Let n be an odd integer and let f be an [n]-permutation of length n, where [n] is the set of integers 1, 2, 3,...n
Show that the number
x = (1-f(1))*(2-f(2))*...*(n-f(n))
is even using the pigeonhole principle
In this case, I don't understand what this function f is. What is an [n]-permutation of length n? Take f(2) for example. Permutations of  would be 1,2 and 2,1. So the way the problem is worded, f(2) must equal 12 or 21. If that's correct, which one? Will this number x still be even regardless of which [n]-permutation f(n) is?