39th Polish Mathematical Olympiad Problems 1988

39th Polish Mathematical Olympiad Problems 1988A1.  The real numbers x1, x2, ... , xn belong to the interval (0,1) and satisfy x1 + x2 + ... + xn = m + r, where m is an integer and r ∈ [0,1). Show that x12 + x22 + ... + xn2 ≤ m + r2.