MathDB

2m, 2n pairs of people

Source: APMO 2003

March 5, 2006

inductiongraph theorycombinatorics unsolvedcombinatorics

Problem Statement

Given two positive integers

m

and

n

, find the smallest positive integer

k

such that among any

k

people, either there are

2m

of them who form

m

pairs of mutually acquainted people or there are

2n

of them forming

n

pairs of mutually unacquainted people.

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