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Let x, y and z be even numbers. This means that (x + 1), (y + 1) and (z + 1) are all odd. Adding these three odd numbers gives (x + y + z + 3). Because the sum of any number of evens must be even as well - which can be easily proven with idea that where a = 2m and b = 2n, a + b = 2m + 2n = 2(m + n), and is even - adding 3 changes it to an odd number. This holds for any set of three odd numbers.

i agree with this... but what about in the form of 2n+1?

Q: Why is the sum of three odd numbers odd?

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The sum of three odd numbers will be odd, whether they are prime or not. The sum of three prime numbers can be even as long as one of them is 2.

There are no such numbers. The sum of any three odd numbers must be odd. 112 is not.

Because the sum of two odd numbers is always even and the sum of that even number plus another odd number is always odd.

That isn't possible. The sum of three odd numbers will always be odd. You can make the sum of 3 prime numbers equal to 32 if one of them is 2 (which is not odd).

The first three odd numbers are 1, 3, and 5. Their sum is 1 + 3 + 5 = 9.

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No, the sum of three odd numbers will always be odd.

The sum of two odd numbers is always even; the sum of three odd numbers is always odd; the sum of four odd numbers is always even; the sum of five odd numbers is always odd; etc

The sum of three odd numbers will be odd, whether they are prime or not. The sum of three prime numbers can be even as long as one of them is 2.

The sum or product of three odd numbers will always be odd.

I guess you want three odd numbers that, when added, give a sum of 30. That is not possible: if you add three odd numbers, the sum will always be odd.

There are no such numbers. The sum of any three odd numbers must be odd. 112 is not.

Another odd number.

Because the sum of two odd numbers is always even and the sum of that even number plus another odd number is always odd.

That isn't possible. The sum of three odd numbers will always be odd. You can make the sum of 3 prime numbers equal to 32 if one of them is 2 (which is not odd).

The first three odd numbers are 1, 3, and 5. Their sum is 1 + 3 + 5 = 9.

The sum of three whole odd numbers will always be odd keeping in mind that zero is neither even nor odd and that 'null' is not a number.

The sum of two odd numbers is even and the sum of an even number and an odd number is odd.So the sum of three consecutive odd numbers is odd but 270 is even.Ergo there are no three consecutive odd numbers that sum to 270.Three consecutive numbers that sum to 270 are 89, 90, 91.Three consecutive even numbers that sum to 270 are 88, 90, 92.