31st British Mathematical Olympiad 1995 Problems

31st British Mathematical Olympiad 1995 Problems1.  Find all positive integers a ≥ b ≥ c such that (1 + 1/a)(1 + 1/b)(1 + 1/c) = 2. 2.  ABC is a triangle. D, E, F are the midpoints of BC, CA, AB. Show that ∠DAC = ∠ABE iff ∠AFC = ∠ADB.