Suppose that n+1 integers are chosen from the set {1 , 2, ..., 2n}. Show that at least

one is even. [HINT: Think about how many odd numbers there are in this set]

I was taking a look at this problem.... and think im doing it wrong because the answer seems too obvious.

My reasoning is that for any n in N, one of the numbers will always be even, and prove this by

n(0) n+1 = 1 = 1,2

n(1) n+1 = 2 = 1,2,3

n(2) n+1 = 3 = 1,2,3,4

Cheers