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@Calgary

孩子的两道相类似的数学题, 问我, 我也不知怎么做, 谁能给解一下? 谢谢.

dvd(weiwei)
1) The Eskimos greet each other by rubbing their noses together. They greet the arctic researchers by giving them a "high five". The researchers say hello to the Eskimos, just as they greet each other. At a party at the North Pole, while everybody was greeting everybody in the proper way, you could hear 444 hello's and there were 432 "high five's". How many Eskimos and how many researchers were present?

2) The Eskimos greet each other with a nose rub, and they greet the Arctic researchers with a "high five". The researchers say hello to the Eskimos, just as they greet each other. At a party at the North Pole, while everybody greeted everybody in the proper way, you could hear 415 hello's. How many nose rubs and how many high five's happened?
(#5227970@0)
Last Updated: 2009-4-29
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Replies, comments and Discussions:

  • 枫下家园 / 望子成龙 / 孩子的两道相类似的数学题, 问我, 我也不知怎么做, 谁能给解一下? 谢谢. -dvd(weiwei); 2009-4-29 {764} (#5227970@0)
    1) The Eskimos greet each other by rubbing their noses together. They greet the arctic researchers by giving them a "high five". The researchers say hello to the Eskimos, just as they greet each other. At a party at the North Pole, while everybody was greeting everybody in the proper way, you could hear 444 hello's and there were 432 "high five's". How many Eskimos and how many researchers were present?

    2) The Eskimos greet each other with a nose rub, and they greet the Arctic researchers with a "high five". The researchers say hello to the Eskimos, just as they greet each other. At a party at the North Pole, while everybody greeted everybody in the proper way, you could hear 415 hello's. How many nose rubs and how many high five's happened?
    • 我的solution：Eskimos=A, Researchers=B.....1. A*B=432, B*(B-1)+A*B=444, so A=108, B=4;......2. B*(B-1)+A*B=415=5*83 ，83是质数，所以A=79， B=5。nose rubs=79×78， high fives=78×5。。。这是几年级的题？挺好玩的。 -hhorse(hhorse); 2009-4-29 (#5228042@0)
      • 第一题方法对了，就有解；第二题，我没有想到质数，不知道该怎么下手了。这题目出得有水平。 -yysunny(漫漫长路); 2009-4-29 (#5228046@0)
    • 我的答案 -lily97(扁舟子); 2009-4-29 {177} (#5228052@0)
      设Eskimos有x人，The researchers 有y人，则
      1）xy+y(y-1)=444, xy=432,解得：x=108，y=4
      2）xy+y(y-1)=415，解得：x=79，y=5，所以：nose rubs有 x(x-1)/2=3081, high five's 有 xy=395.
      • 我觉得nose rub应该和两人见面握手一样吧，属于组合问题。 -lily97(扁舟子); 2009-4-29 (#5228055@0)
        • I was wondering , how did u solve Y * (Y+X-1)=415 ? -bugatlarge(hy); 2009-4-29 (#5228543@0)
          • 上面那位有过程了：xy+y(y-1)=y(x+y-1)=415,而415只能分解成两个质数5与83的乘积，所以，y=5... -lily97(扁舟子); 2009-4-29 (#5229169@0)
    • 谢谢hhorse和lily97! 你们都比我SAMRT. BTW, 这是GRADE 8 的题. -dvd(weiwei); 2009-4-29 (#5228150@0)
      • 不是smart，而是我做了十几年的数学老师呢，有问题尽管贴上来大家一起研究。 -lily97(扁舟子); 2009-4-29 (#5229178@0)

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