1. The problem statement, all variables and given/known data Suppose f is continuous on [0,2]and thatn f(0) = f(2). Prove that there exists x,y in [0,2] such that |y-x| = 1 and f(x) = f(y) 2. Relevant equations 3. The attempt at a solution I got the following 1 line proof. Suppose g(x) = f(x + 2) - f(x) on I = [0,2] this proofs that |x - y| = 1 for x = 1, y = 2 and f(x) = f(y) thanks!