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A lantern and $2n$ batteries...

Source: Danube Mathematical Competition 2015,Juniors #5

October 31, 2015
combinatorics

Problem Statement

A lantern needs exactly 22 charged batteries in order to work.We have available nn charged batteries and nn uncharged batteries,n4n\ge 4(all batteries look the same). A try consists in introducing two batteries in the lantern and verifying if the lantern works.Prove that we can find a pair of charged batteries in at most n+2n+2 tries.