趣味的数学-91【趣味逻辑题】

【有关政客的迷思】

通常认为，100位政客中，每位政客或是说假话的，或是诚实的。我们有以下两个事实：

-至少有一位政客是诚实的。

-任何两位政客中，至少有一位是说假话的。

从这两个事实中确定有多少政客是诚实的，又有多少政客是说假话的？

【原文】

The Politician Puzzle

A certain convention numbered 100 politicians. Each politician was either crooked or honest. We are given the following two facts:

--At least one of the politicians was honest.

--Given any two of the politicians, at least one of the two was crooked.

Can it be determined from these two facts how many of the politicians were honest and how many of them were crooked?

【引自Raymond M. Smullyan的著作】