Answer
There are 2n+1 numbers from 0 to 2n. Of these, n+1 are even and n are odd.
Getting at least one that is odd
If we choose n+2 integers, at least one is odd.
Getting at least one that is even
If we choose n+1 integers, at least one is even.
Work Step by Step
Since we count from 0 to 2n, total is 2n+1.
Now, if we count from 1 to 2n, then there are n odd numbers and n even numbers.
But since we start counting from 0.
Number of odds = n
Number of evens= n+1
Getting at least one that is odd.
To get at least one odd, we need to pick n+2 integers. This is because, in worst case, the first n+1 numbers may be even.
Getting at least one that is even.
To get at least one even, we need to pick n+1 integers. This is because, in worst case, the first n numbers may be odd.
