MathDB

5

Part of 2015 Danube Mathematical Competition

Problems(1)

A lantern and $2n$ batteries...

Source: Danube Mathematical Competition 2015,Juniors #5

10/31/2015
A lantern needs exactly 22 charged batteries in order to work.We have available nn charged batteries and nn uncharged batteries,n≥4n\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.
combinatorics