How is the sum of three odd numbers always odd?

Answer 1

Algebraically, this can be seen:

An odd number is one more than an even number, and all multiples of 2 are even numbers.

Let three odd numbers be (2n + 1), (2m + 1) & (2k + 1) for some n, m & k.

Adding them gives:

(2n + 1) + (2m + 1) + (2k + 1) = 2n + 2m + 2k + 1 + 1 + 1

= 2n + 2m + 2k + 2 + 1

= 2(n + m + k + 1) + 1

which is one more than an even number - an odd number.