \left(2 {k}_{3} + 1\right) = 2 \left({k}_{1} + {k}_{2} + {k}_{3} + 1\right) + 1$