Let f:R1→R2 be a continuous function such that f(x)=f(x+1) for all x, and let t∈[0,41]. Prove that there exists x∈R such that the vector from f(x−t) to f(x+t) is perpendicular to the vector from f(x) to f(x+21).(translated by Miklós Maróti) Miklos Schweitzercollege contestsfunctionvectorreal analysis