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上期那个问题的答案你找到了吗?你如果找到了,在你找到的那一刻,你也许会跟2000多年前的阿基米德一样情不自禁地喊出:“我找到啦!” 以下是我们的解决方案。 1[第一次称]首先把8个球从1到8标上号。然后把头6个球放在天平的两边,一边3个。这时会出现以下两种情况之一: 1.1[第一次称后情况-]天平是平的,表明这头6个都是好的。坏球要不是第7个,就是第8个。2[第二次称](1.1后)现在将头6个球中的任何一个放进天平的一个碟子里,再将球7放进另一个碟子里。假如天平是平的,那么球8是坏的。假如天平是倾斜的,那么次品必定是球7。换言之,此时坏球所在的范围已缩小到两个,只须再称一次便能将坏球挑出。我们把这个称法叫做[二挑一]。
Did you find the answer to that question last time? If you find it, at the moment you find it, you may be tempted to say, like Archimedes 2000 years ago: “I found it!” Our solution. 1 [First time] First 8 balls are numbered from 1 to 8. Then place the first 6 balls on both sides of the balance, 3 on the side. At this time, one of the following two situations will occur: 1.1 [the first post-condition] - The balance is flat, indicating that the first six are all good. The bad ball is either the 7th or the 8th. 2 [Second time] (post-1.1) Now place any of the first 6 balls in one of the balance’s plates and place the ball 7 in another dish. If the balance is flat, then the ball 8 is bad. If the balance is inclined, then the defective product must be a ball. In other words, at this time, the scope of the bad ball has been reduced to two, and only one more ball can be called to pick out the bad ball. We call this phrasing one of the two.