Several irrational numbers are written on a blackboard
Source: Tuymaada 2008, Senior League, First Day, Problem 1.
July 20, 2008
combinatorics unsolvedcombinatorics
Problem Statement
Several irrational numbers are written on a blackboard. It is known that for every two numbers and on the blackboard, at least one of the numbers a\over b\plus{}1 and b\over a\plus{}1 is rational. What maximum number of irrational numbers can be on the blackboard?
Author: Alexander Golovanov