Question #45f47

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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