Question #45f47

Question

2290 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-02-28T12:00:48

It is impossible. See explanation.

The formal proof could look like:

Let the odd numbers be:

$n_1=2k_1+1$ ,
$n_2=2k_2+1$ ,
$n_3=2k_3+1$ ,
$n_4=2k_4+1$ , and
$n_5=2k_5+1$ ,

The sum would be:

$S=2*(k_1+k_2+k_3+k_4+k_5)+5=$

$2*(k_1+k_2+k_3+k_4+k_5+2)+1$

The las experssion is an even number plus 1, so it is an odd number.

Informally you could say that:

The sum of an even number of odd numbers is always even, but the sum of odd number of odd numbers is always odd