MathDB

Powerful sets: a, b in S, then a^b or b^a in S

Source: Iran National Olympiad - 2014 Second Round - D2P2

May 3, 2014

combinatorics unsolvedcombinatorics

Problem Statement

A subset

S

of positive real numbers is called powerful if for any two distinct elements

a, b

S

, at least one of

a^{b}

b^{a}

is also an element of

S

. a) Give an example of a four elements powerful set. b) Prove that every finite powerful set has at most four elements.