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

Lesson 1: Brain teasers

# Toggler brain teaser

Separating the truthteller from the togglers! Created by Sal Khan.

## Want to join the conversation?

• Can't you just ask {not to anyone particular ,so they all answer} "Would the truthteller step forward?" Then take note of who stepped forward. Next ask the same question and the person who took 2 steps in total or stayed in the same place is the truthteller. Right?
• Good idea, but the two questions have to be to individuals. Yours definitely applies if this is not the case, though. Great job!
• THE SOLUTION IN THE VIDEO IS WRONG. If the person answers "no" to the first question, he can answer "everyone" or "no one" to the second question. They are both valid lies and do not violate the terms of the riddle. If he does say "everyone" or "no one", then you don't really get anywhere and still don't know who the truth-teller is.

I'm not trying to be a troll. But this logic does not conflict with any of the premises.
• fallenG...rephrase the question, "Which four are not the truth teller?"
• I think there's a simpler way to solve this:
Just ask anyone: "Who are the togglers?"

If the person names 4 people, then the only person not mentioned is the truth teller

If the person lies and names 1 person, then the person mentioned is the truth teller

That way you can ask one question to anyone and know the truth teller. Am I right?

EDIT: You guys realize that my comment was about 2 years ago? HAHAHA It's just that I still get notifications about people commenting here
• Why would a lying toggler not be able to say four people, one of whom is the truth teller? That would be a lie, to say that all four the toggler gives are all togglers.
• My solution: "If I would ask you to point out the truthteller after this question, who would you not point out?". Either the toggler points out the truthteller, or the truthteller points out a random other guy. Ask any other than the two involved (who is definitely a toggler) the same question, and he'll point out the real truthteller.
• Good solution... But I COULD be a Toggler, or maybe not... OR I'am just Toggling with you... Again, I could be lying, OR telling the truth... But I'am not a Toggler... OR am I just in lying mode?
• i think i solved it by asking are you a toggler and if they said yes, they would have to be a truth telling toggler so then asked who is not the truth teller and they give me the truth teller, if they said no they are either a liar or the truth teller, so then ask who is the truth teller, the truth teller would say "i am" the toggler that lied now has to be telling the truth and would give me the truth teller. anyone see how that doesnt work?
• Yup- I solved it the same way too (or i guess in a similar way)

Q1. Are you a toggler?
Q2. If answer to Q1 is Yes, ask who is a toggler. If answer to Q1 is No, ask who is not a toggler.
• Why can't you just ask someone the question 'Who are the toddlers?'

If the answerer only pointed one person, That person you asked the question to would be a lying toddler, and the person he pointed would be the truthteller.

If the answerer pointed several people, he would be the tuthteller.

Is this method right?
• That was my original answer too, but his makes sense

.He wrote three questions, but he'd only ask two, and only the questions that he actually asks counts as a question.
Same thing the other way around. If the toggler answered "no", then he would just ask "who is not the toggler?" and know the answer.
• Should be able to do it in one question - Ask one person, "Who here can lie to me?" TT - points to the other four / TogTruth - Points to self and other three Togs / TogLie - points to TT - no need for a second question.
• My solution is extremely similar to that of Sal's, but anyways:

Q1: Are you a toggler?
If Yes
--> Q2: Who is a toggler among you?
If No
--> Q2: Who is the truthteller?

The "among you" is very important, otherwise he may just say whatever he wanted.
(1 vote)
• In question #2 why would the Toggler have to tell you who the "truthteller" is, if he is able to lie then he could just say George Washington or something. Therefore leaving you without an answer! Instead ask the same person "who are the Togglers" twice, which will give you the answer!
• What if they said "A, B, C, and E", then "A, C, D, and E". Obiously it's B or D, but you have no idea which.
(1 vote)
ask any person who is a toggler
if he lies he has to point to the truth teller
if he tells the truth he has to point to the togglers
so in the first case you get 1 answer
in the second case you get 4 answers so the remaining person is the truth teller
then ask the person if he is a truth teller
• If you ask someone who is telling the truth, the answerer will just point to one person. That is because the question is "who is a toggler", which is a singular question. A singular question demands a singular answer, so a truth teller or a truthful toggler must answer with just one toggler.
• Couldn't you just ask who the truth teller is twice to the same person
• No, because unless he says I am the truthtelller, both times you ask him, then he is a toggler, and the second person he says will be the truthteller. But if he points to two different people and does not point to himself, then you have no way of knowing who really is the truthteller. Really, only sal's way does it work every time just asking two questions. Hope that answered your question.