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What’sEuler’spuzzle?Koningsbergisanislandandthereisariverbreakingitintotwoparts.“SevenBridgesofKonigsberg”andthefamous“Eulerpath”.Peoplewonderediftheycouldwalkaroundthecitybycrossingthesevenbridgeswithoutgoingoveranyofthemtwiceorgoingbackonhimself,butEulerfoundhecouldn’tcrossallthesevenones.ThisisEuler’spuzzle.Thefirststageinhisresearchistofindtheproblemthathecouldcrosssixofthebridgeswithoutgoingoveranyofthemtwiceorgoingbackonhimself,buthecouldn’tcrossallseven.HowdidEulerprepareforhisresearch?Thesecondstageistothinkofamethod:Hedrewamapanduseddotsandlinestosimplifyhisanalysis.Tryingandobservingoverandoveragain,hefoundageneralrule.Itistopology.Euler’stheoryiscalled“TheEulerpath”,whichisexpressedlikethis:Ifafigurehasmorethantwooddpoints,youcannotgooveritwithoutliftingyourpencilfromthepageorgoingoveralinetwice.Whatarethetheories?SothegeneralrulethatEulerfoundistheevenpointsandtheoddpoints.Lookatthefollowingpictures:ConclusionEuler’stheory(一笔画)可以一笔画只有两种情况：1.没有奇数顶点。2.只有两个奇数顶点。