The Two Guards Riddle is a simple yet fascinating logic puzzle. You are travelling along a road when you arrive at a fork in the road. You know that one path leads to vast riches and the other leads to certain doom, but you do not know which is which. One is guarded by a truth-teller and one by a liar. How do you know which route to take?
Let’s say one path is guarded by Amy, one is guarded by Ben. One of Amy or Ben will always tell the truth and the other one always lies. However you do not know who is which. You can ask one of them one yes/no question to find out which path leads to vast riches.
What question should you ask? Remember, you can only ask one question in total, and you can ask only one of them the question. Firstly, asking an easy question that you know the answer to, such as “What is 1+1?” will not get you anywhere, as even though you know who is lying and who is telling the truth, you are not allowed to ask another question, which means you cannot find the path that leads to riches. Furthermore, you cannot ask a question like “Does your path lead to riches?” as you do not know whether they are telling the truth or not.
However, if you can make the person who always lies have to lie about what they lie about, you can find out what path they are guarding.
To do this you need to ask a question like this: “If I asked you ‘Does your path lead to riches?’ what would you say?” If we assume their path does lead to riches, then if they always tell the truth, they would say yes, as if you asked them “Does your path lead to riches?” they would say yes, and they would truthfully say yes.
However, if they always lied, they would still say yes, as if you asked them “Does your path lead to riches?” they would say no. Then when you ask them “If I asked you ‘Does your path lead to riches?’ what would you say?” they would say yes, as they would originally say no, and would have to lie about saying no, so they would then say yes.
If we then switch around and assume their path leads to certain doom, they would say no, as they would have to ‘lie about what they lie about’ again.
These are some of the questions you could ask:
- If I asked you ‘Does your path lead to doom?’ what would you say?
- If I asked you ‘Does your path lead to riches?’ what would you say?
- If I asked you ‘Does your neighbour’s path lead to doom?’ what would you say?
- If I asked you ‘Does your neighbour’s path lead to riches?’ what would you say?
- If I asked your neighbour ‘Does your path lead to riches?’ what would they say?
- If I asked your neighbour ‘Does your path lead to doom?’ what would they say?
- If I asked your neighbour ‘Does your neighbour’s path lead to doom?’ what would they say?
- If I asked your neighbour ‘Does your neighbour’s path lead to riches?’ what would they say?
The bottom four work, as all of them use one lie and one truth, as the one you are talking to might lie about their neighbour’s truthful answer, or the one you are talking to might tell the truth about their neighbour’s untruthful answer.
I hope you enjoyed reading about this riddle, and you pick the path to riches.