## Tuesday, April 20, 2010

### Usually Two People

On your travels, three men stand at a fork in the road. You're not sure which fork you need to take, but each of the three men do. One of these people tells the truth, one always lies, and the third tells the truth sometimes and lies the other times. Each of the three men know each of the others, but you don't know who is who. If you could ask only one of the men (chosen at random, since you don't know which man is which) one yes/no question, what question would you ask to determine the road you wish to take?

1. Welcome back, and with a tough one - if it was just two men (one always lies, the other never does) and you could ask anything, you would ask either man "If I ask the other man which road to take, what will he tell me?" and then take the other road.

This is much harder. You'll need to ask one man "If I ask him (indicate any other) 'is that (indicate a road) the right road', will he say yes?"

But I worked this through and it doesn't quite work for all the combos. Back to the drawing board.

2. Could you ask, "would the other 2 agree that this (indicating a road) id the right road?"

3. As with the two person (liar and truth teller) version, it's all about the question asked.

Pick one of the men and ask, "If I were to ask you whether the left fork leads to where I'm going, and you chose to answer that question with the same degree of truth as you answer this question, would you then answer 'yes'?"

The truthteller will say "yes" if the left fork leads to where you're going and "no" otherwise. The liar will answer the same, since he will lie about where the left fork leads, and he will lie about lying. The third man may either lie or tell the truth about this one question, but either way he is behaving like either the truthteller or the liar and thus must correctly report the road to your destination.

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