Putnam 1976 
Topic: Algebra

Problem: \[ \sum_{k=1}^n (-1)^k \binom{n}{k} (x-k)^n. \]

Solution: The sum is \( n! \) since it is an \( n \)-th difference of a monic polynomial, \( x^n \), of degree \( n \) The final answer is \boxed{n!}.