The sums of what four odd integers is nineteen?

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Matthew Fonda | eNotes Employee

Posted on

There are no four odd integers with a sum of 19. This is because the sum of four odd numbers is always going to be even. Using the  following rules, we can see why this is true:

1. The sum of two odd numbers is always even.
2. The sum of two even numbers is always even.

odd + odd + odd + odd
= (odd + odd) + (odd + odd)
= even + even    (by rule 1)
= even                 (by rule 2)

Therefore, there are no four odd integers with a sum of 19, since 19 is odd but the sum of four odd integers is even.

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mchandrea | Student, College Junior | (Level 1) Salutatorian

Posted on

The sum of four odd integers could never be odd. Therefore, there is no answer to your question. If you add two odd numbers, the answer would always be even. If you add two even numbers, the answer would still be even. 

For example. 

3 + 5 = 8                                    Odd + Odd = Even

2 + 4 = 6                                    Even + Even = Even

Let's try adding four odd numbers.

3 + 5 + 7 + 9 = 24          Odd + Odd + Odd + Odd = Even

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user9604503 | eNotes Newbie

Posted on

1. The sum of 2 odd integers is even.

2. The sum of 2 even integers is even.

It is impossible to get 19 with 4 odd integers.

(Odd Integer+Odd Integer)+(Odd Integer+Odd Integer)

=Even+Even

=Even

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parama9000 | Student, Grade 11 | (Level 1) Valedictorian

Posted on

This is not possible.

Odd no. +Odd no.= Even no.

Even no. + Odd no.= Odd no.

Odd no. + Odd no. = Even no.

So, this is sadly impossible...

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acompanioninthetardis | Student, Undergraduate | (Level 1) Valedictorian

Posted on

There would not be one because there are 4 odd numbers being added together that would always equal to an even number. So there is no way to get 19. 

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