PigeonholePrinciple(鴿巢原理)HKSKHBishopHallSecondarySchool18Feb2008PigeonholePrinciple(鴿巢原理)Dirichlet(狄里克利)Dirichlet(狄里克利)ContinuePigeonholePrinciple(鴿巢原理)Proof(證明)ExamplesExerciseMarkSix(六合彩)ThefollowingissometendrawsoftheMarkSixLotteryinreverseorder.SomethingtoThinkAboutASolutionPigeonholePrinciple:StrongForm(鴿巢原理:加強版)Proof(證明)ExerciseSolutionSIMHowtoPlaySIM(遊戲規則)?GustavusJ.SimmonsGameinProgress(殘局)AQuestionYouShouldAsk(必問題)Proof(證明)ContinueAnExampleContinueRemark1:ExtensionoftheProofATriangleADrawisPossibleASquareADrawisPossible!APentagonADrawisPossible!Remark2:WinningStrategyRemark3:ExtensionoftheGameProof(證明)AnExampleGeneralization?FurtherGeneralization?M.Gardner,MathematicalGames,ScientificAmerican,February(1973),pp.108-112E.Mead,ARose,C,Huang,TheGameofSIM:AWinningStrategyfortheSecondPlayer,MathematicalReportNo.58,1973,McMasterUniversity.L.E.Shader,AnotherStrategyforSIM,MathematicsMagazine,Vol.51.No.1,pp.60-62,1978.G.J.Simmons,TheGameofSIM,JournalofRecreationalMathematics,1969.SomeMathematicalGamesareAvailableathttp://hkumath.hku.hk/~wkc/MathModel/index.php