Question

How many integers between 0 and 4n (inclusive) must you pick in order to be certain

that at least one of them is odd?

Answer 1

2n+1 integers

Explanation:

There are
`(4n)/(2) + 1 = 2n + 1` even integers (0 inclusive) and
`2n` odd integers between 0 and 4n.

Worst case scenerio: pick all
`2n+1` even integer before picking an odd integer.

Therefore, to pick at least one odd integer, one might pick
`2n + 1` even integers + 1 odd integer =
`2n+2` integers.