How To Solve The Seemingly Impossible Escape Logic Puzzle
ฝัง
- เผยแพร่เมื่อ 19 มี.ค. 2016
- An evil logician takes Alice and Bob captive. They have a chance to escape if they can deduce the total number of trees in the prison. Can they figure it out?
Source of puzzle
wu: riddles forum www.ocf.berkeley.edu/~wwu/cgi...
xkcd forums forums.xkcd.com/viewtopic.php?...
Blog post: wp.me/p6aMk-4wj
UPDATE: It looks like they can actually escape even quicker than I explained! The video is correct, but there are actually a couple of more deductions for an optimal solution. Details here: puzzling.stackexchange.com/qu...
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My video still is correct, but it turns out there might be an even quicker way they can escape! I came across a solution of 4 days at Puzzling.StackExchange: puzzling.stackexchange.com/questions/45664/are-there-eighteen-or-twenty-bars-in-my-castle
Why can they reduce by 1 more day? The reason is Alice sees 12 and Bob sees 8, and they know the total is 18 or 20. Thus, each knows the other person sees an EVEN number of trees. This reduces some of the possibilities. Furthermore, each has to assume the other sees at least 1 tree, so they know the minimum number starts out at 2. If you go through the similar reasoning in the video, they can figure it out on the morning of the 4th day. Here are the details at Puzzling.StackExchange: puzzling.stackexchange.com/questions/45664/are-there-eighteen-or-twenty-bars-in-my-castle
The solution only gets reduced by a day if there's reason to believe that each person must see at least 1 of X object. The iteration provided on Stack Exchange makes it explicit that it's not possible for either participant to see zero steel bars. This isn't an assumption, it's an outright stated fact that both prisoners are aware of. In your video, this is never a fact that's outright stated and the scenario doesn't really make it reasonable to just disregard the possibility that one of the cells may actually see 0 trees. Therefore, you have to factor in that possibility into your reasoning.
Adding to that, the semantic between listing all odd-numbered possibilities or not really doesn't change the outcome in any way because the answer's virtually identical in both scenarios. One's just more complete and the other's a convenient short-hand.
On day 4, Bob realizes she must see at least 12 trees. He sees 8, so when the logician asks Bob, he could easily know that there are 20 trees in total. Easy way to get them out a day earlier.
Note the comment on the StackExchange page of 2012rcampion Nov 15 '16. You gave no rule that the number of trees must be either 18 or 20, so as far as Alice and Bob can determine the correct answer to the evil logician's question could be "no". After day one they can both reason that the other can see at most 20, but I don't see how they can figure out more on latter days.
On the other hand, since you didn't say which statements are "rules of the game", one could take the number of trees each sees as rules, in which case they can answer immediately.
I think it's doable in 2 days.
Why can they not start with the information of day 4 on day 1 and save
them 3 days? They already have the information that the total number of
trees is either 18 or 20 so they can just use simple substraction of 18 or 20 - the numbers of trees they see, concluding that Bob must see 6 or 8 trees and Alice sees 10 or 12. But in the provided
solution it's only at the end of day 3 that Alice realizes that "Bob
must see at least 6 trees", which she should have known from the very
beginning. The same is true the other way around. Bob, seeing 8 trees
and knowing there is 18 or 20 in total, can conclude that Alice sees
either 10 or 12. For some reason, he realizes that "Alice sees at most
12 trees" only on day 4.
Pls feel free to correct me if I'm missing something..., but it looks to me like they could start
day 1 with the same status of information gathered as on day 4 and thus solve the whole thing
in just 2 days which should be in their interest, because prison food is
bad.
I think you're right. From the start, Bob knows Alice must have 10 or 12. And he knows that if she has 12, she knows he must have 6 or 8 (so he must have at least 6). So they can skip right to day 4, the first 3 days will always play out the same, and if they're both perfectly logical they will realize that both would just pass 3 days in a row.
Let's face it, real Alice and real Bob would be screwed
844 likes with no reply! Geez, well now you know!
How do u know the other one has applied the same logic,
@@stoic4life631 exactly.
How does Bob know what Alice is being asked? They cannot communicate and I'm sure this logician isnt telling them what the game is
@@paddykriton3475 Good point.
Question: "Are there 18 or 20 trees?"
Answer: "Yes, there are 18 or 20 trees."
True. The original riddle doesn't give any way of knowing that either of the numbers given are true.
+Calliope Pony I also though at first he was asking logically if there are 18 or 20 trees in the prison, not giving the options between the totals being either 18 or 20...
+Calliope Pony I agree!
WIN
+Calliope Pony There could be 19, or 12, or 25, or 26. How do you know?
“Can they escape with certainty”
Here’s my logic:
If the answer is no, there would be no solution, therefore the answer must be yes.
So, yes, yes they can.
That was an easy puzzle
There could also be a semi-solution that does not guarantee escape but grants a higher probability to get to it. Even though it would not be a perfect solution, it would still be a solution and would provide the best thing to actually do.
When you use 300% of your brain
The answer is Bob’s first guess of the first day, review my work in the above comment!!
My first thought to this puzzle is why would either person see a different number of trees each day? I still don't get how that could be the case. If two prisoners see a different number of trees and can't communicate with each other, and don't see any of the same trees, it stands to reason that they are in separate sections of the prison and there for would only see the same number of trees each day.
Statistically speaking each prisoner is offered the same question with the same two answers. They both have a 50% chance of being right. So a 25% chance total.
The puzzle has a logic flaw. Because there are only three options. Option 1. Alice says "18" gets it wrong and they are imprisoned forever. Bob won't even know why. Option 2. Alice passes in which case the question goes to Bob to answer. Option 3. Alice says "20" and it once again goes to both to answer. But regardless of whether Alice gets option 2 or 3, Bob has no way to know which case it was. This information isn't passed to him. Just like Bob's logic process isn't passed on to Alice so she has no way to determine if Bob has made any logical assumptions on the number of trees there are.
In order for this logic process to work, Bob would have to be told if Alice passed or not and vice versa. Since this is not communicated per the rules of the puzzle, there is no way to validate whether there is 18 or 20 trees total. The best you can hope for is that Alice or Bob guess right while the other passes. Just by the prison warden showing up the next day lets both parties know either the other guessed correctly or passed. So whoever guessed and got the right answer guessed right and just repeats the same answer each day.
I'd argue that even if both people passed, that eventually one or the other would assume that the other guessed a number and got it right since the evil warden keeps coming each day. Eventually one or the other will take a chance and that will be followed by the other who also will chance it. This doesn't improve their odds, but it does bring the game to a swift end. I'd say within one to two weeks both prisoners would guess a number. Right or wrong.
So how to approach this puzzle with no way to communicate?
Let's start with Alice. She sees 12 trees. She is told there is either 18 or 20 trees and to pick. If she sees 12 trees, then Bob must see only 6 for the answer to be 18. So he sees half the number of trees she does. If she thinks the answer is based on some principle of 6, her response will be 18. If she thinks 6 is too low of a number when she sees 12 and there is at most 20 trees total, then she will likely answer with the higher of the two numbers which is 20.
Bob has the sucky part of this as he only see 8 trees. He also has to decide if there is 18 or 20 trees. He has to decide whether Alice sees 10 or 12 trees. Since we are told that the warden of this prison is a logician, we can assume both prisoners are aware of this. Bob will look at the correlation in the numbers. There is no correlation to be made if Alice sees 10 trees. There is a correlation to be made if Alice sees 12. As both Alice and Bob would see a number of trees that are divisible by a factor of 4. By that simple stand of logic it is assumed that Bob would chose 20 as the answer.
Ultimately it would probably come down to Alice. Whether she would chose 18 and thus see the more obvious correlation to the number 6 or chose 20 as she would see the less obvious correlation to the number four.
I was actually thinking the answer was no, because a guess isn’t certainty in my mind 😂
Real life version would be 27 trees and the guy would just kill them anyway, but he just wanted them to feel like they could escape lol
Real life version Alice and Bob would be screwed
*XDDDDDD nice one*
I don’t think 27trees would make any difference
Real life version is that they couldn’t solve it.
@@lightsuplighto4226 no, they mean that the evil guy just wanted to mess with them.
when the logician comes into her cell and asks her if there are 18 or 20 trees, she could just say "yes" and they would both be set free.
TheUnknownBlock if there were 20 trees she would have been wrong because she said yes to 18 first.
Arc Valles no actually he is right.
TheUnknownBlock Nice
roger
hahaha ikr
I have an answer. Are there 18 or 20 trees?
Me: 18
L: NOPE
Me: but if there is 20 trees, there must be at least 18
in total...
Figgin noice.
"are tere 18 or 20 trees?"
"yes"
A logician must agree with that answer
L: TRIGGERED
CamoB2002 no actually lets say alice says 18,ti make sure bob just has to say 20..because fir fuck sake they can hear each other if they can tell if one of them has passed,then one says 18 and the other says 20 ansmd goood
Let's look what would it look like in reality.
Day 1
Alice:I pass
Bob:I pass
Day 999999
Alice: I pass
Bob passed
Alice was imprisoned for 2,740 years? Is she a Time Lord?
day 1000000
alice: ded
lol!
If they can't figure it out by logic, they will just guess -> 50% chance of success and if they fail, is isn't any worse than passing for the rest of the life.
bob passed LMAOOOOOO he ded
Alice on day 5: Oh, so there are 20 trees!
Bob every day: Idk so imma pass.
Logician: *Too bad Alice, the correct answer was 18, you will both be trapped forever.*
alice: y tho
That's why it's mentioned that both are perfect logicians
@@kyro7482 no its not
@@fyoutube2294beginning of the video
But Alice saw 12 trees, and Bob saw 8 trees, and 12+8=20
Since they don't communicate with one another, how do they know who was asked first? Also if Bob or Alice are anything like me they never would of thought logically like this :-P
Omg.. Xisuma also watching this! :-)
haha
+xisumavoid He says at the start that it assumes they both can reason with absolute precision.
+xisumavoid I guess the fact that alice is asked first is in the rules, and it says that both know the rules
heyy fancy seeing you here man. how's it going? are you going to make any more scrap mechanic videos?
The correct answer would be yes.
👍
+Vladimir Karkarov lmao it took you 6 words to answer what took him 6 minutes to answer xD
+Vladimir Karkarov
I love it. Hoist the smarmy logician by his own formal-logic-answer petard.
+Vladimir Karkarov And how do you know that that interpretation of the question is not what he intended? Perhaps he was testing if you could deduce with certainty that there are either 18 or 20 trees and not any other number of trees.
countoonce Because if that were the case, being a Logician, he would have explicitly indicated that. This is catching the guy in a grammatical loophole.
I understand how this type of logic problem works, but I'm not convinced that the reasoning works in this case. Since Alice knows that she sees 12 trees, and since she knows that the total number of trees that she and Bob see is 18 or 20, then she knows from the very start that Bob sees either 6 or 8 trees. She doesn't need to go through the process of eliminating the possibility that Bob sees 0 trees, or 1 tree, etc.
Likewise, Bob knows that he sees 8 trees and that the total number of trees they see is 18 or 20, and so he knows from the very start that Alice sees either 10 or 12 trees. He doesn't need to go through the process of excluding 20, 19, etc.
Yes you do, because you dont know which of those two each person sees, and the only pure logical way to reach certainty about WHICH of those two it is, would be the method above.
@@esmith2k2 But what is the point of eliminating a possible number of trees that the other person sees (e.g., Bob sees 0 trees, etc.), when you already know from the start that the other person certainly does not see that number of trees? Isn't that number already eliminated from the definition of the puzzle, since both Bob and Alice know the only two possible values for the total number of trees?
@@Paul71H theyre eliminated, yes. But what im saying is you need to go through the entire logical process presented in the video to reach the CERTAINTY of 18 or 20. You cant "start" at what youre suggesting because you used a different logical process to reach that conclusion, and that process wont give you certainty. So you are correct that you HAVE that information, that you suggest, but you'd have to just re-learn that information again following the process to get that final outcome. Similar to a fork in the road, one of them goes 80% of the way to your destination and the other goes all the way. If you take the path that goes 80% of the way, you need to walk back and go down the entire full path even if the first 80% of the paths are identical if that makes sense.
@@esmith2k2 I've seen other logic puzzles like this, and I understand how they work. The problem with this puzzle, that makes it different from similar puzzles I have seen, is that Alice and Bob have an extra piece of information (the possible values for total number of trees) that they would both have to ignore in order to go through the logical steps in this video. And why should either of them assume that the other one is going through a logical process that ignores this knowledge?
For example, the video says for Day 1, "If Alice saw 19 or 20 trees, she could conclude there are 20 trees. She sees 12, so she passes. Bob realizes that Alice sees at most 18 trees." This is true, however Bob already knows that Alice sees either 10 or 12 trees. So he already knew that Alice does not see 19 or 20 trees, without needing to wait for her answer to reach this conclusion.
The solution to this puzzle does make sense in a certain way. But I don't think it quite works, because I don't think that either Alice or Bob would reason that way, given that they would have to set aside knowledge they already have. More importantly, I don't think that either Alice or Bob could assume that the other one was reasoning that way, and they each have to reason that way and know that the other one is reasoning that way, in order for the solution to work.
i still dont understand how alive knew bob must see at least 2
while she would be actually thinking bob must see at least 6
"Did you figure it out?"
Sarcasm.
Right!
I'm the guy that goes "20" on day 1.
Logician - "WHAAAAAA??? BUT HOW?"
"Well, you're a logician, and you have planted these trees in rows of four. So twenty..."
If i was alice i will say 20 because she see 12, and she can know he has around the same number, so i will say 20, and boom, i won. (3 years? Who care?)
Standing Ovation for this answer
Phteve what if they were to the side so Alice sees rows of 3 and Bob sees rows of 2?
Alice: there must be 18 trees!
Logician: HA NO
No he didn't, that's just an illustration.
It's not given that it is planted 4 each row...it's just shown in the image for explanation
This riddle is flawed. you said they are both told together they see all the trees. Automatically, on day 1, Alice should know Bob sees either 6 or 8 trees. And Bob should know that Alice sees either 10 or 12 trees.
That's right but how does that help either of them decide how many the other can see?
Because when Ben knows Alice sees 10 or 12 trees, he also knows that Alice knows similarly two potential numbers of the trees Ben sees, and the two have to be out of 6, 8 or 10. And vice versa. So if they are "perfect" logicians, the answer to this riddle is too long. They should be able to figure it out on... the third day?
Actually no, already on the second day.
You sure? I think they can't find it out at all if element47's idea was the case
Pretty sure. As in it's late and I'm tired af mode 100% sure just to get it out of my head.
A more functional version of the riddle is "less than 19 or more than 19?" it takes away the distraction that Alice starts out with more substancial knowledge that "Bob has 6 or 8" and Bob knows "Alice has 10 or 12".
billpuppies
That was my point, as well.
Oftentimes the delivery of this variant of logic puzzle is very poor.
But that would give them hints to follow the right logic. Asking 18 or 20 is a way of hiding the solution. He is an evil logician afterall.
@@sarangajitrajkumar6041 It hides it so well that the thing becomes unsolvable. In particular the "solution" from the video is just wrong. The reasoning presented relies on deliberately ignoring the fact that the other person can figure out how many trees you have down to just 2 options, and on assuming the other person will do the same for some reason.
@@abdulmasaiev9024 That's my thinking as well. Because we know there's no overlap of trees (no tree is seen by both Alice and Bob) then Alice knows that Bob sees 8 or 6, and Bob knows that Alice sees 10 or 12.
On day one Alice passes not because she sees less than 19 trees, but because she doesn't know if Bob see 8 or 6. Bob can NOT assume that Alice passed because saw fewer than 19 and reasoned that she couldn't eliminate 18 or 20 as an answer. This means on Day 2 two when Alice passes he can not assume it's because she sees at most 16 teams. Same on day 3 and 4...
Likewise, Alice can't assume that Bob's passing on the question means that he sees an increasingly larger minimum number of trees because Bob is passing only because he doesn't know if Alice see 10 or 12.
If the logician was truly evil, he would give them that question: "are there more than or less than 19 trees in total?" and the answer would be exactly 19
Day 1
======
Alice realizes Bob must see at least 2 trees.
Seriously? Why did she wait for Bob to "pass" to come to this conclusion? If she sees only 12 trees and the question was whether there are 18 or 20 trees then she would have realized Bob must see either 6 or 8 trees without waiting for Bob to "pass". Bob "passing" would not have provided any additional information to Alice.
They both need to start at common ground in order for their algorithms to iterate
Yes it can be solved in the second day. but it do gives information that Bob passed.
Alice knows that bob see either 6 or 8. (because she see 12 and KNOWS that they have to be 18 or 20)
Bob knows that alice see either 10 or 12 (for the same reason)
in the second day, Alice knows that if bob were seeing 6. he could know that Alice see 12. (because 6 + 10 = 16. impossible answer). But he passed, that means that he see 8.
then Alice can assume Bob see 8, therefore 12 + 8 = 20
@@yceraf it doesn’t work, but I’ve already explained it in detail in three other content threads so just know, it doesn’t work.
@@yceraf nahhh... from Alice's perspective, if Bob were seeing 6 trees then he would still be wondering whether Alice's got 12 or 14. there is missing information, the puzzle simply has no solution
We can also figure out there is no chance there will be two human smart enough to solve this riddle in a such stressing situation.
+SeaWater4ever Not really. I managed to figure it out in around 10 minutes, and they have all day to think about it.
I and my friend both figured it out independently. So in the improbable case that I were Bob and mu friend were Alice it would have worked. But then again, evil people cannot be trusted so he would probably still keep us locked up forever anyway.
A more important question is: when they get out, does Bob say "I knew you'd figure it out today" or "how the heck did you figure it out?"
lmao yes, all bob has to do is stfu in the cell and pass
Even if Alice and Bob weren't perfect logicians, they would still have a 50% chance of escaping, great prison logician.
Only 25%. There are 4 possible outcomes:
1. Alice guesses 18, Bob guesses 18 - prison for life!
2. Alice guesses 18, Bob guesses 20 - prison for life!
3. Alice guesses 20, Bob guesses 18 - prison for life!
4. Alice guesses 20, Bob guesses 20 - freedom!
@@AlcatrazHR Bob only guesses if Alice passes. The chance of escape is 50%.
@@AlcatrazHR Those are not the correct events. The video stated that "If either ever guesses incorrectly, then both are imprisoned forever. If either guesses correctly, then both are set free forever".
@@AlcatrazHR It's 50%. There is one guess by the first person who wants to make it. They either get it right or wrong and BOTH go free or both are imprisoned. It's first come first serve, not that both must guess right to be set free.
One thing I can’t quite get still: the assumption on the 1st day in order for the logic to kick in is that Bob assumes that Alice sees at most 18 trees. Which he already knew. Because he sees 8. Therfore, since he is well aware that the solution is either 18 or 20 in total, he must know that she sees at most 12. Precisely he knows that she sees either 10 or 12 trees. So in his mind, the solution is (8,10) or (8,12). BUT he must imagine that she is thinking about it, and therfore she is imagining he sees either 6, 8 or 10 trees. And the same went for her before: she knew the solution was defently either (12,6) or (12,8); but she also knew that Bob sees either 6 or 8 trees, which meant in her mind that he could think she sees either 10, 12 or 14 trees. Now way to narrow that down from any hand. Both pass. On day 2, as Alice is asked again and knows that Bob hasn’t answer the previous day, she has to assume that Bob thinks she sees either 10 (10+8=18, 10+10=20), 12 (12+6=18; 12+8=20) or 14 (14+6=20) trees. No way for her to throw out any of those possibilities since Bob cannot know for sure how many trees she sees, which would be the only logic reason to reject one of those hypothesis from her perspective. So there is no narrowing of the field. She then has to pass, knowing that the solution is either (12,8) or (12,6), which Bob has no way to know. Still, he has followed the same thinking process, and therfore knows she has to assume he thinks the truth for his view in her mind is either 6(6+12=18), 8(8+10=18; 8+12=20) or 10 (10+10=20). He can only dismiss the solutions he knows for a fact are falls, which are the scenarios in which he sees other than 8. So he does that. He cannot do anything else, so he passes too. That leaves them in the exact same situation as at the beginning of the day. It sounds like an infinite loop to me.
Correct. There is no logical solution to this puzzle.
They have to ignore what they see themselves as a starting point. The starting point is the extremes: Alice could see 20 trees and Bob 0. They both must operate on this setup.
Alice does not see 20 trees, so passes.
If Alice passes, Bob knows Alice doesnt see 20 trees. Then Alice could see 19 trees and Bob must see 1. Bob knows this to be false, so passes.
If Bob passes, Alice knows that Bob does not see 1 tree. Bob could see 2 and Alice 18. Alice knows this to be false, so passes.
If Alice passes, Bob knows Alice doesn't see 18 trees. Alice could see 17 trees and he should see 3. This is false so he passes.
This goes on until they reach what they see. The information they have is the end condition, not the start.
With these logic problems, knowledge gain is always relative to the problem constraints (not relative to other uncertainties). Alice’s initial answer further constrains the problem, as does Bob’s, and so on until you have enough information to solve the problem.
I think the best example of this is the Blue Eyed Man problem if you care to look it up (two possibilities, a constraint of “at least one”, and an initial condition; each day you just add one to that constraint until you know the solution). You learn nothing extra by knowing the two possible solutions.
So why would logical thinkers use the strategy which doesn't solve the puzzle instead of the strategy outlined in the video?
The informaton gained in the fisrst day is that Alice knows that Bob knows that Alice knows that Bob knows that...(repeated any amount of times) that Alice can't have 19 or 20 trees, which they didn't know in the beggining.
Bob knows that Alice is also thinking about what Bob thinks Alice thinks. Alice does the same, and again he knows it, and thinks about it. You could continue that an infinite amount of times. You can build a tree of what one person thinks of the other. At some level 'Alice sees 19 trees' appears. Each one is thinking about both possibilities of what the other one thinks, and they both know that the other one knows that they know that the other one knows ... (repeated an arbitrary amount of times) that they are doing this. So, while thinking, they go 'one step down the tree both ways', imagining what the other would think if they had that amount of trees, but the other person would also go down a step, and so on, eventually reaching that 19.
You only went down 2 levels of that tree(I think), which isn't enough. Try imagining what happens after they both know(and know that the other one knows etc.) that Alice has between 6 and 14 trees.
Sorry for that convoluted answer, I also probably Made a mistake somwhere and I also dont really get it, but the reasoning makes sense
"In reality, they were both average humans, and died of dehydration long before this type of critical, logical thought process crossed their minds. They were too busy complaining about not having an iPhone charger.
hold the god dam phone day 1 if Alice sees she has 12 trees and can only answer 18 or 20 bob must have 6 or 8 and if bob has 8 and can only answer 18 or 20 Alice must have 10 or 12 and if they don't communicate to each other in any way then this logic puzzle is fucking illogical!
*Samsung
+Tomas McCabe go ahead argue and grow up
Tomas McCabe iPhone is more iconic, and also more iconic to the dumber population who have the option. Dumber in terms of smartphone knowledge and operation, that is. Personally, I don't buy either. Both pointless.
after three days they died of dehydration ;)
[I didn't watch the whole video. The answer is clear]
The answer is 'yes'. They can escape, and can escape with certainty. The logician has devised the question with a careless loophole. (Assumption: Bob and Alice have been informed by the logician that the question actually _contains_ the correct count somewhere therein.)
The logician's question is grammatically closed, signalled by opening auxiliaries and modals such as 'are', 'is', 'do', 'does', 'would', etc.
The answer to a closed question is either 'yes' or 'no'.
L: Are there 18 or 20 trees in total?
B: Yes.
L: What?!
B: You haven't given me a choice between the two counts, you've asked a Yes/No question. "No" would be obviously wrong, since I would be excluding any possible correct answer by throwing out the baby with the bath-water.
L: Hey, I meant...
B: Never mind what you meant. I am not a logician. I'm not bound by any conventions over exclusive/inclusive denotations of the conjunction 'or'. I took Semantics 101 in university, not logic.
L: Damn, I should have asked Alice.
B: She was my prof. Sorry.
Right!
Grammar Nazis win again
she was my prof. sorry, thank you for that
I don't get why 'no' would be wrong.
What if their were 19 trees and that was the question? Then "no" would be the correct answer.
Wait, but if there are either 18 or 20 trees, wouldn't Bob immediately realise that Alice sees at most 12 trees
Of course Bob would know that immediately, but Alice doesn't know what Bob thinks. It's more like "Now Alice knows that Bob knows she sees at most 12 trees." So if Alice knows that Bob knows that she sees at max 12 trees and still passes, she can be certain he sees at least 8 trees, otherwise he could conclude that there are only 18 trees as 20 trees wouldn't be possible. This kind of information (also including the previous steps/days) is useful in the sense that both can conclude the same things, which is kind of a way of communication between them.
@@triplem6307 it's still 50 50 at the end of the day in a real scenario. Unless they plan before hand either of them passing can mean many other things.
@@ragingnep Not if they were perfect logicians, as the puzzle stipulates.
@@zaksmith1035 not sure about that but "wouldn't Bob immediately realise that Alice sees at most 12 trees" this means that they sure wouldn't follow the solution in the video if they were perfect logicians
@@zaksmith1035 the guy who trapped them is a perfect logician
After watching and re-watching the video I've realized a few things. It seems you are using recursion, one recursive function for Alice and one for Bob. Alice's recursion is deducting N while Bob's recursion is increasing N and after each recursion a check is performed whether or not you have the said amount of trees, if you don't have the said amount of trees then pass. The only problem is both parties have to know exactly what they're going to do before they get in there and begin their recursion on day 1.
Not really no. They know the rules. Alice is asked a question first, if she passes, then Bob is asked a question. So when Bob is asked a question, he knows that Alice passes. And when Alice isn't released on the same day that she passes, she also knows that Bob has passed. They don't need to know what the other one knows. As long as the other one passes, their assumption works regardless of why they pass.
@@thenonexistinghero This does assume Alice and Bob are indeed smart enough to do this in the first place.
Wouldn't Alice already know on day 1 that Bob has at least 6 trees? And wouldn't Bob know that Alice has at least 10?
indeed
Yes. Not only that, alice would know Bob has 6 or 8, and he would know she sees 10 or 12. But my reasoning isn't strong enough to know which parts of the long reasoning process above that could invalidate
Yeah and they would be out on the second day.
no they can t ,alice needs to know if he has AT LEAST......otherwise there is no progression each day therefore they can never know the answer
Ayman 22 ..they can..after the first day both of then will know the total no. of trees are 18 or 20.. they also know the "at least"
One piece of missing information from this: Alice and Bob would have to know that there's another person and that the other person is a perfect logician. If you don't know that the other person is a perfect logician, then you cannot assume they'd have figured out the trick you're talking about.
If I was trapped with someone like this IRL, they would choose a random option on the 1st day 100%. I know how these situations go down.
+Robin Dude They both know the rules, so they both know the other is a perfect logician.
Limit, are you saying you would guess or the other person?
jberda_95
*They both know the rules, so they both know the other is a perfect logician.*
The perfect logic skills aren't part of the rules. They're part of the set-up. "This riddle is a logic puzzle and it assumes that the characters can reason with absolute precision." That's not part of what Alice and Bob were told (their knowledge of the rules), that's part of the environmental factors. Now if it had been that the assumption was that _everyone_ who exists was that way (ie, that there were no people who did _not_ have the required ability) that might be different. A minor quibble.
One piece ha ? Thumbs up if you remember something ...
Alternate ending: Alice thinks in 4-day solution and Bob in 8-day solution. There's 18 trees. Alice concludes that there's 20 trees. They're trapped in cells forever
The problem as stated does not bear out being able to deduce the solution, because Alice and Bob can rule out specific numbers from the word go. They are not counting up/down toward a solution by eliminating options one at a time. Alice will always know Bob sees either 6 or 8 trees, and Bob will always know Alice sees either 10 or 12 trees, and they can't extrapolate from there. One of them will simply get frustrated at some point and make a guess because they have nothing to lose by guessing.
Exactly. Why would bob ever assume that alice can see all 20 or 18 trees when the que. says none of them can see total no of trees on their own .
I was surprised by the answer as well. Alice would immediately know that Bob sees either 6 or 8 trees, and Bob would know that Alice sees either 12 or 14 trees. Passing the turn doesn't change that, and doesn't convey any information. They will have to take the 50-50.
@@Tinkula you clearly didn't understand how it works...
@GamezGuru1 they actually did.
The proposed solutions are just arbitrary strategies that Bob and Alice are somehow assumed to both follow although they never had the possibility to align on which strategy to gollow firsrt.
This is also the reason why there is more than one way to "solve" the riddle at different times. All these "solutions" just assume that Alice and Bob somehow end up following the same strategy to assign meaning to the visits of the evil logicians, thus being able to pass information to one another about thenumber of bars.
If they follow perfect logics alone, they would immediately arrive to the conclusion stated by the previous comments: Alice would think Bob must see 6 or 8 trees while Bob thinks Alice must see 12 or 10 trees. If they don't follow any strategy, the visits of the logician won't be able to provide any more useful information to either rof them to change what they already know.
MISSING INFORMATION: Both Alice and Bob know that the capturer asks the same question to both of them every day.
Exactly
That's in the rules, which they both know. So it's not missing information.
It was never said that the logician told them that they each would be given the same question.
"If she passes, then Bob is asked the same question in his cell. If he passes too, the process is repeated the next day."
Sure sounds like the rules specify that they would be given the same question.
You are right. Also the problem is resolved very badly. Because you do not have the information if both know they've been told the exact same question you would have 2 possibilities (both did not verified the solution given above):
1. They did not know they have the same question. It is enough to conclude by Alice that: she receive the question in the riddle and Bob receive another question (for example) : ''Are they 15 or 20 trees'' or ''Ar they 15, 17 or 20 trees?''. For this example, the riddle will fall instantly and you do not have a sure answer.
2. They knew they had the same question, then they knew FOR SURE from day 1 that:
Alice knew Bob sees 8 or 6 trees
Bob knew Alice sees 12 or 10 trees.
And in this case they will escape from day 2, not day 5.
yea...but that means you trust the other persons logic
who says they are both perfect logicians? the rules. please read the rules, just as alice and bob did
+Yehoshua S. Second sentence: "This riddle is a logic puzzle, and it assumes that the characters can reason with absolute precision."
Alexander Blixt i know that. I showed how dumb the question was by reasking it and then answering it super simply
@ A Dying Breed: Oh my God. [shaking my head] Seriously?
I just have to reiterate what "Not Applicable" said. "Absolute precision" DOES equate to "perfect". They are synonymous. Try cracking open a dictionary. (If you do, you might also see that "falter" is not spelled "f-a-u-l-t-e-r".)
+Not Applicable only a sith deals in absolutes
There's a higher probability of screwing up this complicating sequence then to guess.
Firstly, the probability of blindly guessing correctly is 0.5
The probability of both of them possibly having the same mindset to carry out this scheme is less than 0.5
Sure, but what of it? They can never go below the 0.5 probability by trying, and whatever little chance they have of figuring it out + 0.5 is still larger than 0.5
I guess you could make an argument that the added chance is so small that spending some days extra in the cell is not worth it, but since the punishment is lifelong imprisonment, you really have to know how many years their life-expectancy to calculate it.
I see a flaw. There is no way to tell if the other is using logic when passing, or just being a wimp. So...
The premise at 0:05 is that the participants "can reason with absolute precision".
This doesn't work unless bob knows that Alice goes first and Alice knows she is going first
They are both told the rules
Also when asked 18 or 20 trees , needs to be told that there is either 18 or 20 in total .
+dynamo I disagree: the evil logician, being a logician, would not give a question that has no correct answer, plus he's the only authority and source of information so he must be honest otherwise the game would make no sense
+Roberto De Gasperi well he is an 'evil' logician
Ladies First :D
Just call the damn cops
EpicFinish9 yea true
lol
How can you if you can't even communicate with the person being held captive with you?
Elizabeth Schuyler how can you not understand a joke?
@@user-gf6nj1lh6i how can the commenter not realize this is a logic question(btw both of them realize that this is a supposed joke and question)
The real mind bending part of this for me is they have to ignore information they have and operate on a weaker assumption.
For instance, B sees 8 trees. If there are either 18 or 20 trees, then he knows A can see either 12 or 10 trees.
So when A passes and he learns A cant see 19 or 20, that information is less informative than what he could tell from his own tree count.
But if neither updates their information because it's less informative than what they already know, they can't iterate to the stronger conclusion
Exactly. I wasted 2 hours on understanding why not starting from Alice knows that Bob can see 6 or 8 and Bob knows that Alice can see 10 or 12 wouldn't be better until I realized in that case the time passing wouldn't provide any extra information and there wouldn't be any progress. Truly mind bending !
I see it like this: they must begin their algorithm on a common ground, which is the extreme situatuon of A seeing 20 and B seeing 0 trees. If A passes, that tells B this is false. That is the only shared piece of information they have. The trees they see individually is the end condition, not the starting point.
Like many have commented, there's no other chance for Alice and Bob to get free but to take a guess. No logic of their own can get them out. Both of them would have had to know and agree before they were jailed, what the passing of the question would mean for them. Problem there being that depending on situation and how the question is presented, there are several different ways this passing logic could and should be arranged. But here it is not mentioned that they even knew what the question would be before they were jailed, so no such agreement could've ever been made even if it would've been allowed.
There's also a false assumption on the first step of the proposed solution. Alice has absolutely no reason to ponder between 19 and 20 trees. Question is 18 or 20. She sees 12, so she already knows Bob sees either 6 or 8 but has no way of knowing exactly, so she has to pass. Same for Bob. He sees 8 trees, so he knows Alice sees either 10 or 12 trees, but no way of knowing exactly. Never ending loop is ready.
It's also not made clear in this puzzle, did Alice and Bob actually know in what order they were started to be questioned. When they get presented the same question the 2nd time, they only know that the other party has passed once or twice. But without knowing that exactly, any kind of accurate counting is out of picture already. This knowledge wouldn't help them out anyway, but points out to the importance of setting the puzzle accurately for us pretending to be them.
This is a good example of a puzzle where outside person who sees the whole picture can come up with some kind of reasoning to seemingly solve the issue....all the while neatly forgetting what the situation for the people in the actual puzzle actually is. Food for thought for people trying to solve other peoples issues. And good luck for Alice and Bob, they need that.
If Alice knows there are 18 or 20 trees and that she sees 12 of them, wouldn't she be able to conclude that Bob sees at least 6 trees just after day 1?
UPDATE: I am leaving this comment up, but we have examined it and determined exactly where this proposed solution falls apart.
=====================================
I think this solution holds together. Someone, please tell me if I got something wrong.
If Alice sees 12 trees, she knows that Bob sees either 6 or 8 AND that he would think that she sees either 10, 12, or 14.
If Bob sees 8 trees, he knows that Alice sees 10 or 12 AND that she would think that he sees either 6, 8, or 10.
They both reason that Bob would know that if Alice saw 14, she could only conclude that he sees 6 and she would be able to answer that there are 20 trees. Therefore, when Alice passes on Day 1, she knows that Bob will know that she only sees 10 or 12.
They can both reason further that if Bob saw 6 trees, he would then know that Alice must see 12 and he would be able to answer that there are 18 trees.
So when Bob passes on Day 1, Alice knows that he does not see 6 trees. She knows, therefore, that he must see 8 and thus that there are 20 trees. She answers correctly on Day 2 and they are both freed.
Am I right?
@@joanhall9381 You are not right. You are forgetting that from Bob's perspective, she will always pass with 14 because Bob can have either 4 or 6. Since this does not eliminate 14 as a possibility, you cannot do the rest of the logic that you have done from there.
@@ac211221 But Bob already knows that Alice doesn't really see 14 trees and therefore that she could not possibly think that he sees only 4. But he knows that she is not aware that he knows this. Thus, the only number that she could match with 14 would be 6. When she passes, then she knows for sure that he is aware that she doesn't see 14 (Bob already knew that, but now he is assured that Alice knows that he knows it). From there, everything proceeds on.
@@joanhall9381 You're on the right track with each starting out telling the other what they already know, but the shortcut you're using is invalid.
Your error lies here: "They both reason that Bob would know that *if Alice* saw 14, she could only conclude that he sees 6 and she would be able to answer that there are 20 trees. Therefore, *when Alice* passes on Day 1, she knows that Bob will know that she only sees 10 or 12." [Emphasis mine.]
*_The hypothetical, impossible Alice who sees 14 is not the one who passes._* She's not real, nobody asked her a question, she can't answer it, so she can pass along no knowledge or meta-knowledge. Both Alice and Bob can _imagine_ that Alice, and imagine the Bob that Alice would imagine, and so on, and they can imagine how any of their imaginary facsimiles _would_ answer a question if asked, but only the real Alice and the real Bob can answer a question. They have no way of telling the other that they are answering _as if_ they were a hypothetical version of themselves. They must answer as themselves using only information they actually possess.
Even if Alice-14 could give an answer, she couldn't use information from the real Alice to do it. That fake Alice sees 14; her Bob sees either 4 or 6. She doesn't know there is a real Alice seeing 12 (which rules out 4), so she cannot conclude that her Bob sees 6, making 20 trees total. So basically, you've got a hypothetical Alice answering with the real Alice's knowledge, while Bob must intuit that the answer real Alice gave actually came from a hypothetical Alice. Nope and nope!
Because only the real prisoners can answer,* and because the only knowledge they share is that the trees number either 18 or 20, Alice has to start from 20 and Bob has to start from 18's complement. As in the video, Alice's first "pass" says "I don't see 20," Bob's says "If I saw 0 I could conclude there're 18, but I can't; therefore I see at least 2." Alice "your minimum of 2 doesn't get me to 20; I see at most 16." Bob "If I saw only 2 I could answer 18, but I can't; I see at least 4," and so on. On the fourth evening Bob says he sees at least 8. This is the first time their common knowledge is news to Alice, but they had to go through that process to narrow it. Once Alice knows for sure Bob doesn't see 6, she can answer.
*There is a way to do the "I know you know that I know that you know" thing. It involves stringing the multiplying potential characters out into layers of branches and having each real answer collapse a branch. You can see that method following the link in Presh's pinned reply but I cannot caution against it strongly enough. The upshot is, you get the same answer (it takes them just as many days) after a lot more work and a splitting headache.
@@noodle_fc When A_12 answers, she is answering on behalf of both herself and A_14. Bob knows that the real Alice is either A_10 or A_12, and he knows that she thinks the only truly possible Bobs are B_6, B_8, and B_10. So Alice is bringing the idea of an A_14 into their real situation, which includes their actual shared knowledge. The message she's sending is, "Bob, you already know that I know that B_4 cannot possibly exist. That means that there is only one possibility in our actual reality that A_14 would fit in with, and that would be B_6. So since I'm not latching onto B_6 as an answer, that confirms that A_14 does not exist in our reality."
meanwhile IT students :
are there 18 or 20 trees? Yes.
Haha, very LOGICAL reasoning there.
That's the actual answer. It said it was a logician for a reason.
I thought it was supposed to be eighteen or twenty
But they could be wrong if you look at it that way...because it implies other possibilities:
« Are there "18 or 20" trees? » implies that there could theoretically be 21 or 15 or 436728134 trees and the correct answer in that case should be «No.»
true that!
Under the assumption that Bob and Alice are logical clones of each other mentally speaking then they could get out in 2 days. My reasoning is this, once they come to the conclusion that they could use the method above, they will then realize that they can skip the first 3 days and go straight to Alice telling Bob whether she has 13/14. Which she does not so she passes. Bob, understanding that she is starting with the higher possible number and skipping will then know that she doesn’t have 13/14 (14 being the only relevant number to him) and will decide that she has 12 or 10 and will pass. After this Alice then acknowledge that he doesn’t have 6 and will pick 20 because 8 is the only other alternative. Because she knows he doesn’t have 9 or 7 she doesn’t need to wait till the next day for him to set them free by making the decision.
As soon as they know the rules (that there's either 18 or 20 trees), Alice will know that Bob sees either 6 or 8 trees, and Bob knows that Alice sees either 10 or 12
The thing is neither can be sure how many the other person sees.
Okay, technically Bob can deduce Alice can see a maximum of 12 trees. As his only options are "18", "20" or "pass" so there must be 18 or 20 trees in order to escape. If Bob sees 8, he deduces Alice must see 10 or 12 as that's the result of adding +8.
But that doesn't get either of them anywhere, they'd have to work through impossibilities first to deduce the right outcome.
Alice knows that bob sees atleast 8 trees , and alice herself knows she sees 12 trees. Now, the no. of trees is not greater then 20. And the minimum no. of trees acc. to the criteria is also 20. so yepppp
@@RituSharma-wy4wm please watch video
@@arjunkhanna2450 They were going for alternative solutions... you cant try present a different solution that relies on the previous one
@@arjunkhanna2450 The video is terribile
No but they can't communicate and they don't know that the other person cannot see into their cell
Day 5:
Logician asks Bob: "Are there 18 or 20 trees in total?"
Bob: Aw shit......
Underrated comment here
@@potest_nucis8012 explain pls... Bob just doesnt know?
@@elohimaka i assume it means that bob finds out alice wasn’t using the same logic
Actually, since he doesn't know her number of trees, he would know by their logic, that Alice sees 10 or less trees, and would guess 18
@@brackencloud made no sense
The solution breaks the rule that they're perfect logicians. Bob should realize that Alice can see either 10 or 12 trees. Alice should realize that Bob can see either 6 or 8 trees. Which makes it so that no information is gleaned from passing. So, it will always be a 50% chance.
they also know that other one knows this. since alice knows that bob see 6 or 8 trees, she knows that bob knows she sees either 10, 12, or 14 trees. by passing, she is implicitly saying she doesn't see 14 trees. knowing alice sees 10 or 12 trees isn't enough info for bobthis still isn't enough info for bob, so he passes. this indicates to alice that he doesn't see 6 trees, and therefore must see 8, so the answer is 20.
@@tweekin7out Why does passing implicitly say she doesn't see 14 trees? Why wouldn't that mean she doesn't see 10 or 12? They are all essentially equivalent. In your answer (and the video's answer), there is an implicit algorithm that Bob and Alice need to follow to come to the correct answer. Since there are multiple algorithms, and Bob and Alice aren't communicating with each other, they cannot know which algorithm the other would be using.
@@wospy1091 if they are perfect logisticians, they would use whichever algorithm finds the answer in the shortest number of turns.
@@wospy1091 premise: there are either 18 or 20 trees. bob and i both know this and are perfect logisticians.
we each see our own set of trees and know there is no overlap in the trees we see.
we take turns saying either how many total trees there are, or passing. if we guess wrong, we lose and the game ends.
problem: what is the minimum number of turns to guarantee knowing the total number of trees?
1. i see 12 trees.
=> bob must see 6 or 8 trees.
a. if bob sees 6 trees, he can infer i see 12 or 14 trees, and can then infer that i know he sees 4, 6 or 8 trees.
he can further infer that i know he will infer this.
b. if bob sees 8 trees, he can infer that i see 10 or 12 trees, and can then infer that i know he sees 6, 8 or 10 trees.
again, he can infer that i know he will infer this.
c. bob can then infer that if i thinks he sees 10 trees, i must also see 10 trees.
he cannot infer that i see 8 or fewer trees, since he only sees 6 or 8.
likewise, he knows i cannot infer that he sees 2 or fewer trees, as i see 14 trees at most, given that he sees 6.
2. bob therefore knows i see either 10, 12, or 14 trees, and can infer that i know that he knows this.
a. if bob uses the same logic, i can infer that bob knows that i know he sees 4, 6, 8, or 10 trees.
3. it is therefore shared knowledge that i see 10, 12, or 14 trees, and bob sees 4, 6, 8, or 10 trees.
4. the valid combinations of trees that bob and i see given our shared knowledge, then, are:
18: [14,4],[12,6],[10,8]
20: [14,6],[12,8],[10,10]
5. on round 1, if bob sees 4 trees, he would know that i see 14 (the only valid combination containing 4), and therefore the answer is 18.
similarly, if he 10 trees, he would know that i see 10, and the answer is 20.
however, since he sees 6 or 8, he does not know which valid combination is true.
=> he passes
6. this confers to me that he doesn't see 4 or 10 trees, which i already knew. however, he now knows that i know this, and it becomes shared knowledge.
=> [14,4] & [10,10] are no longer valid
=> the valid combinations are now:
18: [12,6],[10,8]
20: [14,6],[12,8]
7. it is now my turn. if i see 14 trees, bob must see 6, and the answer must be 20.
however, i see 12 trees, so i do not know if bob sees 6 or 8.
=> i pass, implicitly conferring to bob that i do not see 14 trees.
8. the valid combinations now are:
18: [12,6],[10,8]
20: [12,8]
9. on round 2, if bob sees 6 trees, i must see 12, therefore the answer is 18.
therefore, if bob sees 6 trees, he can answer 18 and the game is won.
if bob sees 8 trees, he still can't know if i see 10 or 12, and passes.
10. if bob passes, he is conferring that he does not see 6 trees.
11. the valid combinations now are:
18: [10,8]
20: [12,8]
12. i see 12 trees, therefore the only valid combination given my current knowledge is [12,8]
=> there are 20 trees
13. the quandary can be minimally solved in at most four passes/two rounds.
The issue in your logic is in step 5. By considering Bob seeing 4 trees, that would change the possible combinations. The issue is, Bobs knowledge is a subset of the shared knowledge set. So Bob cannot consider any other number other than 8 for the number of trees he has.
Alice and Bob sure get into a lot of trouble on this channel.
There is a logical inconsistency here though. You said a logician is someone who can reason with absolute precision.
Therefore the So called "evil logician" should know that Alice and Bob will be able to escape. And therefore cannot be evil.
I think he'd still be evil. Imprisoning someone for any length of time for no reason is pretty evil.
WreckNRepeat Meh, Its a dick move at best.
How does that make him not evil? Far from it!
It's a _possibility_ of escaping unscathed, not a certaintly - he does _not_ know whether Alice and Bob are able to escape.
That's like saying someone shooting with guns in a kindergarden is not evil, because he might not hurt anyone in the process.
Even if you ignore the imprisonment aspect, he's still taking their freedom to force his world view on them.
And failure to meet his standards results in no less than death.
He deems anyone that does not meet a certain standard of logical thinking unworthy of living, and does not even give them the chance to educate themselves in any way before throws them into this scenario.
And _even if_ Alice or Bob were _both_ perfect logicians like him, they could not with certainty escape the prison since they'd also have to know about each other that they react that way, and not just pass out of fear.
So at the very least, he's forcing them to play Russian Roulette even if they both meet his standards.
That's like, four kinds of evil in my book.
»Dick move at best« doesn't even scratch the surface of how fucked up this whole thing would be IRL.
Evil is tied to moral and ethics, which again is subjective, ergo not logical (never an absolute yes or no to whether something is evil or not) => a logician have no concept of good or evil.
Pål Mathisen
»Evil is tied to moral and ethics, which again is subjective.«
Absolutely.
»Ergo not logical [...] a logician [has] no concept of good or evil.«
That seems misleading, if not outright wrong.
It's the premises that are subjective. From there, plenty of logical conclusions can be made.
Ethics are a highly rational subject, and logicians in particular will be able to derive a lot of world views and principles with a given set of assumptions.
or bob just keeps saying pass as he doesn't know and Alice gives him too much credit
+Edward Fisher This.
This is why the video has so many dislikes. The puzzle is so disconnected from any semblance of reality as to lose all meaning.
+Jason Henley the beginning of the video he says they have the ability to reason perfectly, which is not realistic of course but upholds the answer
No, the puzzle is valid. These types of puzzles are supposed to have hypothetical "givens" that are not questioned, even if they don't really make sense in real life. This is fine, as long as these givens are explained. In this puzzle, it is a given that Bob and Alice will pass if (and only if) they cannot logically deduce the correct answer with certainty, using logic. It is also a given that they know the logician isn't lying, so they know there are 18 or 20 trees.
I work as a professor of logic at the University of Science, and I can assure you that neither Bob nor Alice saw a doghouse.
Day 1: Logician comes to Bob's cell and tells him Alice passed.
Bob: I didn't even know she was sick
I have a solution, Alice or Bob should ask the evil logician how many trees he sees. If the evil logician gives a response, then the answer must be the opposite because it would only be logical that an evil logician would lie rather than be honest and truthful.
what the heck you did a AWFUL job explaining that
1. an*
2. He did a great job explaining it. If you didn't like it unsubscribe, there's a slight chance this level of logic is above you
1.im only a 6th grader so thats why i didnt get it
2.im not even subscribed to him
+Hannah McCoy don't watch this stuff if ur in 6th grade, u won't get it most of the time
I agree with you Hannah that he could have definitely done a better job explaining the reasoning. At first watch it is difficult to pick up on exactly why Alice is able to learn from bob passing each day. I hope you don't let rude TH-cam users dissuade you from watching informative and interesting TH-cam videos. I think that is a bad attitude for someone to have on a channel that's all about learning and logic. This should be an accepting community that encourages youths interest in learning.
+Joey Sisk It's not the duty of a TH-cam community to spoon feed a concept already adeptly explained in the video. If she felt he did a poor job explaining it, she could have asked for a clarification or watched the video again to see where she got lost. Simply stating that he did "a awful job" is unproductive and false.
"Are there 18 or 20 trees?"
"Yes."
*Frees self*
But...wouldn't Alice already know that Bob sees at most 8 trees, since she sees 12 and therefore Bob cannot see more than 8 trees?
Alice sees 12, and the total must be 18 or 20. So Alice thinks Bob must have 6 or 8.
At the same time, Bob sees 8, and the total must be 18 or 20. So Bob thinks Alice must have 10 or 12.
This information is an uncertain end result, the process is to narrow down until there is only 1 possible end result.
Alice passes. Bob says to himself _"Alice passed, so the answer based on what she's seeing doesn't make this completely obvious. So, if her trees doesn't make it obvious, then she would have to have 18 or less trees. I mean, duh, I have 8 here, but she doesn't know that."_ and then passes.
Alice says to herself *"Bob passed, so even though he knows I must have at most 18 trees, the answer still isn't obvious. That means he must see more than 1 tree, 2 at the very least. "* and passes.
Bob _"Now she knows I see 2 or more trees, but the answer still isn't obvious to her. She must see at most 16 trees."_
Alice *"So he knows I see at most 16, but it still isn't obvious to him, so he must see 4 or more trees."*
Bob _"So she knows I have 4 or more trees, and it still isn't obvious. She must see 14 or less."_
Alice *"So he knows I see at most 14, and it's still not obvious. He must have at least 6 trees."*
Bob _"...okay. She knows I must see at least 6 trees, and she still isn't answering. That means she must have at most 12. Now, when I pass, that will tell her I have at most 8 trees."_
Alice *"Oh! Bob must see at least 8 trees if he passed. It wasn't obvious whether he had 6 or 8, but now he can't possibly have 6. So the answer is 20."*
Bob _"Now, if you had passed again, I would have known You must only see 10 trees, meaning there was 18."_
@@liamwhite3522 better explanation than the video
@@liamwhite3522 thank you unexplained it better than the video i was dumbfounded for a second
The question says nothing about 0 or 1. The question clearly states that they are both asked the same question daily; 18 or 20.
If Alice and Bob know that there are 18 or 20 trees, that whatever the correct total number of trees is absolute and that they each see a unique set of trees, then on day 1, Alice would know Bob saw either 6 or 8 trees and Bob would know Alice saw 10 or 12 trees.
I had to rewatch the video and stare at the instructions for twenty minutes to understand even Day 1
At least you managed to understand it in the end :)
Boring Molly Yeah a little but they died of starvation on Day 3 so they wouldn't make it out anyway
+croco sillikicks lol pretty true
false, humans can live about a month without food, but not more than 3-4 days wiithout water
***** Okay so they died of thirst then. And sweet avatar
Assuming both Bob and Alice are smart people.
That was part of the given scenario, that they were able to "reason with absolute precision." He says this while the tree graphics are being placed at the very beginning of the video.
He says the characters can reason with absolute precision, but he doesn't say each character knows the other is capable. Without that information, it actually goes against both character's perfect reasoning to rely on some random pleb.
TL;DR: this puzzle is bad and you should feel bad.
actually, Bob could just be a complete idiot and keep passing because he doesn't know. Then they get lucky because it actually works out.
*Random Pleb!? Love it!*
Okay you people are ridiculous, let me spell it out for you: they're both perfect logicians and want to get out of there, here's the thing though, even IF they don't know the other to be a perfect logician, the answer they would give would be random if they weren't and the perfect logician-one at best, so assuming your partner is a perfect logician gives you the most chance of escaping because they COULD be and then not being it just makes it a game of chance, where it wouldn't matter what answer you gave. So assuming your partner is a perfect logician either doesn't change your chance of escaping or increases it depending on what your partner actually is, so assuming your partner is a perfect logician is the best thing you can do if you want to escape. QED. Alternatively, so the riddle isn't bad, QED.
C’mon, there are only 4 possible answers by the prisoners - 18/18, 18/20, 20/18 & 20/20 BUT trees are planted in rows of 4 in each. In Both groups. So 20 is more likely than 18
I think I have a quicker way:
Day 1:
Alice sees 12 trees and the possible amount of trees is either 18 or 20, so she concludes that Bob has either 6 trees or 8 trees, but she doesn’t know for sure so she passes
Bob sees 8 trees so by the same logic, he concludes that Alice must have either 10 or 12 trees. He deduces that if Alice had 10 trees, she would conclude that Bob has either 8 or 10 trees, and if Alice had 12 trees, she would conclude that Bob has 6 or 8 trees. Notice that if Bob had 6 or 10 trees, he would’ve instantly realised how many trees Alice has since 6 or 8 trees appear only in one of the two scenarios i.e. if Bob had 6 trees, he would’ve known Alice had 12 trees and if Bob had 10 trees, he would’ve known Alice had 10 trees. But since he has 8 trees, and this number of trees is a possibilty in both scenarios, he can’t say for sure so he passes
Day 2:
Alice deduces the same things as Bob and so now that Bob passed the last day, she knows that Bob was not sure about the number of trees otherwise he would’ve guessed instantly. So, she knows that Bob has 8 trees, therefore she adds 8 to the amount of trees she sees(12), and so she know that there is a total of 20 trees with certainty, so she says 20 trees and both of them are freed instantly
Edit: I think I see the flaw in my logic, Alice doesn’t know Bob has 8 trees so she wouldn’t reach the same conclusion that Bob did
If Bob saw 6 trees, he has to reason that Alice may see 12 or 14 trees (because 6+14 = 20). You're using logic from Bob who has 8 trees incorrectly.
Faster Solution: XD cut down 2 trees, burn them, pass, wait for him to ask the question again. If he asks 16 or 18 you know it was 20, so the answer is 18... ect. :P
Alice: Brilliant! I'll do just that! Now, how do I get pass these bars to burn two trees?
It doesn't say where they a trapped? She burns the 2 trees in her cell... How do you not understand this?
he wouldn't allow that. he would say 'were there 18 or 20 trees?'
+Robbie V i love it when my cell smells like stinging woodsmoke and i can't see any trees now because i'm blind
??????????????????????????????????????????????????????????????????????????
I've got a headache.
Lets face it, had Alice and Bob been that clever, they would have not ended in prison in the first place.
I don't understand why bod realizes alice sees at most 18 trees , can you explain ?. Thank you
because if alice sees more than 18 trees she can answer the question if alice see 19 or higher trees there cant be total 18 trees cuz bob cant have negative tree number :)
Yes, there are 18 or 20 trees in total. Can i have cockies now?
+HoermalzuichbinderB cockies huh?
+HoermalzuichbinderB Actually, that's a good question. Is the evil logician asking whether the total number of trees is equal to 18 or whether the total number of trees is equal to 20?
Or is he just asking whether it's true that the number of trees is equal to either 18 or 20?
+Scurvebeard ikr
Sure you can have a cockie, but I'm taking the cookie.
I'll stick with my cookies
I think there is a fatal flow on the logic of the solution here...Day 1 : "Bob realizes Alice sees at most 18 trees" is a very flawed logic. Bob knows he sees 8 trees and the answer is either 18 or 20 trees. Thus Alice sees at most 12 trees, it is impossible for Alice to sees 18 trees. And so forth, their logic is flawed...I think this is not how the puzzle should be
Alice could definitely say that the answer must be 20 if she could see 19 or 20 trees, therefore Bob knows that she must see less than that amount of trees, since she would have answered the question otherwise.
+Tyrian3k Ah, yes I understand that logic in the video. However Bob seems to disregard the logical conclusion that : If the Evil Logician is asking whether there are 18 or 20 trees total, and Bob can see 8 trees, it meant that there are only 2 possibilities for Alice : Seeing 10 trees or 12 trees, any other number is impossible. Thus the speculation of "Alice sees at most 18 trees" is illogical, since Bob knows that the only possible answer is 10 or 12, therefore "Alice sees at most 12 trees". If Bob is assuming that Alice sees at most 18 trees, that would mean that Bob is disregarding the fact that Alice sees at most 12 trees...Is this what a logician supposed to do ? Ignoring fact and making up new conclusion ? I honestly don't know
+Nito Terrania Same. Alice would think Bob probably sees 6 or 8 trees, while Bob would think Alice sees 10 or 12. That's my thought on day 1. Dunno if I missed anything.
+Nito Terrania I see your point, but here is what I am thinking. They kinda have to follow it down from the top to be able to figure it out, if they didn't do that it wouldn't work.
Let's say that Alice passes on the first day and it goes to Bob.
Bob then looks at his 8 trees and knows Alice has to see 10 or 12, but he doesn't know so he passes.
It then comes back to Alice without any more information than she already had, that Bob has to see 6 or 8 trees, and they would be stuck.
Thus it is logical to use a method that allows them to pass some sort of useful information.
+Nito Terrania Okay, here goes the thorough explanation (sorry for the length!):
It might seem as though no new information is communicated when Alice and Bob pass since each prisoner already has the other's number of trees narrowed down to two possibilities. However, new information IS being gained from each pass, and this new information is called "higher-order knowledge." What's changing is not what they know, but what they know about what the other knows about what they know about what the other knows... and so on.
From the very start, contrary to what is implied in the video, both Alice and Bob know that Alice doesn't see 19 or 20 trees. In fact, Alice knows that Bob knows this, and Bob knows that Alice knows that Bob knows this, and Alice knows that Bob knows that Alice knows that Bob knows this, and so on. The problem is, at the beginning of the puzzle, we can't extend that "and so on" infinitely - to be specific, we can only go 8 layers deep (that is, Bob knows Alice knows Bob knows Alice knows Bob knows Alice knows Bob knows Alice knows she sees less than 19 trees, meaning Bob has only "8th-order knowledge" of the fact that she sees less than 19 trees). Only AFTER Alice passes does the "and so on" become infinite, because this pass gives Alice and Bob a separate, independent source of this knowledge that they both share; they both now know exactly where the other's information is coming from and that the other knows the same about them. In logic, as you probably know, that means that this fact is now infinite-order knowledge or "common knowledge." It is by steadily accumulating common knowledge that Alice and Bob are eventually able to go free.
It's easiest to grasp this by first considering one of the later days, when Alice and Bob are closer to gaining first-order knowledge, and then adding layers as you work backwards. For example, on Day 4, let's take for granted (because it is in fact true) that Alice would only have passed if she saw less than 13 trees. Bob himself knew from the very beginning that she saw less than 13, so this doesn't change his first-order knowledge of how many trees she sees, but until that moment Bob doesn't know that Alice knows that Bob knows she sees less than 13 trees, so it changes his third-order knowledge. To put that in a less confusing way, until Alice passes on Day 4 Bob can't be sure that Alice is aware of how much he knows; Alice could be thinking that Bob sees 6 trees, in which case Bob wouldn't have yet ruled out the possibility of Alice seeing 14.
Once Alice passes, however, it makes no difference; whether Bob sees 6 trees or 8 (or 80 million for that matter) he''ll know that Alice doesn't see 14. So at that moment, something that Alice only knew to the first-order (she knew she saw less than 13 trees, but didn't know if Bob knew that) she now knows to an infinite-order. We can say that she has gained NEW 2nd-order knowledge (she now knows that Bob knows she sees less than 13 trees) as well as new knowledge of all higher-orders (because she now knows that Bob knows that she knows that Bob knows, ad infinitum). This new higher-order knowledge makes the fact the she sees less than 13 trees "common knowledge" between Alice and Bob. From Bob's perspective, something that he only knew to the second-order (Bob knew Alice knew she saw less than 13 trees, but Bob didn't know if Alice knew he knew that) he now knows to an infinite-order. We can say that he has gained NEW 3rd-order knowledge as well as new knowledge of all higher-orders. This "completes" Bob's knowledge of the fact that Alice sees less than 13 trees (whereas before it was "incomplete" because he only knew it to the 2nd-order) and makes the fact common knowledge between Alice and Bob. So, though neither has learned anything new about how many trees Alice sees and they both remain with the same two possibilities they started with, they are getting closer to being fully "on the same page."
It gets even more meta as you work backwards through the days, but by applying the same logic you can see that Bob gains 5th-order knowledge when Alice passes on Day 3 (that is, what used to be only 4th-order knowledge for him is now common knowledge), that he gains 7th-order knowledge when she passes on Day 2 (that is, what used to be only 6th-order knowledge for him is now common knowledge) and that he gains 9th-order knowledge when he passes on Day 1 (as I explained above, what used to be only 8th-order knowledge for him is now common knowledge). Likewise, Alice gains 3rd-, 5th- and 7th- order knowledge when Bob passes on Day 3, 2 and 1, respectively. So, even though it's subtle, information is always being gained, and each day Alice and Bob are "completing" knowledge that was less and less complete (that is, known to a lesser order) initially. Eventually, Alice gains 1st-order knowledge when Bob passes on Day 4 (that is, what she used to not know at all - that Bob sees at least 8 trees - is now common knowledge) and she can deduce, based only on conclusions drawn from their common knowledge, that there are exactly 20 trees.
Alice see's 12 Trees - EL Ask's "Are there 18 or 20 in total"
Just from this, Alice should know that Bob can see atleast 6 trees.
she passes to bob,
BOB can only see 8 trees, this tells him Alice see's Atleast 10 trees.
He passes to Alice,
Day 2 they're out? Skips the unnecessary 0 or 1 trees at the beggining.
This is what I came up with too. The puzzle appears to be set up so that we are to take the logician at his word, we either take his word and believe he's being honest with 18 or 20 and exclude possibility of 0 or 1 OR we assume he's lying and we have to check for 0 and 1 but then why would we also believe 18 or 20 trees to begin with?
If it is 18 or 20, then they both know this before anybody even passes. Before the first question is asked, Alice knows Bob can see either 6 or 8, and Bob knows Alice can see either 10 or 12.
I was looking for a comment like this; my exact solution as well!
So basically this channel is for poorly worded or poorly constructed "math problems" or "logic puzzles" that aren't really either one and generally have wrong answers. Or it's stuff you could have done in your head in two seconds without unnecessary formulas. So much fun.
This doesn't work. On the first day, just from hearing the rules, Bob already knows that Alice sees either 10 or 12 trees, and Alice already knows that Bob is seeing either 6 or 8 trees. Sure, they can ignore that knowledge to come up with a logic path that reaches the answer, but why would they assume that both are ignoring the obvious knowledge? They wouldn't.
Plus, and this isn't to make fun of the puzzle because logic puzzles aren't meant to be realistic, but it's kind of funny to imagine trying this solution in real life... Your partner would never come to the same conclusion. On the other hand, there's no reason not to try, because if they didn't follow your logic you'll have a 50% chance to get it right, but if they did follow your logic you have a 100% chance to get it right. Whereas, just randomly guessing is 50%. So you may as well try this solution.
+Nemo's Channel
There is reason not to try it when you're not sure your partner is doing it too: You always check the higher number first, so when your partner isn't doing it, you're bound to pick that one. Since the pick isn't random, a truly evil logistician would make it 18 trees, dooming every couple when only one of them gets the solution.
So, when you're sure your partner is an imbecile and the logistician is truly evil, pick the lower number.
23PowerL I like it. But if they were that evil, they didn't intend for you to have a chance anyway and may not let you out regardless.
+Nemo's Channel "it assumes that the characters can reason with absolute precision." Literally the first sentence after he says hello to us.
MrPolus24 I know. That's not good enough.
+Nemo's Channel using the knowledge that Alice knows bob sees 6 or 8 and Bob knows Alice sees 10 or 12 yields the same answer. It's just a little more complicated to explain
Why are evil logicians so trustworthy?
+Brian Schiefen because he knows he can't be a liar and try to explain everything like villains in movies normally do until some friends have enough time to kill him.
because he is a logician, lol.
The Evil Logician is Charlie from the other video. He could only reduce 9 minutes of work by working together with Alice and Bob. The whole world laughed at him. This is his revenge.
Too bad he stoopid.
Either of them can answer the question immediately using this deduction:
Alice can see 12 Trees.
She knows that there are either 18 or 20 trees.
There for she knows bob can see either 6 or 8.
Inversely she knows bob would therefore either guess (12 or 14 ) even if he could see 6
Or Guess (6 or 8) if he could see 12
Doing the math knowing that she can see 12 trees she knows that Bob cannot see 6 trees (because 12 + 12) or (12 + 14) exceeds 20.
And therefore, BOB has to see 8 trees.
She can conclude this without ever needing or passing information, and BOB could use the same logic as well.
The first day A sees 12 trees and assuming that either 18 or 20 is the total number (since one of the options must be right), she can conclude right away that B sees 6 or 8 trees. So at day 1, when A hears the question, she already knows that B must see at least 6 trees. The same goes for B: the first time he is given the question he realizes that A is seeing either 10 or 12 trees, so at most she sees 12 trees.
+x nick This.
+x nick +Feyyaz Negüs This is exactly how I thought about the problem. But I could not solve the problem this way. I finally decided to give up and watch the video. I watched it and it was disappointing, because based on our logic which I believe is the right logic, 1. the thought process described for day 1 is illogical, 2. I did not understand the logic following.
+x nick Yes, but after day 1, A does not know that B knows that she sees at most 12 trees.
+x nick Exactly what I thought in the beginning. If there are only 18 OR 20 trees, I wouldn't start off with "if he saw 20 trees". Or, as you said, continue the logic until the question comes to "does he see 6 or 8 trees?". Thanks for posting, so I can spare that. :-)
+x nick This was what I thought, but you can't use the same logic in this case: A knows B sees 6 or 8 trees, B knows A sees 10 or 12 trees, and either of them passing tells the other nothing about which of these two is correct. The incremental method shown in the video only works because you can start at the extreme end and work backwards, when you're already in the middle you're unable to eliminate the higher values. I don't think it's possible to solve from this starting point. This makes no sense; how is it that by knowing more from the start we have ended up being able to learn less?!
I figured it out, mostly thanks to that green eyes evil dictator puzzle being similar.
Ted-Ed?
Yup!
+pumpkinik I watch Ted-Ed I'm 9
im 6 and half and i wach teded and tedex
+Shlovaski I'm a zygote and I watch ted ed.
I read that question completely differently. I thought the it was a single yes or no question: "is the number of trees either 18 or 20?"
I had this going with the 2 tree difference on the first day but as you continue to add the logic from the previous day I got the understanding why Bob couldn't have confidently called 20 on day 4
"It is assumed that Alice and Bob can reason with absolute precision" - But it is not assumed that both of them know this. Therefore, it is possible for them to think that the other person might not be reasoning with absolute precision. Therefore, they cannot extract precise information just from the fact that the logician passes by. Therefore, the logician is truly evil.
The answer is Bob’s first guess of the first day, review my work in the above comment!!
Since they know that there are 18 or 20 trees, wouldn't Alice know that Bob sees either 6 or 8 trees and Bob know that Alice sees either 10 or 12 trees? Why all this time spent excluding cases that are known to be false from the start?
Because he needs to superimpose a pattern on passing. Which one he takes doesn't really matter, but both parties knowing of said pattern does matter.
Which leaves us with the problem of how both can come to an agreement over which pattern to use.
That was my thought too. Did they never learn simple subtraction?
Roddy MacPhee but cant they use the steps provided in the video just starting with the basic knowledge that Alice has either 10 or 12 and bob has either 6 or 8
Roddy MacPhee you can but it you will just get a higher 50% probability of getting it right. For ex. Imagine you're in a lottery with your friend and you have a chance to win 100$. There are 4 balls. Ball1, ball2, ball3 and ball 4. You can only pick one ball and your friend can also pick one ball. Let's say you both thought that ball2 was the right one, then only one of you should pick the ball2 and the other another ball since if u both picked the same your chance would be 25% but if u pick a different one it's 50%. Now imagine you're Bob you know for a fact that Alice sees either 10 or 12 trees, so if she saw 10 then she would think that you see 10 also so you could both pick 10 which would give you a smaller probability of getting the answer right, therefore you'll have a higher probability of getting it right if u decide that she sees 12 trees.
It was clearly stated in the rules that if one guess incorrectly, they both stayed in jail forever. Chances would be 25% no matter what with your theory.
My answer would be: Alice passes until day 12. On day 12 she stalls the time so bob doesnt even get asked that day. Because Bob didnt get asked and he can count the days he knows how many trees alice sees.
Or.....
Alice and Bob:
We du nottt speek engliesh.
Boom.
They both start out knowing the other's number within 2 trees.
+Ian Albert But, but they don't know what the other knows, and that's the key.
At the very start, Alice knows that Bob sees either 6 or 8 trees. And Bob knows that Alice see either 10 or 12 trees. BUT, Alice does not know what Bob knows, and Bob does not know what Alice knows. Alice only knows that Bob knows one of two things: If Bob sees 6 trees, then Bob knows that Alice sees 12 or 14 trees. If Bob sees 8 trees, then Bob knows that Alice sees 10 or 12 trees.
Likewise, Bob does not know what Alice knows, he only knows the she knows one of two things. And this continues. Alice does not know what Bob knows that Alice knows. Alice only knows that Bob knows that Alice knows that Bob sees either (10 or 8), (6 or 8), or (4 or 6).
Every day that passes with neither Bob nor Alice removes some of these possibilities, this is how Alice and Bob gain new information until one of them is able to answer the question. This is the same solution that the video gave, I've only described it a bit differently.
This is based on the HUGE assumption that both Bob and Alice know this logical thought process going into this scenario otherwise the who thing is fucked....because remember, they can not communicate.
This never actually happened... It's a riddle. ya silly mongoloid
Alexander Knox And a shitty one at that
ill agree with that... but since it's a riddle you have to have a little imagination on the people and that fact that they know how logical the other is.
Alexander Knox Fair enough, just seemed a little far fetched to me. Personally I think a lot of assumptions have to be made for it to work properly
yes it is, congratulations
„An evil logician“ haha awesome, Imma call myself that from now on
None of this would be conveyed back and forth to the prisoners in a real life situation, one of them would take a guess and that would be that.
it does, if they get asked the question, it means the other passed.
@@Blockoumi - They wouldn't actually 'know' anything, they would have to assume things and hope that they are right.
damn these evil logicians
I think this problem is formulated in a slightly misleading way. The problem with the solution, is that in order for it to work, each side will have be able to assume that the other side is also aware of the solution and is willing to implement it. If A and B are *never* able to communicate, then this cannot be assumed.
The way the problem is stated here makes it seem like there could be a way for either A or B to reason their way out of captivity, *independently* of what the other side does or thinks. And this is simply not the case.
It would be better to state that before being locked into the cells and seeing the trees, they are explained the terms of the challenge and are able to discuss with each other once.
their captor would not ask a question that did not have an answer. the total number of trees has to add up to either 18 or 20. so since Alice sees 12 trees she knows Bob has EITHER 6 or 8 trees, and Bob knows Alice has EITHER 10 or 12 trees. I just haven’t figured out where to go after that. But that should skip the whole of day one at least. that is the only part of the solution i have seen so far
Day 3: Alice knows Bob sees at least 6 trees? That's obvious from the beginning. They both know there are either 18 or 20. Alice sees 12. She knows Bob sees either 6 or 8.
The sad end of the story is that, when they finally will get the correct answer, Bob will say "There are 20 trees..." but the logician (clearly a Russian) will understand "There are 23"... so they will never be free again...
the rules say they know the rules, that means they know the amount of trees, because it is stated in the rules. but also the rules say that they don't know the amount of trees. so the answer is that it is a paradox and can't be solved
Three logicians walk into a bar.
Barman: So, beers all round is it?
Logician 1: I don’t know
Logician 2: I don’t know
Logician 3: Yes
The problem is that there is no logical reason for this pattern to begin. An intelligent person would immediately reason that the other person can either see 6 or 8 trees. Therefore the fact that the other person can see more than 1 tree is irrelevant information. I have seen puzzles where this logic is applied more smoothly but it doesn't work with this example.
Wrong. If an intelligent person assumes the other person can see 6 or 8, then they also can assume that that person will assume that the intelligent person has 10, 12, or 14 trees. The purpose of using a limit/guessing method is because of the layers of complexity.
Thank you! That is exactly what I found... shall we say "impossible" about the puzzle. There is ABSOLUTELY nothing for them to begin the count from day 1 as each person already knows how many trees the other person should see by sheer deduction. And if they did begin, ok Alice and Bob pass on day 1 and they realize that they must each see a minimum number of trees. But what happens when they reach the day on which Bob realizes Alice should see a minimum of 6 trees? What logical insight is there that will compel him to stop saying "pass" to the logician and answer 18 trees? In other words, what in the pattern relays a bit of information that tells them how many trees the other person actually sees. NOTHING. That's how I saw it.
@@josecasillas4081 this is a flawed puzzle. Doesnt work logically
@@josecasillas4081 there isn't; you're misunderstanding the solution. alice realizing bob sees a minimum of 6 trees at the end of day 3 tells her nothing. it's at the end of the next day, when alice now knows bob sees a minimum of 8 trees that lets her stop saying "pass". as you said, alice already knew from the start bob could only see 6 or 8 trees. but, she didn't know which. knowing bob sees a minimum of 8 trees eliminates the possibility that he sees exactly 6 trees. THAT'S what compelled her to stop saying "pass"
@@x3mskbord Yes, but the solution's logic is flawed. Alice and Bob were told at the beginning that they can see all of the trees between the two of them. Given these parameters, Alice and Bob immediately know that the number of trees the other sees is one of two options. Alice sees 12, so she knows that either Bob sees 6 and there are 18 total trees or Bob sees 8 and the total number of trees is 20. Meanwhile, Bob sees 8, so he knows that either Alice sees 10 and the total is 18, or she sees 12 and the total is 20. They can't logically assume on day one that "Bob saw at least 2 and Alice saw at most 18" as a means to a solution because they both know there are only two possible outcomes, and either one is just as likely.
There is no more information that can be gathered, passing or otherwise. Alice and Bob can pass for days on end, and they still will have made zero progress towards any new information. The only way to correctly solve this riddle is a 50/50 guess.
If it actually were a logician who imprisoned Alice and Bob, then he'd asked them either to answer 18 or 20, not simply 18 or 20. In that case, a simple 'yes' would suffice, since there actually are '18 or 20' trees. This is assuming that the logician always provides the correct answer, which can be assumed, since he is a logician and he knows he must give the correct answer for them to figure it out. Boom, released on day 1!
+Erik Huizinga Brilliant!!
with that interpretation there might be 100 trees and the answer might be no. would you risk your freedom over it or would you ask for clarifications?
+Sauron I think you might be correct... The logician just needs a logical answer, so he could say any number unrelated to the number of visible trees. This would leave a guess: if there are more than or equal to 18 trees, then the answer still is yes (since 100 trees also are 18 trees in set theory). Alice and Bob both see less than 18 trees, so they can't know for sure what to answer. So the solution in the video still holds, with two side notes: Alice and Bob must know from the beginning they both use the same logic and they must both know who was asked first.
Erik Huizinga true, but they do know who is asked first, as they know the rules, and one of the rules is that Alice is asked before Bob.
This is why I fail school exams- they break their own rules! They WERE communicating! But the puzzle said they couldn't.
Teacher: There is only one question on the test
The question on the test:
But Alice knows from the beginning that Bob Sees at least 6 trees, otherwise neither 18 or 20 Would be possible
+J-J-J-Joule At the beginning Alice only knows that she can see 12 trees, but she doesn't know if Bob can see 6 trees or 8 trees. If he sees 6 trees, there's 18, but if he can see 8 trees, there's 20.
+The_Only_Zac But she knows he sees at least 6 trees, because the original question "18 or 20?" implies that there are only these two options. So Bob sees either 18-12 or 20-12 = 6 or 8 trees. And Bob knows that she sees 18-8 or 20-8 = 10 or 12 trees.
She doesn't know wheter it is 6 or 8, so she has to pass (at this first point, where she is uncertain) and Bob doesn't know how much she sees at most, so he needs to pass, two. Thus the 4th day in the video only needs to be the first day and Alice can tell the answer on day 2 already.
Skyletwings Oh yeah, I see what you mean now.
+Skyletwings That's what I worked out too. Therefore, Alice and Bob are not perfect logicians.
+Skyletwings no because on day two alice wouldn't be able to exclude the case that bob sees only 6 trees.
You've already lost me at the pictures
Same
same
yup
me 2
But it's so simple. All I have to do is divine from what I know of you. Are you the sort of man who would put the poison into his own goblet or his enemy's? Now, a clever man would put the poison into his own goblet, because he would know that only a great fool would reach for what he was given. I am not a great fool, so I can clearly not choose the wine in front of you. But you must have known I was not a great fool, you would have counted on it, so I can clearly not choose the wine in front of me!
I think Bob can solve by the end of day 2? He sees 8, so he must be able to figure Alice has 10 or 12. When they both pass the first day, that conveys to both that neither have 10. So on the second day when Alice once again passes because she still can’t tell if he’s got 6 or 8, that gives him enough of a clue that she’s got 12 and he can confidently say 20.
nope, they arent allowed to communicate, so how can they agree on this abitrary plan? obviously Alice has 10 or 12, but how does a pass on Day 1 automatically rule out 10? then if she ACTUALLY had 10, this strategy completely falls apart...
He's right though he didn't explain how Bob passing on day 1 rules out 10. This gets a little convoluted, they BOTH know that they both know Bob has 6,8 or 10 and Alice has 10,12 or 14. If Bob were to have ten, he'd know Alice had 10 (as 12 and 14 are bust) since Bob passes, Alice knows Bob knows Alice doesn't suspect him of having 10
The information passed from day to day would only be valid if both Alice and Bob trusted in the others ability to be this logical. Otherwise the certainty goes out of the window.
This would never really work, because both people would have to come to the same reasoning prior to their second guess. Since no collaboration is allowed, the individuals would have no way of knowing if the other person was just passing because they were unsure, or passing due to this reasoning.
But he said that can they reason with certainty so they're both just gonna pass
Gianna Archuleta My point is one has to suspend their disbelief, because without interaction neither person can know that the other person is making the same assessment when they pass.
+Litigious Society you have to suspend your disbelief for the whole thing, bro... it's a logic puzzle
It says they're perfect logicians which means that the only reason they would pass is if it is impossible to logically deduce the number of trees. If they're perfect logicians, the only reason for them to be unsure is due to this reasoning.
Kevin Widmann Does each logician know the other is a great logician? That would be a requirement too. An example would be trying to communicate with an alien through numbers, but not knowing what base their number system uses; it could be done, but not as easily.
I don't trust Alice enough to wait 5 days
The assumption that they reason with ABSOLUTE PRECISION means that Alice can free them on day 2.
Both people will assume that the other person as well as themselves will reason with ABSOLUTE PRECISION.
They will both know the entire order of operations for communicating by passing. They will both be able to reason this before anyone passes.
They will also know which numbers on the order of operations are already solved by looking out the window and knowing there are 18 or 20 trees.
Alice will know the first possible number that Bob could think she can see is 14. Bob also realizes this.
For this reason Alice will pass on the first day knowingly communicating that she does not see 14.
Bob will know this and pass communicating that he does not see 6.
Alice will know that because Bob does not see 6 he must see 8.
[Note:] I realized because of the legally vague phrasing of certain parts of the rules:
The answer is that yes Alice and Bob can do better than random chance and No they cannot answer with Absolute certainty.
This is due to the fact that we don't know if Alice and or Bob actually want to escape as soon as possible. It only says that they don't want to stay in the evil logician's prison forever.
So both Alice and Bob have no idea if the other person wants to stay in prison as long as possible in which case they would select the slowest possible method for communicating.
If the rules as stated also said: It is known by all that Alice and Bob want to be set free as soon as possible. Then we could say there is certainty that they would be set free. ( On day 2 by Alice)
As it is now , choosing the fastest possible escape seems to be the safest way to prevent being locked in prison forever. Although not a certainty.
"Did you figure it out?"
lol nope!