小学教育网 发表于 2016-8-15 10:36:47

四年级奥数题及答案:自然数(高等难度)

  自然数:(高等难度)
       
          互为反序①的两个自然数之积是92565,求这两个互为反序的自然数.
       
          
        更多试题:
       
       
       
       
       

jzsix 发表于 2016-8-15 11:29:51


          自然数答案:
       
          注释:①例如1204与4021是互为反序的自然数,而120与21不是互为反序的数.
       
          解答:①这两个自然数必是三位数.
       
          首先,这两个自然数不能是小于100的数,因为小于100的两个最大的反序数是99和99,而99×99<92565.
       
          其次,这两个自然数也不能大于998,因为大于998的两个最小的反序数是999与999,而999×999>92565.
       
http://www.aoshu.com/e/20110921/data:image/png;base64,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
       
          由于a×c的个位数字是5,可以推得:
       
          a×c=1×5或3×5或5×5或7×5或9×5;
       
          而当a×c≥3×5时有
       
/collect/201608/14/40440.html
          即
       
          这是不合题意的.因此,我们可以断定:
       
          a×c=1×5,
       
          不妨设 a=1, c=5.
       
          又由于b是0,1,2,…,9之一,经检验,只有b=6符合题意,这时有165×561=92565.
       
          答:所求的两个互为反序的自然数是165和561.
       
页: [1]
查看完整版本: 四年级奥数题及答案:自然数(高等难度)