25th Canadian Mathematical Olympiad Problems 1993

25th Canadian Mathematical Olympiad Problems 19931.  Show that there is a unique triangle such that (1) the sides and an altitude have lengths with are 4 consecutive integers, and (2) the foot of the altitude is an integral distance from each vertex. 2.  Show that the real number k is rational iff the sequence k, k + 1, k + 2, k + 3, ... contains three (distinct)