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131.(DS)22 students 给他们发pencil 每人至少一支
问
会不会有两个人拿的pencil数是一样的
(1)每人少于22支 (2)总共250支
(1): not sufficient
could have 2 people with same number (ex: 7 pencils)
or everyone has different numbers since there is no limit on the total numbers of pencils
(2): 1+2+.......+21=126
250-126=124; so 22 people each has different numbers of pencils
or 1+2+.........20+20=125
250-125=125
two people have the same number of pencils
so 2 is not right
1+2: consider the first 21 students, if each of them has different numbers of pencils, then the total numbers for them would be 1+.....+21=126, because any number before 22 can be counted once, then the 22th student must have 124 pencils, but it is against condition (1). Then it means that my assumption that each of the 21 students has different numbers of pencils is false.
So the answer is C
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发表于 2009-3-11 13:10:00
