How does odd and even output work in this code?

Question

int n = new Scanner(System.in).nextInt();

System.out.printf(new String[]{"even","odd"}[n-n/2*2]);

Answer 1

Well it indexes the array {"even", "odd"} using a formula that evaluates to 0 if even, and 1 if odd.
Let's see what is happening here, the formula happens to be n-n/2*2, but wait! Couldn't I simplify that to 0? The answer is no because n is an int, so n/2 is an integer division. An integer division results in the quotient of that division:
eg: 5/2=2 (even though it wouldve been 2.5 if it was a floating point division)
if n is an even number, the result of the integer division wouldve been the same as the floating point division (no remainder), but if n is an odd number, the 0.5 from the result is "lost". Now there is a way to tell the difference between an even an odd number!
When we multiply this result by 2 n/2*2, if n is an even number then n/2*2==n, but if n is an odd number then n/2*2==n-1.
We can rearrange it so that 0 or 1 is on one side: n-n/2*2==0 and n-n/2*2==1. Notice the n-n/2*2 repeated? This is the formula we need to get 0 or 1 to index the array we made based on whether n is even or odd.

Answer 2

A simpler way is to index the array using by getting the remainder of that division, which is essentially what n-n/2*2 does: n%2.