CMO 1987

Find all solutions of $a^2 + b^2 = n!$ for positive integers $a$ , $b$ , $n$ with $a \le b$ and $n < 14$ .

On a large, flat field $n$ people are positioned so that for each person the distances to all the other people are different. Each person holds a water pistol and at a given signal fires and hits the person who is closest. When $n$ is odd show that there is at least one person left dry. Is this always true when $n$ is even?