MathDB
Game with n numbers smaller than n-th prime

Source: European Mathematical Cup 2012, Senior Division, Problem 4

July 27, 2013
algebrafunctioncombinatoricslinear algebra

Problem Statement

Olja writes down nn positive integers a1,a2,…,ana_1, a_2, \ldots, a_n smaller than pnp_n where pnp_n denotes the nn-th prime number. Oleg can choose two (not necessarily different) numbers xx and yy and replace one of them with their product xyxy. If there are two equal numbers Oleg wins. Can Oleg guarantee a win?
Proposed by Matko Ljulj.
Back to ProblemsView on AoPS