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标题: 在六张纸片的正面分别写上 1， 2， 3， 4， 5， 6 [打印本页]

作者: 野菜花 时间: 2005-3-11 22:01
标题: 在六张纸片的正面分别写上 1， 2， 3， 4， 5， 6

，在它们的反面也随意地写上这六个数，然后计算每张纸片两面数字之差的绝对值。证明这六个绝对值中至少有两个是相同的。

作者: fzy 时间: 2005-3-11 22:05
标题: 回复：在六张纸片的正面分别写上 1， 2， 3， 4， 5， 6

Because the range is 1 to 5.

作者: 野菜花 时间: 2005-3-11 22:08
标题: 回复：回复：在六张纸片的正面分别写上 1， 2， 3， 4， 5， 6

Not that easy, range is 0-5,

作者: fzy 时间: 2005-3-11 22:17
标题: Sorry, too quick

Have to go to a meeting. Will come back

作者: yma16 时间: 2005-3-11 22:23
标题: 回复：回复：回复：在六张纸片的正面分别写上 1， 2， 3， 4， 5， 6

When each paper has different two numbers, the number of differences we got from the 6 papers is 5. There are 6 papers. applying PHP, we got the answer. If there is a paper with the same 2 numbers. The difference is 0. For the rest 5 papers with 5 numbers, we use this argument: When each paper has different two numbers, the number of differences we got from the 5 papers is 4. There are 5 papers. applying PHP. If there is a paper with the same 2 numbers, The difference is 0. Then we have 2 0s.

作者: fzy 时间: 2005-3-11 22:23
标题: 回复：Sorry, too quick

If no equal, then they are 0,1,2,3,4,5. But before applying absolute value, they add up to 0. For these 6 numbers, they now add up to 15, an odd number. So you cannot assign + and - to make the sum 0.

Really have to go now.

作者: 野菜花 时间: 2005-3-11 22:44
标题: Great! [@};-]

Great!

作者: 野菜花 时间: 2005-3-11 22:53
标题: 妙！ [@};-]

如果这些绝对值是 0， 1， 2， 3， 4， 5

Sum |a-a'|=15

而 Sum (a-a')=0

(a-a') 和 |a-a'| 的奇偶性相同，矛盾。

(我重新写一下是怕有人没搞懂。 )

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