odd
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Odd + even = odd
If you're adding an odd number of numbers, if two are even and one is odd, you will get an odd number as a result. Three odds are odd. If two are odd and one is even, you have an even result. Three evens are even.
The sum of one odd number and one even number is another odd number.
odd
Any pair of one even and one odd number will have an even product and an odd sum.