DK-GEORGMOHR 2011 Problem 1

Georg writes the numbers from $1$ to $15$ on different pieces of paper. He attempts to sort these pieces of paper into two stacks so that none of the stacks contains two numbers whose sum is a square number.Prove that this is impossible. (The square numbers are the numbers $0 = 0^2$ , $1 = 1^2$ , $4 = 2^2$ , $9 = 3^2$ etc.)