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标题: 30 statements (ZT from WXC) [打印本页]

作者: 野菜花 时间: 2005-12-3 06:42
标题: 30 statements (ZT from WXC)

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In a paper there are statements numbered from 1 to 30. Statement n says "exactly n of the statements on this sheet are false." Which statements are true and which are false? What if we replace "exactly" by "at least"?

作者: yma16 时间: 2005-12-3 09:18
标题: 回复：30 statements (ZT from WXC)

What is the range of n? (i.e. is n one fixed number or is n from 1 to 30?)

Thanks.

作者: 大头羊 时间: 2005-12-3 12:08
标题: 回复：30 statements (ZT from WXC)

都是第n-1个对吗？

或者说，at least 的情况，至少有“第n-1个是对的”的情况，其它的情况还没琢磨，先出个门。

作者: 野菜花 时间: 2005-12-4 04:59
标题: from 1 to 30 [:)]

from 1 to 30

作者: 野菜花 时间: 2005-12-4 05:02
标题: 你说的 n-1 是29 吗？

你说的 n-1 是29 吗？

作者: Archi 时间: 2005-12-4 09:11
标题: The key to these kind of problems is

"assume the number of false statements is k"

For "exactly" case:

Only the k'th statement is true. So k=N-1.

For "at least" case:

The statements 1,2,...,k are true; the statements k+1,...,N are not true. So N-k=k, k=N/2. This problem is a valid one only when N is even.

作者: 野菜花 时间: 2005-12-4 20:02
标题: Very good! [@};-][@};-]

Very good!

作者: husonghu 时间: 2005-12-6 04:26
标题: 阿基米德就是厉害哦！[:))][:))][:))][:))]

阿基米德就是厉害哦！

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