I do not understand the significance of the word "riddle" in the question, but related to math, non-integers are neither odd nor even. For example, 1.5 and pi are neither even nor odd.
0 is an even number. See "Parity of Zero" in the Related Links for a discussion of why many people mistakenly believe 0 is not even.
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No. In fact, you NEVER get an odd number.
Odd. Even + Even = Even Odd + Odd = Even Odd + Even = Even + Odd = Odd
odd * odd = odd answer even * even = even answer odd * even = even answer
Yes. Even + Even = Even, Odd + Odd = Even and Even + Odd or Odd + Even = Odd
even times even = even odd times odd = odd even times odd = even