h*****0
发帖数: 4889 | 1 发信人: GGGGDDDDK (原价万倍出售残奥会各场门票,残疾人打九折), 信区: IQDoor
标 题: 称球问题
发信站: 水木社区 (Tue Aug 26 09:46:11 2008), 站内
有6个球，三个各重a克，另外三个各重b克，b>a，但不知道具体各是多少
用天平称三次，确定哪三个是重球，哪三个是轻球。
每次两边放相同个数的球，每次称量怎么选球无视前面称量的结果。 | p*****k
发帖数: 318 | 2 it would be a much simpler problem without the last constraint:P
i can prove that every time you have to put two balls on each side, but
simple-minded construction seems not working. does such a solution exist? | p*****k
发帖数: 318 | 3 first, hero080, could you confirm whether the solution exists or not?
WARNING: for completeness, i spent some time writing down the proof, but it'
s pretty messy, so most of you might want to skip the details.
here is a sketch:
there are 3 outcomes for each weighing:
left side heavier (L), balanced (E), right side heavier (R)
so total of 3*3*3=27 outcomes.
note there are only C(6,3)=20 ways of picking 3 balls out of 6.
let's label the balls from 1 to 6. if there exists a way to fulfill the
req
【在 p*****k 的大作中提到】
: it would be a much simpler problem without the last constraint:P
: i can prove that every time you have to put two balls on each side, but
: simple-minded construction seems not working. does such a solution exist?
| h*****0
发帖数: 4889 | 4 the question should be: "if not exist, prove it".
Actually personally I believe that it doesn't exist.
I don't have time to view your answer now. I'll check it tomorrow.
it'
【在 p*****k 的大作中提到】
: first, hero080, could you confirm whether the solution exists or not?
:
: WARNING: for completeness, i spent some time writing down the proof, but it'
: s pretty messy, so most of you might want to skip the details.
: here is a sketch:
: there are 3 outcomes for each weighing:
: left side heavier (L), balanced (E), right side heavier (R)
: so total of 3*3*3=27 outcomes.
: note there are only C(6,3)=20 ways of picking 3 balls out of 6.
: let's label the balls from 1 to 6. if there exists a way to fulfill the
| p*****k
发帖数: 318 | 5 i c. good to know that we are on the same boat.
unfortunately, so far all i have been doing is just exhausting all the
possibilities... |
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