mekh{mat entrance examinations problemsnew

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1、EH-ATETRACEEXA
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lanVardiThere entarti leofAnatolyVershikandAlexanderShen[21℄[19℄des ribes

2、dis riminationagainstewsinSovietuniversitiesduringthe1970'sand1980's.Thearti le ontainsareportbyAlexanderShenonthespe i roleofexaminationsindis riminationagainstewishappli antstotheekh{matatos owStateUniversityduringthe1970'sand1980's.Thearti legoesontolistk

3、illerproblems"thatweregiventoewish andidates.However,solutionstotheproblemswerenotgiveninthearti le,soinordertojudgetheirdiÆ ulty,onemusttrytheproblemsforoneself.Theaimofthisnoteistorelievereadersofthistime onsumingtaskbyprovidingafullsetofsolutionstotheproblems.

4、Hopefully,thiswillhelpreadersgainsomeinsightintotheethi alquestionsinvolved.Se tion2 onsistsofapersonalevaluationoftheproblemsinthestyleofareferee'sreport.
twaswrittentoprovideatemplateforreaderstomakeasimilarevaluationoftheproblems.Thisevaluationalsore e tstheaut

5、hor'sownmathemati alstrengthsandweaknessesaswellashisapproa htoproblemsolving.Readersarethereforeen ouragedtomakeuptheirownminds.Theproblemsaregivenexa tlyasin[19℄withthenamesoftheexaminersandtheyear(A.Shenhasexplainedthatinhisarti le,thenameoftheexaminersandyeari

6、sgivenbyasetofproblemsendingwiththename).Someina ura iesof[19℄bothinthestatementoftheproblemsandattributionofexaminershavehavebeen orre ted,seeSe tion4.Someofthestatementsareneverthelessin orre t.Theseerrorsareare e tionofeithertheexaminationsthemselves,thereport

7、givenbythestudents,orthearti leof[19℄.
nany ase,thisisfurthereviden efortheneedofa ompletesolutionset.ThesesolutionswereworkedoutduringasixweekperiodinulyandAugust1999.
nordertoretainsomeaspe tofanexamination,nosour eswere onsulted.Asaresult,thesolutionsre e tgap

8、sintheauthor'sba kground.However,thismightoersomeinsightintohowone andealwithawiderangeofelementaryproblemswithoutthehelpofoutsidereferen es.Aneortwas