"Impossible" Logic Puzzle - How Many Liars Are At The Party?
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- čas přidán 22. 05. 2024
- A party has 100 people who are either liars are truth tellers. Liars always lie and truth tellers always say the truth. After the party you ask each person, "How many truth tellers did you shake hands with?" Each person gives a different answer from 0 to 99 (the whole numbers 0, 1, ..., 98, 99). How many liars were at the party? This seems like it's impossible to figure out, but it's not! Watch the video for the surprising solution to the logical puzzle.
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It must've been a nightmare to host this party if 99% of attendees said they couldn't make it, then they all showed up.
That's how Person 0 knew all 99 were liars. Person 0 was the host. They were never told they were hosting.
hum.hum
😂 cracked the code!!
Maybe this party is a meeting for pathological lairs? That's why the host knew exactly that those 99 lair will come.
So this party was full of politicians....got it
3 logicians walk into a bar. the bartender asks "Do you all want beer?"
The first says "I don't know"
The second says "I don't know".
The third says "Yes!"
a, at least to me, very well known problem. the problem being that most peoples are not logicians.
Hehe, clever! If person 1 and 2 didn't know whether or not they all wanted beer, then that would mean they do want beer, but don't know if the others do. The third person notices this, and since he wants beer, then he can affirm that everyone wants beer!
+Bronze To Challenger exactlly ^^
+Bronze To Challenger
lol you play LoL. me too :)
Aw man, I didn't get it until I read the comments on the comment ;_;
"You callin me a liar?"
"Well I ain't callin you a truther!"
Nice Drake & Josh quote!
A crucial unstated assumption in this puzzle is that everyone in the party already know each other's identity (lier or truth teller). I thought they revealed their identities to each other while shaking hands, telling a truth or a lie. That got meta ready quickly.
Fun fact: Under THAT assumption, the puzzle can be solved pretty easily. However, in the way it´s described in the video, the puzzle actually IS impossible.
and that they all shook hands with each other.
@@lewis72 True, that part also isn´t cleared up in the video. It´s only implied by the presented solution.
@@Finstersang The solution necessitates that persons 0 and 1 did not shake hands, since then person 1 would be telling the truth.
@@invenblocker True, that´s another explanation. However, if we assume that not everyone had to shake hands, there are multiple other solutions to the puzzle. F.i. it may also be true that 0,1 and 2 are all truth-tellers and 0 and 1 merely didn´t meet all of the 2 other truth-tellers. The explanation in the video heavily implies that they all had to shake hands - and then OP just "overlooked" that it creates a logic loop for person 0 and 1. Come to think off, OP maybe wants to revisit the whole thing now that the almighty YT algorithm resurrected it :P
Isn't that scary to be in a party of all Liars? My sympathy to Person0
It must be a political party.
Omar Goodman,
You are waaaay too optimistic! :P
Typical US Government Party....
The truth hurts tho :/
You never been to a party before lol?
I started with "what if nobody shook hands?" and saw that only Person 0 would be telling the truth.
Then I went "meh; that's probably right"
You're my kind of guy.
You... I like you.
We've found p0...
Of course, a good riddle only has a single solution. You found a solution. Therefore given the assumption that it is a good riddle your answer must be correct.
Also, what if person 0 is a liar and was just LYING about shaking hands with 0 truth tellers, HOW BOUT THAT
For me, this problem became much simpler when I worked on a slightly different problem, a party with 4 people where each of them gave a different number of handshakes (0, 1, 2, or 3) with truth tellers. Once I had a small enough group to actually work with, it was easy to figure out that 0 must be a truth teller and everyone else must be lying, and then the same logic works perfectly fine with the full puzzle.
So the one who aid he shook his hand with 1 truth teller.... is a lier? Since person 0 is a truth teller? There is a flaw in this puzzle
@@jonathandpg6115 person 1 didnt shake hands with person 0 ig
Yes!!! I did it this way.
Well done! This is a powerful way to tackle a problem: first try out a toy example with small numbers. You can be almost sure that the exact number 100 is not the key - there is nothing special about 100. Hence, n=4 should work fine.
Not everybody needed to shake hands with everybody else.
It also means that person 0 and person 1 didn't shake hands otherwise person 1 told the truth
True. Remember how many people each and everyone shook their hands with is irrelevant and a misdirection. Their report is all that matters
"Hey this is pressure locker" -youtube auto generated subtitles
Lol
It was perfect in my ones
@@targetiitbcse1761 switch from english to auto generated
Woah
What if they just... didn't shake hands with everyone at the party?
That's never exactly made clear.
Then 0 would still be the only truth teller and the rest of them liars for stating they shook hands with someone.
mickiooo
I suppose so.
Still, that's some remarkable co-ordination on the liar's part to have such perfectly sequential answers.
OnEiNsAnEmOtHeRfUcKa It is, and it's unlikely that in a real situation this would occur. But the sequential thing is an extra challenge to the hypothetical scenario.
***** It's a hypothetical scenario, it is indeed highly unlikely the people would all state a different number in a real situation.
+Melvin No
Well, this is taking into account that the other persons answered 99 to 1, which in case nobody shook hands would certainly be lies. There's offcourse more reasons for them to be liars(like thedm claiming there were multiple truth tellers), but just this mere fact rules them out for being truth tellers already.
First problem of your channel that i was able to solve in less than 2 minutes. Yay!
That last bit of reasoning only works if person 1 did not shake hands with person 0 otherwise he'd be telling the truth about having shaken hands with 1 truthteller.
Exactly atleast someone else noticed it
No, he would be lying, because then person 0 has to be a liar claiming to have shaken hands with 0 truth tellers.
Wrong. If 1 shook hands with 0 and 1 is a truth teller then 0 has to be a liar, because 0 said he didn’t shake hands with any truth tellers. This means 1 has to be a liar, just like 2-99, and 0 has to be a truth teller.
Nobody shook hands with anyone, boom person 0 is telling the truth everyone else is lying.
Yes, and this is the only way that doesn't lead to a contradiction.
Alternate answer: Everyone is telling the truth, but everyone shook Person 0's hand when he was asleep.
true
+Robert Antonius p0 is drunk
its true tho... lel
would still not work tho
Yeah really to get only one possible answer, it needs to be specified that each person knows how many truth tellers they shook hands with.
That would make person 1 a truth teller though! This doesn't solve the problem, it just makes it more difficult!
Person 1 is a liar because person 0 shook hands with person 99.
Person 0 and person 1 didn't shake hands.
If person 1 was a truth teller, that would mean they would have shaken hands with person 0. But they didn't, because person 0 said they didn't shake hands with any truth tellers.
@@trondordoesstuff so 1 and 0 didnt shake hands?
@@godthefathersonandholyspir5431 Correct. If they did, then 0 would have to be a liar, and if 0 was a liar 1 wouldn't have been able to say they shook hands with a truth teller.
Ive only just come across this and the logic to this is interresting. I love these predicaments where a sensible answer is seemed to be impossible, it just takes some thinking is all.
It took me like 20 seconds to solve this. He used a more complex approach. I never felt so smart in my life :D
Hey Could you please explain how you solved it, I really did not get what was told in the video
Note that we are _assuming_ that everyone at the party knows whether everyone else is a liar or truth teller. It could be the case that they think they are telling the truth, but are mistaken; or think they are lying but accidently be correct.
They spent a party with each other. They could probably figure it out
What isn’t stated in the original riddle, but is an essential detail, is that they were members of the RNC and therefore we can assume they’re all lying.
Truth tellers ALWAYS tell the truth (whether or not they know it)
liars ALWAYS lie (whether or not they know the truth).
@@trondordoesstuff *grabs a truth-teller* okay sit down now tell me when will the world end
Truth tellers would have said "I don't know".
Unstated assumption: Handshakes are mutual. If A shakes B's hand B then B also shakes A's hand. This sounds obvious, but you never know, maybe A used her foot to shake B's hand.
Indeed. Nevertheless, this particular one is one of the cleanest of these type of videos, assumptionwise.
Other assumptions: Nobody shook hands with themself. There was no 3-way handshake or worse. Nobody shook hands with someone outside the party. Nobody changed their identity mid-way thru the party, thus counting twice under some answerers' interpretations of personhood. The answerers understood the question. You understood the answerers' answers.
Etc. Once you start outside-the-box, there are few limits. But like I said, this video is one of the cleanest, assumptionwise.
Yes, of course. Mostly I was just riffing on the many incorrect "unstated assumption" comments which are on this video.
Also assumed: Liars and Truthers are capable of identifying each other accurately during handshakes.
+Alex Gilmer this is the only thing that imo should have been stated in the vid that wasnt
That's a given in the blog post.
I thought of it differently, though now, looking back, i assumed(perhaps unrealistically) that everyone shook hands with each other, no one missing anyone.
Anyway, there can only be 1 truth teller, because each person has a different answer. The truth is a constant, therefore if there were more than 1 truth teller, we'd have repeat answers.
The problem is that you can't get the right range that way, because there will be a liar that did shook hands with the truth teller.
@@sebastiaankoopman3304 I thought the same way than OP. If there is 99 different answers and everyone shook hands with each other, then there is a maximum of 1 right answer. If 2 guys said they shook hands with only one truth teller, we could not deduce anything since P0 would say he shook hands with no truth teller and P1 and P2 would say they shook hands with 1 truth teller and therefore one of the two statements would be right. However, since there is 99 different answers and one tells that everyone is a liar while another tells everyone is a truth teller, then the guy saying they are all liars is right. There is no way the number of truth tellers can vary when asking everyone. Everyone would need to tell the same answer for it to be right.
However, here is the tricky part. If everyone shook hands with each other, than P1 is a truth teller and P0 would then be a liar, which would make P1 a liar, which would make P0 a truth teller, etc. Since the first part of my theory proves at least one is telling the truth, then P0 is the real only truth teller.
Based solely on the fact there is 100 different answers.
this is how I figured it out by reading the thumbnail. and clicked the video to see if I was right.
@@snookymaster And then you take a step back and realize that this would also mean that P1 can´t be a liar, because if only P0 is a truth-teller, then he shook hands with 1 other truth-teller, so his statement would be true. Since liars always lie, he has to be a truth-teller. And that´s impossible, because then P0 would suddenly be a liar. It´s logical knot. OP didn´t realize that the puzzle IS actually impossible.
At least in the way it´s described in the video: If you assume that the guests also have reveal their identities to each other (and each lying or telling the truth according to their role), the puzzle can be solved pretty easily.
I thought of it in the same way - if every answer is different, then there can only be one correct one, therefore one truthteller, who didn't shake hands with another. If you assume that there are 2 truthtellers, then they would either shake hands or not, so there'd be 2 answers of either '1' or '0'. If there were 3, then there would still be repeat answers of either 0, 1 or 2, and so on. Assuming being asleep doesn't count. If there were no truthtellers at all, then the answer '0' wouldn't be given as that would be the truth. But the problem is "Who said 1?" - this is the correct and honest answer, but if there's only 1 truthteller, then his answer would be 0 (he can't shake hands with himself). I think this genuinely makes it impossible to answer, because an honest answer can never be given if there are no repeat answers.
I found a simpler/more intuitive way to figure this out:
They can’t all be liars, since then the one who said 0 would not be lying, so there must be at least 1. What if there was more than 1?
If there was 2, they must have said 0 and 1 (can’t say 2 or more since each only had 1 other truth teller to shake hands with); however, the 1 could only have shaken hands with the 0, who didn’t shake hands with the 1, so this is impossible.
Similarly for any other number greater than 1 (for 4, they must have said 0-3, and 3 must have shaken hands with all the others, including 0, which is impossible).
So the only truth teller is 0; everyone else is a liar.
This is easy, if "everyone gave a different answer," then obviously everyone is lying ('duh!') except for 1 person because the amount of possibilities left.
That's only true under the assumption that every one shakes hands with everyone. It's possible for person A to shake hands with 5 people, all truthtellers, while person B shakes hands with no one, and giving a different answer (0 handshakes with truthtellers) both of which are true. The logic provided in this video is necessary to prove that this scenario is impossible, which would make your comment redundant. Truth be told, it wasn't that clear that not everyone shook hands though, and I assumed the same thing
ehhh, at least a little. But as long as all of them gave different answers, and kept them believable (Which liars usually do), then it is safe to assume on one truth teller can be present because there are only as many different numbers as there are people. If one number had been repeated or one number had been outlandish, then the entire problem crumbles and becomes impossible.
yeah, i figured it out the same way, but i doubted my own answer because "well that's too easy, it surely can't be so easy."
But i thought more about it and thought, well, there's no other way.
I thought that too, (assuming everyone shakes hands, which I failed to notice *wasn't* the case)
one problem however is that say person 99 speaks the truth because there are 99 other people that are all liars. This would however mean that person 98 would speak the truth as all the liars minus himself (he can't shake hands with himself) is 98, in which case 2 people would be speaking the truth. However more than 1 people speaking the truth is impossible as in case of 2 truth speakers they would both have to say 98. Which would mean number 99 isn't mentioned because person 99 is now saying 98, breaking the requirement that numbers 0-99 are all mentioned.
I thought that too, (assuming everyone shakes hands, which I failed to notice *wasn't* the case)
one problem however is that say person 99 speaks the truth because there are 99 other people that are all liars. This would however mean that person 98 would speak the truth as all the liars minus himself (he can't shake hands with himself) is 98, in which case 2 people would be speaking the truth. However more than 1 people speaking the truth is impossible as in case of 2 truth speakers they would both have to say 98. Which would mean number 99 isn't mentioned because person 99 is now saying 98, breaking the requirement that numbers 0-99 are all mentioned.
But that means 1 is telling the truth too?
No, it means that Person 1 did not shake hands with Person 0.
+Martin Poulter that would make person zero a liar because the statement was that everybody shook hands with everybody
Not really. even if person 0 shook hands with person 1, one of them must be lying if person 1 says 1, and person 0 says 0.
if person 1 shakes the hand of person 0, and says he shook 1 truth teller, if he is telling the truth implies person 0 is a truth teller, that means person 0 and person 1 are truth tellers, but person 0 said he shook 0 truth tellers, if he's lying makes person 1 a liar for calling him a truth teller. This means person 1 is also a liar.
+Tamuno-Oribim Obene-Harry so it's a paradox person one cannot tell the truth because a person 0 + person 0 cannot tell the truth because a person 1
SWITCH DUBz Take aMilli "the statement was that everybody shook hands with everybody" Look again. There is no such statement in the problem.
I incorrectly assumed that everyone shook hands with everyone else. Thus, it is impossible. If Person 0 is a truth teller, then it would necessitate Person 1 as a truth teller, which would then necessitate Person 0 as a liar. It’s a paradox. So, I think this solution’s explanation would have been better by explicitly stating that it is necessary for Person 0 and Person 1 to have never shook hands ... and there is no assumption that everyone shakes hands. Therefore, Person 1’s statement about shaking 1 truther’s hand can be a lie even though there is exactly 1 truther at the party.
If everybody shakes everybody's hands then clearly person 0 is telling the truth still if everyone else is a liar (which we know by the inductive reasoning).
If you see the truth tellers as nodes that are connected with handshakes, you can't get a unique number of connections for all of them unless there is just one.
Or zero. That's what I did, too. But if everyone is a liar no-one can say zero.
@@goldenalt3166 and someone did say 0 so the only possibility is 1
I love these videos so much that I feel addicted. Please never stop this brilliant quality of content.
I agree 👍👍
How were we sure that person 0 wasn't a liar himself?
Then at least one other person is a truthteller. Contradiction.
+vidicate but how do we know that all of them weren't liars, including person 0?
As he explained, it is impossible for person 0 to say what he said and be wrong. What person 0 said has to be correct. And a liar will only tell lies. Because what person 0 said is not a lie, he is a truth teller.
person 99 said he shook hands with 99 truth tellers,
person 0 said he shook hands with 0 truth tellers,
so if 0 lied, that would mean 99 also lied bcuz he really would've only shaken hands with 98 truth tellers not 99, and they both can't be lying bcuz then 0 would actually be telling the truth when he said he shook hands with 0 truth tellers
if everyone lied then that means 0 was telling the truth when he said he shook hands with 0 truth tellers making him a truth teller
Watching pretty little liars finally came in handy. Solved this in seconds.
What about person one, if he shook hands with everyone and person zero is a truth-teller then didn't he shake hands with one person who is a truth-teller?
Except you've now created a contradiction. If P1 shook with P0, and they are both truth tellers (as per your stipulation), P0 has shaken hands with a truth-teller and thus his claim of shaking with 0 truth tellers is a lie, so he can no longer be considered a truth teller -- contradiction! It's essentially the same logic as when ruling out person 99 and 98 and so on.
Got it right :) I used inductive reasoning similar to how this was explained.
I figured two things out. First of all, I had no idea whether or not to assume that they all shook each other's hands (this should have been specified in the directions). Even though it wasn't specified in the directions, I did figure out that if they all shook each other's hands, the problem would be impossible because any truth tellers would supply the same answers after the party, breaking the stipulation that everyone had a different answer. In the hypothetical case that everyone shook hands and there was only 1 truth teller, then the person who said he shook 1 truther's hand would be telling the truth even though he'd have to be a liar since the person who reported shaking 0 truthers hands would have to be the truth teller.
Having established that everyone couldn't have shaken everyone's hands, I considered the case that everyone was a liar. If everyone was a liar, I noticed the problem that the person who reported shaking 0 truther hands must be telling the truth. So then if one person told the truth, the other 99 people could have all shaken nobody's hand, for example. And voila that's how I found the answer!
If they stated that everybody shook hands with each other, the solution is simple. Only one person would be a truth teller because if there were multiple truth tellers, they would all have to give the same answer. Which isn't possible in the puzzle (they all give a different answer as per the rules of the puzzle).
@@monkfishy6348 and the sole truth teller would have to have answered 0. But then the liar who answered 1 shook hands with 1 truth teller and must be a truth teller. This leads to a paradox, no matter how you proceed.
Therefore it cannot be the case that everyone shook hands with everyone else.
We know 2 things at the end:
1. The person who answered 0 was the only truth teller.
2. The person who answered 0 did NOT shake hands with the person who answered 1.
"I got 99 liars, and a zero ain't one."
Simple solution: nobody shook hands with anyone, thus only the person that says 0 is a truth teller. The rest must be liars
this seems illogical, as the description says that liars ALWAYS lie, and therefore person 1 was telling the truth. tell me what I am missing.
By repeating the process we find that person 99 to 2 are all liars. Person 1 hand shakes with person 0. If person 0 is a liar then person 1 is also a liar But if person 0 is a truth teller person 1 is also a truth teller. This is a logical contradiction because person 0 being a truth teller handshakes with a truth teller but says he handshakes with 0 truth tellers. So we can take another possibility that person 1 does not handshakes with anyone and lies about handshaking. If person 0 was the liar person 1 is also a liar but this is also a contradiction since person 0 being a liar says that he handshakes with 0 truth teller which is true, so person person 1 is a liar and person 0 a is truth teller. Since 99 to 1 are all liars. Person 0 tells the truth that he handshakes with 0 truth teller. Hence person 0 is a truth teller and everyone else are liars.
I hope this helps.
@@mihadbinislamtanim6267 I follow that, my argument is that IF person 0 is a truth teller, person 1 (who must ALWAYS lie) has told the truth in saying he has shaken hands with a truth teller, which he is categorically unable to do. This means that person 1 must be telling the truth... which makes person 0 a liar, making person 1 a liar, and we wind up with person 0 and person 1 being simultaneously liars and truth tellers.
@@jakesnake5501 I agree with what you said. This whole puzzle is paradoxical. But there is no such condition given that every person handshakes at least once. Which means there can be a possibility that person 1 doesn't handshake with anyone and lies that he handshakes with a truth teller. And notice that person 1 not handshaking with anyone doesn't affect person 99 to 2 or person 0 being liars or truth tellers. So we can conclude person 1 is a liar and person 0 is a truth teller. Unfortunately the video was too short and directly comes to conclusion with some gaps of logic and made the viewers confused.
Hmm I failed and thought it impossible at first because I had assumed everyone at the party shook hands.
I thought of it like this: if there was more than one truth teller, they would have shook the same amount of hands, and said the same number, which is a contradiction. If there were 0 truth tellers, then everyone would have shook hands with 0 truth tellers, meaning that if someone said 0 it would be the truth, which is a contradiction, therefore there is 1 truth teller (and 99 liars).
I figured it out, but I started from the other end. I reasoned that if there were zero truth-tellers ("knights"), then the person who said zero must be telling the truth, making him a knight, which contradicts the assumption that there were zero knights. If there were exactly one knight, he would have shaken hands with zero knights, but the person who said one could still be a liar ("knave"), because it is possible that he did not shake hands with the one knight during the party, and all the others would be lying. So that would work. If there were exactly two knights, and they shook hands, they would both answer one, but we know only one person answered one, or if they did not shake hands, they would both answer zero, but only one person answered zero, so we can rule that out. If there were three knights, and they each shook hands with the other two knights, they would each answer two; if only two shook hands, those two would both answer one. And we can induce from there that there cannot be more than one knight. Ergo, there must be only one knight. So my solution was essentially the same, just starting from the opposite end.
Well, it becomes impossible when you assume that everybody shook hands with each other... as I did. :D
IT becomes trivial when you do that (as I did), because only one answer can be true.
@@Person01234 Not really. If everyone shook hands with each other, it makes Persons 0 and 1 answers contradictory. If 0 is a truth teller, 1 cannot be a liar and still speak the truth, saying he shook hands with only one truth teller.
Person 1 shook hand with person 0 who is a truth taller and person 1 says :''i shook hand with one truth taller''. So person 1 tells the truth!BANG my mind blows!
Well but if person 0 is a truth teller, if you scenario he would have said I shook hands with 1 person which he dint making person 1 a liar.
I got 99 problems and a liar is one.
Wait, wouldnt there being one truth teller (person 0) mean that person 1 also told the truth, because they shook hands with 98 liars and one truth teller?
Numbers 99-2 are determined liars.
If:
Nr1 is a truth teller and shook hands with one truth teller, nr0.
Then:
nr0 did not shake hands with zero truth tellers, which makes him a liar.
-------
If:
nr0 is a liar
Then:
Nr1 did not shake hands with any (1) truth tellers, which makes him a liar.
So:
If nr1 is a truth teller, then nr1 is a liar 😅
@@ThisUserHasBeenCanceled So nr 1 and nr 0 didn't shake hands.
Not everyone shook hands with everyone.
This answer is condradictory:-
If person 0 is the truth teller then person 1 is also truth teller because he shook hands with person 0, hence u can continue on and everyone becomes truth teller. this question has same results as:-
thstatement below is false
the statement above is true.
0 and 1 never shook hands.
No, that would have made person 0 a liar
No it isn't. If person one shook hands with person 0, then person 0 has to be a lair. See? This answer is the only outcome that works.
The answer is contradictory if they all shook hands. Person 0 could have not shaken hands at all and he would be telling the truth. If person 0 shook hands with person 1 then it loops back and forth making them both liars, but that would make all 100 people liars. Conclusion person 0 was lying about being a liar, making him a liar if that makes sense.
He never said "they all shook hands", so it is possible that no one shook hands at all. All we know for sure is that p0 is germophobic :D
Simple bruh. 1 truth teller, 99 liars, the guy who said he shook 0 hands was the truthful guy and the guy who shook 1 Truthteller's hand simply didn't shake the truth tellers.
Since there's implied to be only one answer, this is what I'm going to assume is the only answer.
Yeah, I just assumed no one shook hands with anyone, because implied 1 answer, therefore only person 0 told the truth
so we even know that p1 never shook hands with p0
Best riddle from this channel
Me: Tries to solve riddle deduces that person 99 is lying. Gives up and concludes that there are 99 truth tellers XD
The solution presented here becomes more questionable when you take another look at Person 1's answer.
@@rodh1404 Person 1 must be a liar. Assuming you already worked out that person 99 through person 2 are lying, we know Person 1 must be a liar. If person 1 was telling the truth because he shook hands with person 0, who is also telling the truth, then Person 0's claim to have shaken hands with 0 truth tellers is false. It's a contradiction. So person 1 is lying. I guess we can deduce that he and Person 0 never shook hands.
Can you explain person 98 to me because I get that person 99 has to be a liar because if he’s telling the truth everyone at the part is telling the truth but person 0 can’t be telling the truth becuase there’s no liars, but with person 98, person 0 could shake hands with person 99 and would then be telling the truth.
@@lukerockbot8748 With Person 98, he would need 98 truthers to shake hand with. We already know 99 is a liar. So he would have to shake hands with persons 97 through 0. But person 0 shook hand with no truthers. So person 98 cannot be telling the truth -> 98 is a liar.
But if 99 is a liar than person 0 could shake his hand and be telling the truth
I FREAKIN NAILED IT!!!!
We can also deduce, that person 0 didn't shake hands with person 1. If person 1 shook hands with person 0 and person 1 told that he has shook hands with one truth teller, he would be telling the truth, which is contradictory. Hence person 1 mustn't shook hands with person 0. I wonder if we could induce that property.
This was simple for me because if 0 is a truth then he can't have shaken hands with himself.
Or can he?🤔
WOOAH HOLD ON A SECOND!..
there was a party?
A party comprised 99% of liars. Getting invited would be an insult!
Was probably before the lockdowns
It can be very easily solved using a mathematical subject called graph theory.
en.wikipedia.org/wiki/Graph_theory
Strategy:
Use the fact that every finite simple graph with more than one vertex has at least two vertices with the same degree. This means that at a party of (at least two) people, there are at least two people who shook the same number of hands at the party. Knowing this fact you can see almost immediately that the number of truth teller at the party must be less than two (otherwise at least two truth tellers would give the same answer). Furthermore there can't be zero truth teller, for else one liar will be telling the truth (namely that he shook hands with zero truth tellers).
I posted this solution below. But no one seamed to react so I reformulate it here in laymen terms.
But what if person 0 is a liar, which means he did not shake hands with 0 people, which means he shook hands with more than that?
I got the correct answer immediately in a very simple way: I incorrectly assumed that everyone at the party shook hands with everyone else and therefore only one of the answers could be correct.
Person 0 could have not shaken anyone's hands.
And that would still make the 99 person a liar since all of them say that they shook hand with person 0
it was not given that everyone shook hands with everyone else, therefore the deductions provided are flawed.
It was not given and it was not needed for the proof. On the contrary, if it WAS given deductions would be flawed, because then person 1 would have shaken hands with 1 truth teller and should have been labeled truth teller, etc.
It isn't guaranteed that the 1 guy shaking hands with 1 truth teller is the one to tell the truth. And if he DID shake hands with 1 guy telling the truth, then the guy who said 0 would be a liar. This would mean 1 is a liar, which would mean 0 is a liar, which would mean 1 is a liar, etc...
It's a never ending loop.
what if there were 4 truth tellers and 1 of them shook hands with 3 people 2 liars and 1 truth teller. the 2nd one shook hands with 30 people including 2 truth tellers. the 3rd shook hands with 25 people including 2 truth tellers and the 4th one shook hands with everyone including the other 3 truth tellers. you have 3 different truthful answers. in this case answers 1,2, and 3 are all truthful answers. thats why it matters if we know that they all know whether everyone else is a truth teller or liar and if they all shook everyone's hand.
No man, you say there are 4 true tellers and the 4th shook hands with the other three. Before that you said 1 of them shook hands with only liars, but how about the 4th who shook hands with all the other true tellers? you are contradicting yourself. xD
I think you are very confused man, better go and think again!
Jose Antonio Marron Martinez oops you are right i did contradict myself - i'll edit it to fix that
The liars could still have shook hands with the other liars, so person 1 could have shook hands with person 99, even though person 99 was lying.
Isn't the info at the start incomplete if you don't make it clear that not everyone necessarily shook hands with everyone else?
My main issue with this is that nowhere in the problem does it say everyone shook hands with everyone, and they have to know they're liars and truth tellers beforehand to be able to accurately guage how many they shook hands with.
It only really makes sense when you make assumptions, and assumptions tend to be the folly of man.
First, it doesn't matter how many people each person shook hands with, only how many truth tellers. For 99 to tell the truth, he must have shaken with everyone else AND everyone else was a truth teller. Since both conditions are necessary for him to be a truth teller, disproving either is sufficient to prove him a liar. The existence of person 0 provides a contradiction because it's impossible for 99 and 0 both to tell the truth, so we know 99 lied about how many truth tellers he shook hands with. How many total people he shook hands with doesn't change the outcome. Whether he shook hands with everyone or no one or any number in between, he still shook hands with no truth tellers.
Second, the puzzle is for you to figure out how many liars and truth tellers were at the party, not for them to do so. You are given the information that liars always lie and truth tellers always tell the truth. This eliminates the possibility of uncertainty. All reports are either 100% accurate or 0% accurate. The mechanism by which you know their accuracy is irrelevant because it is one of the givens of the problem. It's not a practical situation. It's a logic puzzle. All logic relies on initial information and rules for extrapolating additional information based on the initial information. Of course in any practical situation you must be skeptical of the accuracy of self-report information, but that's a problem for the social sciences.
0:55.
I got right awnser after looking at this for 10 seconds....
It took me a while to figure this one out, because I started and had to finish singing ,
99 bottles of beer on the wall.
So hang on a moment... if person 0 is the only truth-teller, then how come person 1 is a liar if he correctly said he shook hands with one truth-teller? That'd make him the truth-teller and person 0 the liar. But that would then mean there's another truth-teller somewhere for 1 to have shaken hands with, which would render the whole situation impossible and therefore make him a liar, but this then brings us back to the original point. The only way out of this is to assume 1 and 0 never shook hands.
5:27 for answer, god these videos are drawn out
plot twist: some people shook hands with themselves
I did a different approach. I started with assuming there is only one truth teller, which makes him/her person 0. All the rest of the members could pick a different number from 1 to 99 whichever they want. Make sense. But when there are two truth tellers, they would need one more truth teller to meet the requirements. When there are three truth tellers, they would need (at least two)more truth teller again etc... So to meet the requirements, the numbers of the truth tellers would go to infinity, which doesn't make any sense. So there can only be one case: there is only one truth teller and he/she replies "0".
Wait a minute... in your scenario, person 0 is a truth teller and all others are liars. The problem is, person 1 said he shook hands with 1 truth teller, which would be a true statement. Hence, person 1 can't be a liar. This makes your scenario contradictory.
Then person 0 should be the liar as he told he shook hands with 0 trueth tellers. Then Then person 1 cannot shake hands with anybody as all others are liars.Then he is lying. Thus p1 is the liar and p0 is the truth teller.As simple as it is!!
Yes!! I did it!! But I guessed...
I figured it out with different logic. How many people told the truth? You cannot have more than 1 telling the truth because then you'd get contradicting statements, therefore 1, done. Both of our arguments however assume everyone shook everyone else's hand. I bet the logic get's a lot more complicated if you take that into account.
If everyone shook hands then it's easier to think but still same answer either they all the same answer which is one less than total or they all different so P0 is the truth.
This is the same logic I followed and it works. Suppose that there are only two truth tellers. And now suppose they didn't shake hands to each other. Then both would have answered "0". That is not possible because we only have one person that said 0. Now suppose that they did shake hands. Then both would have answered "1", but that again is not possible because there's only one person that answered "1".
You can try all possible combinations but with any given number of truth tellers there is not possible way to make them shake hands in a way all of them would have shaken hands with a different number of people in the end. There will always be at least two of them that shook hands with the same number of truth tellers.
Therefore the only possible situation that works is for one and only one truth teller to be in the group.
54m0h7
It does get more complicated that way. That would mean that person 1 would ALSO be a truth teller because he shook hands with person 0 who is a truth teller and he said he shook hands with one truth teller. Person 0 though, said he shook hands with no truth tellers, and since he is a truth teller that must be true, then making person 1 a liar. If person 1 is a liar so is person 0, but that would mean person 1 is telling the truth subsequently making person 0 a liar.
A good old paradox.
It actually only works if not everyone has shaken hands with everyone.
I had some trouble with this, because I had assumed that everyone had shaken hands with everyone... It was obvious to me that we were looking at person zero, but then person one (a liar) would be telling a truth since he would have shaken person zero’s hand.
If 1 shakes his hand with 0 then 1 would be a truth teller.
I GOT THIS RIGHT! Ahhhhhhh ahaha got a little too excited 😂
What if they shook hands with someone more than once?
Doesn't matter. How many or few handshakes is inconsequential because the question asked to each person is, "how many truth tellers did you shake hands with". If person 99 were presumed to be a truth teller, he might have shaken hands with each other person at the party twice (198 total handshakes), or maybe he shook hands with one poor guy 1 million times and everyone else just once. It doesn't matter; a person only counts once as either a truth teller or a liar regardless of how many times you shake hands with them.
Yes exactly. Person 0 could have been shaking everybody's hands 555678765 times each, it still would've made his statement true. Well, except from having shaking hands with person 1, since that has been concluded could NOT have happened!
I just came accross this puzzle 7 years later. Nice explanation, however it can be made more precise if someone knows a bit of graph theory: consider the graph of truth tellers, where the vertices are the people, and the edges are handshakes between them. It is easy to see from the pigeonhole principle that any simple finite graph with at least 2 vertices has at least 2 vertices with the same degree. The degree here is the number of other truth tellers a truth teller shook hands with. From this, we can see that if there were more than one truth teller, there would be at least one number duplicated in the list. Therefore, there is at most 1 truth teller. It is again easy that 0 truth teller is impossible as well, so there is exactly 1 truth teller.
The argument by induction is elegant, but I came up with an alternative:
1. All truth tellers would give the same answer. Since there are no duplicate answers, there can be at most one truth teller.
2. Since any possible answer (0 to 99) has been given (at least) once, the correct answers must have been given (at least) once i.e. there is at least one truth teller.
From 1 and 2 follows there is exactly one truth teller.
My way was:
1. there must be at leadt 1 truth teller because if everyone is a liar then the answer 0 had to be the truth which is a contradiction.
Then i checked for 1 and it was fine if the truth teller is person 0.
Then i checked if it would be possible to have more than one truthteller.
If there were 2, they either shook hands or not, so they either both said 0 or 1, so 2 is also wrong.
With every other number greather than 2, there have to be at least 2 truthtellers who shook hands with the same amount of truthtellers than at least one truthteller, since the number of handshakes has to be smaller than the number of truthtellers. So the only way would be if every truthteller shook hands with 0 to n other truthtellers but if somebodey is a truthteller and didnt shake hands with an other truthteller, the maximum amount of handshakes a truthteller could make with other truthtellers would be n-2.
Amd between 0 and n-2 are only n-1 integers, and every answer greater than 2has to be wrong
This sounded much less confusing in my head... I hope you get the idea 😂
I got that! I'm impressed by myself :-)
Daniel Greis it can't be one because if if he said one that means he shook hands with another truth teller and i doubt he shook his own hand
I'm not gonna claim I read into this comment too much, but it wasn't fine if the truthteller that person1 shook hands with is person0, because person0 claimed he didn't shake hands with any truthtellers.
What if person 0 is a liar.
He said that he didnt shake hands with any truth tellers even if he would have.
not possible, at the beginning of the video is stated that truth tellers always tell the truth and liars always lie
How do you know that 0 is one of those who always say the truth? If 0 is a liar, then 98'statment can become truth
+BEST LEE SIN LAN If 0 is a liar that means 99 is a liar too so 98 could shake hand's max 97 true tellers so 98 is a liar too.
If person zero was a liar, then there would be no truth tellers, thus creating a paradox.
Well, there is an infinitesimally small chance that person 1 shook hands with person 0, therefore disproving this answer and actually making it impossible to solve (thanks to infinite regression)
I love it! 😊 NOT being sarcastic. 😍
OOOOOOOOOOOOOOOOOOOOOOO
I GUESSED THAT!
If you answered like this:
"There can't be 99 truth tellers at the party because the liar would have lied. So... What about 98? *and so on*"
You did what I did.
I KNEW IT. But the way I got my solution is different: with 100 different answers, then it obviously boils down to just one
There is no paradox as long as person #0 and person #1 never actually shook hands. Shaking hands was never a requirement.
The correct answer is no one is a truth teller, as the riddle never states that anyone knows what anyone else is. It's therefore impossible for anyone -- even Person 0 -- to know how many truth tellers they shook hands with; they'd be lying if they said 0 or any other number.
This is incorrect. If a truth teller gave a definite answer despite not knowing how many truth-tellers they shook hands with, that would mean they'd be lying which is not something a truth-teller can do, instead they'd say something like "I don't know". If someone provides a definite answer that means it's a either a truth-teller telling the truth or a liar telling a lie, so there's no ambiguity.
@@ceasebenjaminbeast3947 Incorrect. It is absolutely impossible for any of them to give an answer if they're truth tellers. Even the guy who says "0" is lying, as he has no idea if he shook hands with a liar or truth teller at any point.
No one -- absolutely no one -- in the scenario said "I don't know." Thus they're all liars.
@@DocFunkenstein Actually you are correct. If you follow my logic that means person 0 is undefined. If he's a truth-teller that means he knows he didn't shake hands with a truth-teller, but he could also be a liar that doesn't know how many truth-tellers he shook hands with. The true answer would be "I don't know" but since he's a liar he wouldn't say that.
So person 0 is either a liar or a truth-teller, but since the video never explicitly stated that anyone knows who the truth-tellers are and nor are there any truth-tellers aside from person 0 then it makes the most logical sense that person 0 is a liar as well
@@ceasebenjaminbeast3947 No it’s not correct. You cannot have all liars. if person 0 is lying that means he shook hands with at least 1 truth teller since he cannot say the truth...so there would be between 1-99 truth tellers....if there is a truth teller, then there number has to be correct. If their answer is correct then a contradiction will happen.
Therefor 0 can’t be a liar. 0 could easily have been the truth teller, maybe he was a germaphobe and touched no ones hand...he doesn’t have to know who is who to be saying the truth
@@jonathandpg6115 That's not really what I was talking about. My point was that if liars will always lie and they also don't know who's a truth teller or not then they'd be lying if they gave a definite answer. If they don't know who's a truth teller or not then answering "0" is as good a lie as any other
I see a big flaw here
Where in the question is the specification or indirect reference that the person with a number has stated they have shook hands with the same amount of truth tellers as the number assigned to them?
Where is the info that indicates that ensures that each person gave a unique answer... And not have multiples of the same answer... It only states range, not specifically saying that each person said different number
"Each person gave a different answer..."
+LegendBegins Gah ur right
I skipped over that despite spending 5 mins on the screen paused.... My bad
Adil Zia
"each person gave a different answer"
That obviously implies what you tried to say wasn't there.
As for the numbers being assigned to the people, that really doesn't make a difference. I'd assume it was just a way to explain it a bit more easily, and with no real effect on the final answer. They're asking about quantity, not the specific number assigned to the people, so that doesn't change anything.
Nice try, but those objections are invalid.
if nobody shaked hands there are 99 liars
My favorite strategy of taking things to an extreme worked on this one: Assume no one shook hands. In that situation, everyone shook 0 truth teller’s hands, therefore only the person that reported 0 is a truth teller. It doesn’t show that it’s the only solution, but if there were multiple solutions you couldn’t provide a conclusive answer and it wouldn’t be a very good riddle.
If they're allowed to shake their own hand, everyone can be a truth teller, and 0 didn't shake anyone's hand. :3
Yeah but then you’d have to still prove that’s the only solution for it to be complete but it would be a quick way to get a starting point.
The answer to your puzzle is wrong. The question creates a self referential answer and creates a paradox between 99 & 100 liars at the party.
If person 0 is a truth teller. Then person 1 is telling the truth in that they shook the hand of 1 truth teller. Which makes person 0 a liar, which makes person 1 a liar, which makes person 0 a truth teller, etc....
Thank you! The puzzle actually *is* impossible, at least when the process goes down like this.
Even weirder: When I initially tried to figure this one out, I first assumed that each of the 100 guests would also *ask* each other guest upon shaking hands if they are thruth-tellers or liars, who would then each lie or tell the truth. Seems more complicated, right? Well, under *that* premise, the puzzle *can* actually be solved, and it´s super simple: If you ask a truth-teller if he´s a truth-teller, he will tell you he´s a truth-teller. If you ask a liar, he will also tell you that he´s a truth-teller. In short, everyone will tell everyone else that he´s a truth-teller. This means that there´s only one actual truth-teller: The one who claimed to have met 99 other truth-tellers.
Your logic is flawed, there is no self referential loop. If we assume person 1 is a truth teller then that means he is telling the truth about person 0 being a truth teller, but this is impossible because person 0 cannot be telling the truth about shaking the hands of 0 truth tellers because he shook the hand of person 1 who is claiming to be a truth teller! Therefore person 0 has to be lying, but that's also impossible because if person 0 is lying then that means person 1 lied about saying person 0 is a truth teller!
Therefore, it's impossible for person 1 to be a truth-teller.
There is no condition that says 0 shook hands with 1. But yeah should have been mentioned in the video that 1 can't have shaken 0's hand.
@@user-zj9rr6yc4u Why? The reason person 1 didn't shake person 0's hand is the same for every other person in the group
@@ceasebenjaminbeast3947 2-99 can have shaken 0's hand just fine but yes it is in the options for how 1-99 might be lying. But why it should have been mentioned is because it is an explanation and that is a point that obviously confused quite a few people as you can see in the comments.
My logic: Because they all gave different answers, only one can be the truth. So there is one truth teller, and thus 99 liars
But they didn't have to shake hands with everyone at the party, so it was possible that there were more than one truth tellers.
Not necessarily. In this example, it is claimed that between 0-99 truth teller's hands had been shaken. If the numbers instead had been 1-99, then the answer would have been different.
It's the 0-answer that makes person 0 being a truth teller, not that it automatically has to be a truth teller since everybody else is lying.
I dont even get the basics here.
how should any of the 99 people know if they shook hands with a truth-teller or not?
But what about person 1? Since person 1 said there is one truth teller which would make his statement true (assuming the video's answer is correct) and he cannot shake his own hand and that also makes person 0's statement false? Then working upwards it gets confusing.
Person 1 cannot be a truth teller. This problem does not contradict itself.
Person 1 did not shake hands with person 0. This is a conceivable fact.
If they did shake hands, then it would break the universe.
What about person 1? He shook hands with one truth teller?
You're right Presh. Or this entire scenario can be turned upside down by saying 0 is the only liar and 99 shook hands with themselves.
Or presh talwalker is one of the liars and this entire question is a lie
0:09 my goodness, what an idea, why didn't i think of that
This problem: *exists*
Person 0: *there are 99 impostors among us*
Somehow I guessed the answer intuitively. Now I am trying to figure out how I did that. Much easier to follow the logic of the solution give.
There's an extra detail that should be noted: person 0 could not have shaken hands with person 1. If he did, then person 1 would've been telling the truth but we already know he's a liar.
this riddle can easily become a paradox.
if you state person 1 and 0 did shake hands then person 1 is telling the truth and 0 is a liar but then that means the opposite is true and it is a state of constant swapping till your head explodes or you give up
But if only person 0 is a truth teller, person 1 can't be lying because he has shaken hands with person 0 and therefore has shaken one truth teller's hand.
That was really easy, I mean my thought process was a watered down version of what you did, but it should have been obvious. Like I'm stupid and I didn't have to pause the video.
Since this problem is equivalent to any number of guests you can easily deduce the argument for only three guests. Assuming 2 truth teller you immediatly see a contradicition. One says "2" and the other "1" (or any two different numbers 0,1,2). Either way, one must then be a liar.
lol i just guessed it in first glance by assuming no one shaked hands with no one at all during the party, in which case only 0 was telling the truth