Question

Prove that among any six people, there are always three mutural acquaintances or three mutural strangers. If among five people, can we still have such a conclusion?

Answer 1

Answer Consider any 6 Peoptc vep serled b in a cîrcle. tet evey clot be Connectael to every olher lot by a line erther blu ie(f they known each olhen on a real lfne (f they are stranger) Choose any of the cdot, say alot x we can au that x s Connected to5 dloti by a line. By prgon hole Prindipe 3 of those lines are the Same Co lor say red fthe Proos ana logous we ehoose blue stead of red other ouo, enamine the 3 do Connected to x Tt anj hese 3 Peopie are Connec ted by a red ine then we have founo a rfang te hich epvesenti 3 people who know each other the 3 People are not onnected by any Ted ines,then atl 3 of these are Connected by blue ines forming a blue triangle ohich represents 3 Peopl not Knowing cach othe

Thu the ven stattment s true The region hole Principle appifes because every Petson ts related to every other Person in tioo waYs Incase of 5 People Consider, black alottco line to represent tha they are strangers and blue line represen1 that they knoo each other