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## Math for fun and glory

### Course: Math for fun and glory>Unit 2

Lesson 1: Brain teasers

# Liar truth-teller brain teaser

How to get correct advice when you can only ask one question from either a liar or a truth-teller (when you don't know who is what). Created by Sal Khan.

## Want to join the conversation?

• My question is, can't you simply ask either one of them the question:
Do you know which door has the treasure?
The truthteller will tell the truth saying yes and the liar says no.
This is based on your assumption that both of them know the door to the treasure.
• This would allow you to figure out who is the truth teller, but not which door to choose.
• I like this because there are a few different questions that would work. My answer was that you can ask either one of them "Suppose many people had come before me and asked which was the door of the riches. Which would you have pointed to?" The truth-teller would point to the correct door, and the liar would lie about his previous answers (for which he would have pointed to the wrong door), and point to the correct door!
• That is probably the best way to get a simple answer.
• an alternate question to asked to either the truth teller or liar would be " If I were to ask you which door opens to the treasure what would you answer" Both the truth teller and the liar would answer with the correct door.
• this is tough. would the liar straight out lie, or would he know he would lie and lie against his predicted lie. It comes down to a human characteristic, so I wouldn't chance asking this question. I'd just ask:"What would the other guy say is the incorrect door?", and then both would would say the correct door.
• Another way I think is to ask them both a math problem like 5x5
the liar would say -25 and the truth teller would say 25.
• that would work, but then you would not know what door has the tresure
• if you ask the lier and he tells you the brown guy would open door two how do you know that hes the liar and hes not just lieing
• liar is lying.
(1 vote)
• you could just ask each one to open their door
• that is not a? 0 0
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• Hi, this brainteaser was fun but it also confused me. Any one who can explain it more thoroughly
• Oh yeah, this also confused me but I understood it later. So basically what Sal is saying is that if you ask the truth teller "What would the other guy say?" the truth teller would tell you the truth and say that the other guy would say Door Number 1 (which let's assume is the misery door). If you ask the liar "What would the other guy say?" then the liar , who knows that the truth teller would say Door Number 2, would say Door Number 1. In this case you know the incorrect door. Just pick the other door and you will have the correct door!
• how do you know who is true but not a liar
• You dont know who the liar or truthteller. Thats the point. You need to ask a question that would always give the correct answer . It should be a question that both the liar and the trutheller would tell you the same answer. The question Sal asks is correct because if he were to ask the truthteller , he would get the same answer the liar would vave given if he asked the liar. They both give the wrong door so you have to choose the opposite one
to get the AMAZING TREASURE! hOPE THIS HELPED YOU!