Can you add 3 odd numbers and get an even number?

The sum of any three odd numbers equals an odd number.

Explanation:

Proof

Lets consider three odd numbers

$a = 2 x + 1$
$b = 2 y + 1$
$c = 2 z + 1$

where $a , b , c$ are integers and $x , y , z$ integers as well

then the sum equals to

$a + b + c = 2 \cdot \left(x + y + z + 1\right) + 1$

The last tell us that their sum is an odd.

Sep 17, 2015

For example, in arithmetic modulo $7$ we find:
$1 + 3 + 5 = 9 = 2 = 2 \cdot 1$