IMO 1969 LL YUG69

Origin: YUG

Problem

Suppose that positive real numbers x1, x2, x3 satisfy x1x2x3 > 1, x1 + x2 + x3 < 1 x1

• 1 x2
• 1 x3 . Prove that: (a) None of x1, x2, x3 equals 1. (b) Exactly one of these numbers is less than 1.