Re: [中學] 100板橋高中教師甄選試題

[JohnMash (Paul)]

※ 引述《RainIced (我好想念快速的宿網)》之銘言：
: 2.n > 4、n為正整數，S = {5、6、7、.....、n}，將S分成
:   兩個部份，至少有一個部份內有a、b、c，使得ab=c，其中
:   a、b、c不需相異。求n 的最小值。

    The answer is n=3125

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    when n=3125

    S1∪S2=S, S1∩S2= { }

    We just point out the elements 5,25,125,625,3125.

    The other elements are neglected.

    (i) S1={5}, S2={25,125,625}, done

    (ii) S1={5,25}, done

    (iii) S1={5,125}, S2={25,625},done

    (iv) S1={5,125,625}, done

    (v) S1={5,625,3125}, done

    (vi) S1={5,625}, S={25,125,3125}, done

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     when n=3124

     S1={5,6,...,24}

     S2={25,26,...,624}

     S3={625,626,...,3124}

     if a,b in S1, then ab NOT in S1∪S3

     if a,b in S2, then ab NOT in S2

     if a,b in S3, then ab NOT in S1∪S3

     if a in S1, b in S3,then ab NOT in S1∪S3

     Then we can divides S into two parts S1∪S3 and S2.

     Neither S1∪S3 nor S2 satisfy the required property.

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※ 編輯: JohnMash        來自: 112.104.171.228      (06/04 00:55)
推 RainIced    :感謝。
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→ RainIced    :分成這三個部份好神奇。