Clubbing
A village is full of clubs. Each club is named after one of the villagers. A villager can be a member of any club; they do not need to be a member of the club named after them.
- If a villager is a member of a club, they are either an open member or a secret member.
- If a villager is NOT an open member of the club named after them, they are called suspicious .
- If a villager is a secret member of the club named after them, they would be known as a spy .
It is known that the set of all suspicious villagers forms a club.
Are there any spies in the village?
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1 solution
We are given that the set of all SUSPICIOUS members forms a club. This club must be named after someone. Call that person Jim.
Assume Jim is not a member of the club. Then he is not suspicious. Therefore he must be openly a member of the club. This is impossible.
Therefore, Jim must be a member of the club, but not openly. He is therefore a secret member of his own club, hence a spy.