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From: khanacademy
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  • i thought he was saying Magicians the WHOLE TIME! even in the first video, and i was like, why would they have perfect magicians? LOL

  • WAIT WAIT WAIT... wouldnt they leave at 99 times? because by the process of elimination you are the 100th person so you have to have your head painted blue

  • trully mind-blowing

  • Wouldn't it be a prison if 100 "Dudes" are in a room and the light goes on and off?

  • ooooooooh i get it cause there has to be someone in the room with a blue forehead at all times so... AHAHAHAHAHAHAH

  • if you didn't have a blue forehead everyone would be looking at you.

  • @MatimusGodfrey You're thinking too much!

  • The logic works for one, two or three logicians. I don't see any solution with a number greater than three, except that they would all sit there forever. Am I missing something?

  • @richardwasserman yep. a brain....no offense but u should use ur brains while lisnin to wat he's saying.

  • You spent 11 minutes to explain this simple logic. Which most of the time is just repeating the question or waiting for you to write some notes or drawing...

  • I think that all logicians will leave the room at the second time the light is turned off. They will all leave at the same time.

  • I still don't see why they all wouldn't leave after the first showing if there were 100 people all with blue foreheads. Wouldn't a perfect logician deduce that everyone has a blue forehead, the odds of him not having one would be 1/100/

  • @trainerMC well, there still is a change of him not having a blue forehead.

  • @trainerMC as in "perfect logician", no one would leave without knowing 100% that he had a blue forehead

  • @trainerMC

    A perfect logician wouldn't take that chance. 1/100 is still a chance that he could have a blue forehead.

  • After 100 times of light switchings, we would have 100 blind logicians and one confuddled audience. I conclude that this would make a very bad reality TV show.

  • 3:22 lets call him bob

  • A better explanation would be that in the case of only 1 blue forehead, the person would walk out the first time the light gets switched off. If there are 2 people with blue foreheads, they would walk out after the second time. And so on.

  • @Krunkalunga That explains nothing, just what is actually happening.

  • @Krunkalunga that's how I worked out the answer I minimized it and then found the pattern.

  • You can also think of it this way:

    With 3 People:

    1 Blue, 2 White; Blue leaves during first darkness

    2 Blue, 1 White; Blues leave during second darkness (when none leave after first darkness both Blues realize their head is not White)

    3 Blue, 0 White; Blues leave during third darkness (etc.)

  • Nobody thought that they could... remember having their forehead painted?

  • In the case with 3 logicians, all would know their hat is blue after the first round, not after the 3rd. Person A takes the case where his hat is notBlue. He would know that if Person also took this case where his hat is notBlue, then Person C would know his hat is blue.

    But after the first round person C does not walk out, so person B knows his hat is blue.

    But this person A knows neither B or C walked out, so after the first round, person A (and everyone else) knows their own hat is blue.

  • my conclusion: this would be a very boring show

  • Also, if you are a perfect logician than you would notice if you were the only one with out a blue forehead because if you were the only one without blue then everyone would look at you more than anybody else right?

  • I disagree with the solution. I think that these perfect logicians would figure out that after the lights turn on, "I see 99 blue foreheads, possibly mine is non-blue." Then when the lights turn on the 2nd time, they would think "If no one left, that means I too have a blue forehead," then when the lights turn off, everyone leaves thinking the same thing. anyone else agree?

  • @sxsvbm No, because his is a perfect logician, he doesn't think his number is 2 he thinks his number is 100, in fact that might be a better way to do it. Put numbers on everyone's head and they are all 100, but yours might be less. Since you can't observe it, you don't assume it. Since you don't assume it, you don't leave until your number is called, by the time it is called, you know it's yours. Now, there would have to be givens on the numbers being called sequentially and 100 being last.

  • i dont get the 3 people one. all i get is when there are 1 and 2 people --____-

  • This could be much shorter video...He repeated some things more than five times...

  • This gave me a headache! Anyway, funny idea! And what would happen if you leave the room and your forehead is not blue?!

  • hm, the rules didnt state that u cant talk to each other.

  • i hate the way you explain the situation.. you keep repeating the same statement over and over... actually you can make a shorter video...

  • Let's move halloween to november 5

  • So you are in a room with 99 people whose forehead is painted blue and you need to figure out if your forehead is blue or not. Your big clue? At least 1 of these people has a blue forehead... umm no kidding 99 do I could have told you that. Oh they leave after 100 times.. Do you believe that because big brother told you so? Sometimes 2+2 = 3.. sometimes 5.. sometimes both at the same time.

  • @xandror What?

  • If they left the room and they didn't have a blue forehead, were they fed to crocodiles. I'd watch that.

  • What if one did have a red mark, how would it work out then?

  • trying to leave a room with 100 people in it in the dark sounds quite dangerous to me.

  • Wouldn't you feel them paint something on your forehead?

  • @gabstersmom1 every1 has paint on their forehead u just dont know if its blue paint.

  • @gabstersmom1 They would have a different color painted on their forehead, i.e. Orange

  • This works if less than all foreheads r blue. If 50 foreheads r blue & 50 r not, then all those with blue foreheads leave after lights have been turned off 50 times. Everyone sees either 49 or 50 blue foreheads. If you have blue, you count 49 other blue foreheads. If nobody leaves after lights have been turned off 49 times, you know you have the 50th blue forehead & you leave after lights r turned off for the 50th time. If u don't have blue forehead, u do nothing, even after 50th time.

  • I really don't get this.

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  • @izilude Thus you have now changed your logical condition (number 1 in the video) from at least one person must be blue to at least 2 people must be blue. When the lights flicker again, if no one leaves, then that means everyone saw at least 2 blue people and thus there must be at least 3 people with blue foreheads. Thus, everytime the lights flicker your logical condition changes to "There must be M number of blue foreheads, where M=the number of light flickers.

  • got it as soon as i started this video :)

  • Silly logicians. Just ask the guy next to you!

  • i thought about it this way:

    the first time the light go on you look at a random person and you watch how he/she reacts after seeing all the people with blue foreheads.

    now IF she looks at you for a bit longer than the other ones you know that you are different.

    that would mean you have a blank head and you are allowed to stay in the room.

    if he/she does NOT react in a strange way while looking at your forehead than you know you all have the same blue forehead. so you leave the room !

  • my suggestion is that you would 1st present the problem without repeating, or over explaining the situation ... , much less confusing that way ..I think

  • To simplify this a bit, imagine instead 3 logicians, with only one having a blue forehead. Well he would know instantly, and leave when the light goes off. If two had a blue forehead when the light went went off and neither leaves they now know they are also blue, and would then both leave when the light goes off on the next cycle. If all three had blue foreheads then none would have left, but would leave when the light goes off one more time. The same logic works for 4,5,6+++ etc.

  • They all leave the first time after asking each other if anyone in the room has a blue forehead. Or if talking is not allowed, they would logically realize that if they were the only person in the room without a blue forehead, people would be focusing on them disproportionately. Upon realizing everyone is looking around or deep in thought they could correctly assume their forehead was also blue and leave.

  • lol, love you videos! but this one was tough to get through because of all the repeating XD

  • I'm Blue da ba dee da ba die...

  • this tells us that sometimes for seemingly very simple solutions we have to write lengthy codes

  • this is the problem with being a logician, they have to turn the lights on and off for 100 times... if they were normal people, they would have said, "screw it I must be the one without blue forehead." and they all would have stayed

  • I can't believe I figured this out on my own, but I did. I might not have been able to do it without the hint at the end of the last video though,

  • @krazjazzfan lol its pretty easy to figure out.... i figured it out without the hint, its just, kinda obvious

  • I DID NOT AGREE

    I THINK THEY WILL LEAVE IN THE SECOND TIME (AS I WILL DO IF I AM IN THE SAME ROOM)

    WHY ? BECAUSE YOU MUST REALISE WHEN THERE ARE NO ONE LEAVING IN THE FIRST TIME THAT THEY ARE IN THE SAME DILEMMA YOU ARE IN ..!!

    AM I RIGHT ?????

  • @tayh212 I suggest trying it with 3 logicians instead of 100. And imagine what would happen if 1,2 or all 3 had blue foreheads.

  • This was obvius to me. After to light goes on the 100th time, they alle see, that noone has left. This means, that they themselves must have blue foreheads, and they will all leave.

  • Interesting... what computer science (or any other) application can this logic be extended to?

  • @ROsCoALwAys you'll figure it out when you become a pro dealing with real life problems...

  • Hopefully this will help with some of the confused comments.

    Assume that your forehead is the only one not blue. Then you would see 99 blue foreheads and everyone else would only see 98. On the 99th turning on of the light everyone but you would leave because their count was less than yours. No matter the ratio of blue to not blue, the blue people will all have a count of one less than the not blue people and thus will leave first. Assuming they are all perfect logicians...

  • Let us say that hypothetically your head is red and 99 are blue. No one will ever deduce their head is blue because no one will leave even if the light was to come on 100 times. If everyone left on the 100th light..then you would be leaving with a red forehead. I can see why it works for 1 or 2 people. 3+ all blue doesn't work logically.

  • @AgnosticNinja oops I mean 4+ all blue doesn't work logically. 3 blue does make sense.

  • wtf, i didn't get this and i'm actually getting pissed off at the fact that this doesn't make sense. i even read the comments and it still doesn't make sense. AAAAAAAARRRRGGGGGG!!!!!!!!!!!!­!!!!!!!!!!!!

  • lol after 100 times they all leave? why not leave after the second time? It's obvious after the second time that if none of them left, you all have it. Otherwise everyone but you would have left the first time. You only need 2 times to figure this out.

  • @tyniehawk So you did not understood the logic of this thing. Watch again 8.20.

  • How bout this. They each ask 1 guy if his forehead is blue then they will figure out that all of them have s blue forehead. He never said they couldn't talk

  • It's funny, I can understand the example shown using 3 people yet when I try to visualize it with 100 I can't, even tho I know the structure of how it works is the same.

  • @Judeau0311 lol. In your solution, they aren't perfect logicians. They all have a hunch.

  • I'm pretty sure that I'm blue and if I was green I would die.

    Eiffel 65 - Blue (Da Ba Dee) (Original Video with subtitles)

  • Which are undoubtedly true, but they only give me a massive headache.

  • the arguments below are correct, if these guys are infact perfect logicians, they can certainly figure out that everyone else will have realised that everyone else will have opted to go ahead and assume that everyone else is thhinking for the easier path, by rule of it being an easier path. (i just read that again and loled) ^^

  • @KillaNinja0 I don't think so. Lets say there is some negative consequence for being wrong. In that case, these perfect logicians will not risk guessing. They will wait for the 100th light. All of them should know immediately that the 100th lighting will be proof positive.

  • @philnoll ya, i thought about it again after i posted the comment and i realise actually that the logic is infact based on the asumption that you have a blue forhead. when you say "everybody knws that everybody else knows there at least 98 ppl with a blue forhead" that actually presumes you have a blue forhead, because if you didnt have a blue forhead, the truth would be that everybody knows that everybody else knows that there are 97, and so you cant know where to start using that logic

  • @KillaNinja0 If your forehead is blue, they will see 99 blue also. If your forehead is not blue, they will only see 98 blue. Where did you get 97 from???

  • @AprilBillingsley yes, if you are one fo the other 99 you will seee 98 BUT you will only know that at minimum, everybody else sees 97 ( when it was 100 ppl looking at 99 other blues, this minimum was 98 like we said). the conclusion is that you cant know what the minimum number of ppl everyone knows everybody else knows about unless you actually know if you have a blue forhead or not in the first place. get it or no?

  • @KillaNinja0 You are not making sense. if you are one of 100 people, you can see 99 people total. So can everyone else. They see you (which you can't see), so minus one, and then they can't see themselves, minus 2. 100-2=98. You can see 98 of the same people's foreheads. And that is true for everyone in the room. 97 has no place in this equation. No matter the ratio of blue to not blue, people with a blue forehead will always count exactly one less blue than people without.

  • @KillaNinja0 That is, unless, everyone has a blue forehead, and then everyone's count would be the same. The logic makes sense.

  • @AprilBillingsley look, you are right to say that thats how many blue forheads everyone else is going to count, but if you are trying to establish the logic of starting on round 98 because it would be faster, you'r forgetting one thing - if you dont have a blue forhead, the 99 other ppl in the room dont count you at all. its like they would be having their own little think about 99 ppl like we did with the original 100, and jhust as you got 98 for the previous answer, we have one less at 97

  • @AprilBillingsley you get what i mean with when you dont and do have a blue forhead. yes they will count what you say they will when i do and dont have bfh, but when i dont, they'r attempt at the shortcut will lead to a different starting point then if i did have a blue fh. no?

  • @AprilBillingsley you see your problem is that you'r assuming that everyone else knows everyone else knows that eveyone can see at least 98 blue fhs, but they DONT. YOU know that. but if you dont have a blue forhead they dont know that. they would see 98 blues, but wouldnt know that everyone else can. take it back to how you solved the original problem, you have to think about not only what ppl are seeing, but what they are thinkin about also.

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  • i think they would leave before 100 because of the perfect logic they would all think they wernt the one with blue because everyone else is blue and they catch on that nobody is leaving and the surprised looks will take for everyone and they will all just assume they are all but the 100 turns is flawless logic my way is common sence with guessing

  • @EDOM666DEVORE What if I told you that if you leave the room and you don't have a blue forehead, you lose your chance at winning $1,000,000. Would you still be so confident then? Or that you will die. Nothing happens if you leave the room last, but if you leave and you don't have a blue forehead, you die. Would you take that chance then?

  • @sicness4ooooo infalible logic alone yes but adding the human element they may figure out before but from a non emotional point and non human element and only logic i see what you mean and if the stakes are so high they would probably not take thachance good point but there is no such thing as a perfect logician because nothing is perfect although i clould be wrong its all theoretical anyways no reason to take it so serious this is a fun exercise i enjoyed it

  • 5. However, when the lights go out and then on again, no one leaves, because they still don’t know the state of their forehead, but they all would have known it if my forehead been blank. So my forehead is blue, and we all leave the room when the lights next go off and on.

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  • @dgitting This is how I see the problem:

    At the time of the first lighting, seeing 99 blue foreheads you immediately realise the 2 possibilities: either you have a blue forehead or not. In order to be perfectly sure, that you are the 100th blue forehead posessor, you have to wait ‘til the 100th lighting, because only than you can eliminate the 2nd possibility ( in which case everyone else sees you being different, and wonders whether he is the 99th

  • @dgitting with blue forehead or not, and waits for the others that are waiting until the 99th lighting to eliminate their 2nd possibility, in which everyone else would wonder whether he is the 98th blue forehead possessor or he isn’t, in which case they wait for the others waiting for the 98th lighting to eliminate their 2nd possibility, in which.....and so on...)

  • @dgitting You cannot communicate with others. Since your decision for leaving can only be based on what you’re seeing, there isn’t a possibility of a consensus to shortcut the procedure. Waiting until the 100th lighting is the only way to be certain. I think , the interesting fact in that brainteaser is, that in every possible case, those with blue foreheads leave together

  • @totyessz You only need the lights to go off twice. The first time if the lights go off and nobody has left, then its obvious everyone has blue otherwise you'd be the only one in the room after the first time the lights go off. So they go off, everyone stays, next time everyone should leave or at least the smart people.

  • @tyniehawk

    genius!

  • 4. Hence, if my forehead is blank, each of the other 99 experts would know that his or her forehead is blue, and the other 99 would all leave the room when the lights are turned off and on for the first time since the lights were turned on initially.

  • 3. Each expert reasons thus. If my forehead is blank, then the other 99 experts are looking at my blank forehead and 98 blue ones; at this point, they might wonder if their forehead is blank as well, but, as mentioned in the previous paragraph, we all know that we all know that there can be no more than one blank forehead.

  • 2. To see why this is true, note that any two experts are both looking at the same 98 blue foreheads. Since everyone knows that everyone knows that there are at least 98 blue foreheads, everyone can conclude that all the experts can conclude that there can be no more than one blank forehead, because if there were two blank foreheads, then 98 people would be looking at two blank foreheads, which everyone knows that all the experts know is not the case.

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  • After the lights are first turned on, each expert knows that there is at most one blank forehead, viz., his or her own, but, since they don’t know about their own forehead, they don’t know that the other 99 experts also know that there is no more than one blank forehead. Here is the critical observation: Everyone knows that everyone sees at least 98 blue foreheads.

  • Okay, here is what I believe is the solution.

    Dennis Gittinger, Ph.D. Professor of Mathematics.

  • My logic:

    I imagine I have a different color than blue, e.g. red. Then I imagine 'what would the others do if I had a red forehead?'

    Next logician would imagine his was red, make same conjecture. Same for the next logician. By the 98th logician it would be:

    '97 others have red foreheads. If I have a red forehead, one of the remaining 2 will be gone once the light goes. Light comes on again; both still there. Light goes out again, then everyone leaves...

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  • What's tricky with this is that each one has to consider the possibility that every body else will consider the possibility that more than one person has a non-blue forhead, when they all know that not more than one has a non-white forhead.

  • Man, my brain has had enough exercise for a week.......!

  • ow my head hurts

  • Khan is wrong. When the lights come on the third time, all 100 leave the room. For details send a note to me at dgittinger@alamo.edu

  • @dgitting I think the 100 logicians could leave after only the second light. What if the 100 logicians pair up and look at the person next to them, or their "partner,"......and then essentially you have these independent two person situations. It only takes them 2 light switches.

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  • @dgitting So you mean that they all leave once the light goes out for the second time? That's what I think. Would you outline it here, even? I've been thinking about it and it'd be nice to see if we have a similar answer :/

  • Khan is wrong. When the lights come on the third time, all 100 leave the room. For details send a note to me at dgittinger @alamo.edu

  • Wow you really explain this well without making me feel stupid!

  • I'd just leave because no prize was mentioned and this is stupid!

  • They al leave at 100 of bourdom

  • So the first time, Sal sees 99 logicians with theirs foreheads all painted blue. The lights go off, and none of them leave. Therefore Sal can deduce that none of them know they have blue painted heads, because they are perfect logicians. But, because we know that AT LEAST one must be blue, the only logical conclusion is that everybody's forehead is blue, and therefore, they would all leave during the 2nd "Lights out". Obviously there is some error in my logic, any help?

  • @goose434343 Bit of a non sequitur. All 99 others are blue, but don't leave. Therefore I am blue. That's the flaw, I think. Anyway I reckon that they would leave during the second light out too, but for different reasons.

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  • Haha, 4:25 - "I have an appointment meeting.....cancel that."

  • so whatre the implications of this brain teaser?

  • lol I actually got it right.

  • for each round, each (every) guy in turn says:

    1) if i see no blue, i am blue -- so, i go now.

    2) if i see n blues total that did not leave in round n,

    it must be because i am also blue -- so, i go now. (they will all say this and all go now.)

    it helped me to draw the matrix of all possible combinations, and notate when (which round) each blue goes.

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  • I thought that the lights only turned off once, but when you said that they turn on and off 100 times I got it very quickly

  • Yeargh, same.

    See, the guys assume that imagine there was 2 people.

    Then 3 people, etc etc.

  • I need a life.......................

  • I got this before you gave the solution :)

  • MINDFUCKK

  • You guys bickering over the result is pretty indicative of your intelligences. It's all perfectly logical process of elimination. What's the problem?

  • Well Mr. Intelligence - I would like to know the logic. So put it in black and white. Do 6 people in the room. Explain it to me. Assumptions are not good enough. The moon is not made of cheese and the world is not flat. I am not going to take this answer on faith. So prove your logic and if you do I'll change my name to dumbass.

  • Mr2ndlook, you shouldn't think of assumptions as guesses - they aren't. In logic, when chosen carefully, they are plenty good enough. The idea is called a proof by contradiction. It works when you have a binary choice (only two options, like True/Not True). What you do is ASSUME one choice is true, and then proceed logically without any other assumptions. If you find a contradiction with something you know is true, then your assumption was wrong, and the other choice must have been right

  • 2ndlook, here is an example: Your moon/cheese claim is binary - either the moon is all cheese, or it isn't. So, ASSUME the moon is all cheese. We know the moons shape and mass. We also know the density of cheese. This is enough information to calculate the cheese-moons volume and diameter. However, when you do this you get a diameter that is different from what we know is true. So, we can conclude the assumption is false. Google "contrapositive" or "proof by contradiction" for info :)

  • looks like you are going to change your name : )

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  • 1 to 3 people is obvious but 4 or more is not. Doing 4 there is no reason to conclude you have a blue forehead because you know the other 3 don't know the color of their forehead so they also can not conclude they have a blue forehead. Work through 4 and prove me wrong.

  • @Mr2ndlook

    well for the case of 4 , like A B .. C D

    If A was not blue:

    say like, if u were D, u know that A was not blue and u would think if i were not blue the two other guy would have left the room as soon as the light turned off and on 2 times, but in fact they didnt, and u can deduce that u are blue. and then 3 of people including u will leave the room.

  • But the other 2 have no way to determine they are blue no matter how often the light is turned off unless something changes such as removing at least one person with a blue head.

  • @Mr2ndlook Likewise, if 4 were painted blue, and if u were D again, and saw 3 guy were blue, and you knew that if you were not blue , the 3 other guy would have left the room as soon as the the light turned off and on for 3 times, but in fact those 3 guys didnt do so, so u can deduce that u have a blue forehead and when the light turn off , all the 4 people will leave the room.

  • process of elimination...If you have 4 people & say only 1 person had a blue forehead then obviously the person with a blue head would see 3 other non blue heads & leave the room..

    If 2 out of the 4 had a blue head then each one of the blue head would look & see that there are 2 non blue heads & 1 blue head & when the light turned & still saw the other blue head there you would realize that he didn't leave because he saw another with a blue head & by process of elimination it would be you..

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  • I'll do 3 out of the 4 & try simplifying it.. Mike,Bob, & James have blue heads & Steve does not..

    Mike sees Bob & James have blue heads & therefor at least 2 people have blue heads.

    Bob sees Mike & james have blue heads & there knows at least 2 are blue

    James sees Mike & Bob & knows at least 2 are blue..

    This is actual fact & now comes their process of elimination..

    Mike thinks if James & Mike are the only 2 blue heads then they will wait after the 1st light was turned off.

  • Mike thinks if James only sees a blue mark on Bob & not him & Bob does not leave then James would leave after the 2nd light turned off..

    Idk its hard to explain but basically you have to make assumptions & try to perceive what the other people would do..

  • Well see that's just it. Logic as far as I know is not guesses. Would a perfect logician make an assumption?? As Spock would say that's not logical. What if it was certain death if you left and didn't have a blue forehead? Also in your example you group 3 out of the 4 and you simply can't do that. You must use the 4 as a whole. I actually think I see how to do 4 now but to be truly convinced I would have to have 10 proven to be logical. Until then I disagree with the answer.

  • Yeah but logic isn't fact either or absolute truth, look at logic the way Sherlock Holmes would or how some of thesemovies are set.. They take into account people react in a certain way to a set of circumstances.. That maybe someone not being afraid when someone next to them is shot or that they moved a little to the left before the person was shot....its all assumptions..you may assume the person knew the man was gonna get shot & thats why he moved but it could of been really anything..

  • maybe the man moved away because the man stank, or to get a better look at a woman bending over...its all assumptions & the only reason the question states that the people are all logictians is that they are just trying to state the people are not idiots & are capable of figuring this out as intelligence would effect the outcome.. But I agree with you in that it is a flawed question as it requires everyone to come to the same conclusion & we know thats almost impossible..lol

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  • @Mr2ndlook Going thru 4 people. Bob Carl Dan and Eric. Call them B, C, D, E.

    B says "If I am not blue then C sees only two blue heads. Thus C would say, if I am not blue, D sees only 1 blue head. Thus D would say if I am not blue, E sees no blue heads, and will leave. If E does not leave, D would know he is blue, so E and D will leave. If E and D do not leave, C knows he is blue, and all C,D,&E will leave. If C,D,&E don't leave, then I am blue. So we will all leave."

  • i would leave after the first light cuz everybody else is blue i would assume im blue too :D

  • @djswizzair you would not be a perfect logician. So you would not be in the room.

  • In other words, everyone knows that everyone else knows that no one will leave in the first 97 rounds, so they would skip those. Everyone also knows that no one will leave in the 98th round, but they have to start with that round to cover the case where their own forehead is non-blue, which means everyone else needs to see what happens in the 98th round.

  • There is a shorter equally logical solution: They can all deduce that no one thinks there are fewer than 2 nb foreheads, so they should assume the first round is actually the 98th round. Anyone who saw 2 nb should leave. In next round, anyone one saw 1 nb should leave. In 3rd round, they all leave. Calling in Marilyn for backup...

  • Meant to say no one thinks there can be *more* than 2 nb foreheads.

  • Am I overlooking the reason of why they can't speak to each other? Would that not make it easier (with the pretense that all logicians are 100% honest)?

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  • i love these brainteasers, nice videos

  • Haha pretty sure if you did this a hundred times one person would lose count and the whole game would get messed up, especially if there were a time limit between each time the light got turned on and off! Personally I would have just licked my thumb and wipe the paint off my forehead and then try to convince the pretty experimenter with the paintbrush to follow me out to the next room so we could do some more worthwhile experiments!

  • I liked it a lot. Thanks!

  • This one really brought out the crazies didn't it? I basically understand your solution but the assumption bothers me. I know that your question was, "What would happen if all foreheads were blue?" So from your point of view it made sense to assume all were blue; but to the guys or gals in the room they would need to assume 2 things sequentially: (1) Assume all are blue, (2) assume 99 are blue, and then compare their results. Am I right?