趣味的數學-91【趣味邏輯題】

【有關政客的迷思】

通常認為，100位政客中，每位政客或是說假話的，或是誠實的。我們有以下兩個事實：

-至少有一位政客是誠實的。

-任何兩位政客中，至少有一位是說假話的。

從這兩個事實中確定有多少政客是誠實的，又有多少政客是說假話的？

【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】