Can you crack these 2 logical puzzles?

[@aliasmask]

The first question, "Is you number double mine" will also eliminate all numbers above 15 since if their number was higher, asking the question would automatically be false and thus should never be asked.

[@adambregard502]

Completely agree! That was the first deduction I made from the problem, and in the end i was confused as to why I didn’t get a solution, only to realize the problem was flawed in the first place..

[@toddblackmon]

I did consider this myself, but I know that logic puzzles generally have the implicit assumption that asking a question does not convey information. This is because, on pure grounds of logic, there's nothing that says a person cannot ask a question that they already know the answer to.

[@kirimaru73]

This may not be true. Even if this question may be nonsense, there are no rules or conditions in this puzzle to prevent A from asking this question. In fact, A does get additional information from B's answer (not an odd number), so asking this question is not totally useless.

[@Exiitar]

Can someone explain me Why that question eliminates odd numbers? For ex if A 's number is 7 than B can also have 14 as a number, how did it eliminate odd numbers?

[@SilverStagVT]

No it is absolutely true, because A knows that B is limited to 1-30. by asking the question is yours double mine, he is indicating he has to be less than 15.

[@thebitterfig9903]

With the combination puzzle, there's a cool interaction between Rules One and Three. Because Rule Three has one number in the right position, and 2 is in the same position in both rules, you know that 2 must be wrong. Not necessarily a useful interaction, depending on the order you consider things, but that's an observation which can be useful in similar puzzles.

[@mstmar]

I found this too and is really useful when used on clue 5. it cant have a 2 nor a 5, so must have 8 and 4 as correct numbers

[@SgtSupaman]

It definitely depends on the order in which you consider things. For me, that was how 2 was the first number I eliminated (after the obvious 'none of these are correct' clue). So, it was more quickly clear that 8 and 4 were in the answer.

[@Reaper-jr7sz]

Good thing I'm not the only one who thought of this

[@88Nieznany88]

That's what I thought as well and thanks to that 1 was the correct number (because 0 and 5 are not correct in 5201, and 2 is not as well). And after that it was more or less easy

[@global2829]

I found the 1 using this, right after I eliminated all the numbers from the "none of these are correct" line.

[@griffonu]

The logicians problems breaks down if we assume the question "Is your number double mine?" is asked by one logician only if he does NOT know the answer to it already. After all, a perfect logician wouldn't "waste" a question he already knows the answer to. This means that, for instance, when A asks the question, this already brings information that A's number is not greater than 30/2 = 15. If we assume the same logic for B, the problem doesn't work anymore. Thanks for the content! :)

[@ToyKeeper]

^^^ This. B's "I don't know. Is your number half mine?" proves that B isn't cooperating or isn't a very good logician... and the puzzle falls apart.

[@michaelm.2781]

Correct!

[@andrevanderkant6616]

The question should be : "could your number possibly be double mine"? it all comes from the fact that the questions are closed and therefore binary (yes/no). They are asking each other about possibilities, which implies uncertainty, and the correct answer would be "possibly"

[@jesan733]

My thinking as well, I got stuck at that.

[@bennmurhaaya8518]

My thoughts exactly!!!! I was running in circles trying to find where I made a mistake!

[@hao2000ki]

Took a long time figuring out why a number couldn't be reached in the second puzzle. Jumped to the solution and realized they didn't account for excluding all numbers above 15 for the asker every time they asked whether the other's number was double theirs. Glad to see I'm not the only one confused by the wording of the second puzzle.

[@colinfun]

See that was my issue, if Person A had the number 20, they couldn't ever get a positive answer asking if B's number was double theirs because they would know the only answers are no or I don't know. But this is still true of a number below 15 until you have already had your own range reduced below 15 also.

[@MocaLykke]

If I'm playing wordle and know the word is gonna be "_oats" with 2 tries left, my next try is gonna be "gumbo". I know it's wrong, but it'll tell me if the answer is "goats", "boats" or "moats". It's a perfectly logical course of action. The most vital rule to logician puzzles is that the logician doesn't make assumptions beyond the rules (=> answers are true). "A wouldn't ask a question they know the answer to." would be an assumption on B's part. We don't know why A is asking the question, therefore we cannot apply intent or meaning to it and only focus on the answers, which we know are true statements. To illustrate, let's get into B's head for a second. "Is my number double theirs? Does that imply theirs _can_ be doubled? Or is that what they want me to think? Or do they want me to think that's what they want me to think so I don't think that? Or!..." And there you go, a broken logician.

[@comicmoniker]

@@MocaLykke I know it's not your main point, but even in your own example, you're making an assumption outside the given bounds. In order to create your "broken logician" you add the stipulation that A would have some reason to *not* want B to guess their number. Otherwise, why would B second guess what A wants him to think?

[@MocaLykke]

@@comicmoniker Indeed, I do. But for the opposite, you have to make the equal assumption that A *doesn't* have a reason to not want B to know their number. Otherwise, why would B not second guess what A wants him to think? All of it is assumptions. The only solution is to ignore why A is asking the question or what B thinks of A asking the question. Therefore, ignoring the question entirely and focusing on the answers.

[@leif1075]

​@@comicmonikerWait I think Infound a POTENTIAL.FLAW in the ANSWER..avyer the last question B asks, A knows H has 4, 8., or 12 since those are the only evens that divide to an even number since B knows A has am even number between 2 and 14..and since A knows if B had 8norn12 he wouldn't have asked in the first round if As number was double his since double 8 or 12 is greater than 15 so A WOULD KNOW THAT N has the ANSWER 4 AND WOULD NOTNSAY INDONT KNOW!! OMG DIDNT anyone else notice this?? So A wouldve said yes my answer is half of yours since A has 2 and B has 4..COME ON I amnright..didn't anyone else see tbis flaw??

[@stkosta2482]

Another approach to the first problem is deducing that 2 cannot be a correct number by the fact that it doesn't change it's place in clues 1 and 3, but in clue 1 we have a misplaced correct number while in clue 3 we have a correct number on it's place.

[@alastairgreen2077]

its place

[@brlinrainf]

my comment section broke again again

[@brlinrainf]

my comment section broke again again AGAIN (a reply from me appeared on another video)

[@me-myself-i787]

That's what I did. So I got 3841.

[@michaelmetcalfe4882]

@@brlinrainf If it is the same thing that happens to me it just appears to you that your reply comment on a video has migrated over to another comment on another video. If you refresh the page it should go away.

[@Toopa88]

My approach to the second puzzle was to find a number that you can multiply by 2 twice and divide by 2 twice and it still being an integer and between 1-30. That only works with 4 (4-8-16; 4-2-1). I guess I solved the puzzle intuitively without understanding the puzzle.

[@nicholaskehler9169]

The problem is the puzzle is wrong by the time B asks his second question B has been whittled down to 2,4,6 and A has been limited to 4,8,12 none of which can be half of one of B’s available numbers as such B would not have asked this question. To clarify the first question limits A to 1-15 as anything higher would not have an available double. The answer to question one limits B to evens the follow up question limits those evens to ones that have a double under fifteen 2,4,6 A’s answer limits them to doubles of those three numbers 4,8,12 the follow up question means nothing as it is all known information but when B repeats the question it creates a problem because none of A’s options is half of one of B’s options

[@Monkey-fv2km]

It makes sense as an abstract maths problem, not so much as an interaction between people.

[@elianjoensen2756]

@@nicholaskehler9169A can still ask the question if his number was higher than 15, because A doesn’t care what the real answer is he just cares what B thinks the answer is

[@pentaxian7455]

@@nicholaskehler9169 agree

[@martincattell6820]

That's a clean way of expressing what's happening here. Though I got the correct answer, your way of stating it has clarified something for me. If both individuals are strictly logical, you don't need to treat them as individuals to find the solution.

[@ps.2]

Cool thing about the combination puzzle: my first thought was "the rules should state whether there can be duplicate digits," but as it turns out, the 4 distinct digits are deducible, so it is solveable whether you presume uniqueness or not.

[@tomthoe]

Before checking to make sure they were all there, I was also wondering if there was a number not listed that was one of the numbers of the code.

[@asdfqwerty14587]

That can be deduced but the puzzle is missing some extra statements that a lot of people are just implicitly assuming about the puzzle. It does not state that the values are exact (so for instance, you could argue that 4891 is a solution, because "one number is correct but in the wrong position" in statement 1 is technically still true.. I mean, there are 2 numbers that are correct but in the wrong position, but there also is 1 number that's correct but in the wrong position too). It's also missing some information in the 1st statement that there are no numbers that are correct and in the correct position, and in the 3rd statement that there are no numbers that are correct but in the wrong position - without making that assumption a solution like 2381 becomes possible too. I mean.. I got the idea behind the puzzle that it's "supposed" to always tell you exactly how many numbers are correct and how many of them are in the right position.. but that was never explicitly stated by the puzzle anywhere - it's just something that's being assumed.

[@deerh2o]

I always am impressed at those who create these logic puzzles.

[@mj9765]

I ask my kids to create logic puzzles so they can think. Some of the questions they came up with were so amazing I used them while interviewing engg candidates.

[@deerh2o]

very impressive@@mj9765 Congratulations to them.

[@mrosskne]

With the combination puzzle, it's pretty easy to make your own. Create any random code, then make one rule that eliminates four numbers - almost half the possibilities. From there, it's pretty simple to create a set of clues given you know the code. It's a lot like sudoku.

[@Anonymous-jo2no]

If you have heard of Einstein's riddle... That one I am still wondering how anyone made that

[@karhukivi]

There are books by the late Martin Gardner who collected them and added his own - well worth sourcing!

[@Braunfolk]

When logician B asks their second question "is your number half mine" Logician A knows B's number must be 4, so his answer of "I don't know" is illogical.

[@Alanalan12297]

Exactly

[@jericalnaudes9444]

When A said "I don't know". A actually can deduce that is giving crucial information about they number. But A still doesn't know B's number. Even after A answered "I don't know".

[@Jonassoe]

The first puzzle is basically the board game Mastermind, but with numbers instead of colors. It's a fun game if you like this sort of thing.

[@swordgeo]

I was just explaining to my girlfriend why I could figure out the first one so fast when it took me time on the second. I’ve always loved Mastermind so much the final project for my first coding class was to make whatever I want and I made Mastermind in Python, with the computer making the codes

[@thethird-brawlstars6634]

Same lol every weekend i would play mastermind with my family. it took me seconds

[@mikepanson314]

Yes. I really need to dig it up out of my closet

[@SarahAbramova]

I was thinking "wordle prepared me for this!"

[@Cathowl]

Yeah I was like "wait this is a mastermind style puzzle, I'm good at those!" and screencapped it, dropped it in an art program, and started solving it.

[@grumpylibrarian]

Got a slight fail on the second puzzle. When A asks "is your number double mine" and B replies "I don't know," the puzzle only eliminated B's odd numbers. But B also knows that A's number was given as in range of 1--30, and if it were possible for B's number to be double A's, then A is now also down to 1--15. So A eof {1..15}, B eof {2,4,6,8,10,12,14,16,18,20,22,24,26,28,30}. When B then asks "is your number double mine" and A replies "I don't know," the puzzle puts A to {4,8,12,16,20,24,28}. But this should be {4,8,12}, as it needs to be a multiple of 4 and eof {1..15}. B also has to be < 8, because 2*8=16 which was outside of A's range. As B must be even, we now have A e-of {4,8,12}, B e-of {2,4,6}. Now when A asks "is your number half mine," the needle doesn't move at all: all of B's options are half of A's options, but there are still more than 1 option. So B could never know, and the sets remain A e-of {4,8,12}, B e-of {2,4,6}. Next, B asks "is your number half mine," and this is where the puzzle fails --- the answer should be NO, not I don't know. B has no available numbers which are half of any of A's available numbers. This is where the puzzle ends, but even the correct answer of NO doesn't move the needle! The sets remain A e-of {4,8,12}, B e-of {2,4,6}. The solution the puzzle provides relies on B assuming that perhaps A has asked a question to which A knows the answer cannot possibly be yes, in not assuming that A would not ask of B's answer is double A's if A was e-of {16--30}. But it later assumes that neither would ask a question that the answer could not possibly be yes in trimming the results to multiples of 2 or 4. So the rules are inconsistently applied.

[@binethepitawela9974]

The fact that A asks whether B's number is double his does not tell us that A's number is in the range of 1-15 as even though potentially his number is greater than 15 he could potentially still ask such a question as the purpose of the question might have only just been to determine whether B's number is odd or even. The puzzle only tells us that all statements made by A and B were true. A question is neither true or false and as logicians they would strategize and come up with questions to infer useful information based on the other's response. You cannot argue that as perfect logicians A's first question doesn't make sense if his number is greater than 15, as it does the job of inferring useful information based on B's response regardless of the fact that A knows the answer to the question if his number is greater than 15, as A knows that B doesn't know this and as therefore B's response would halve the possibilities for B's number in A's mind. Therefore it would not be logical for B to infer such a thing from A's question as for one you cannot make inferences based on questions unlike statements which are mentioned to always be true, and second as logicians, A's intent would have been clear as daylight for B.

[@runoke]

Why wouldn't A ask B "is your number double mine" if his number is more than 15? What prevents him from doing it?

[@letsgoloca1846]

u said b has no available numbers which are half of a's numbers here :- Next, B asks "is your number half mine," and this is where the puzzle fails --- the answer should be NO, not I don't know. B has no available numbers which are half of any of A's available numbers. This is where the puzzle ends, but even the correct answer of NO doesn't move the needle! The sets remain A e-of {4,8,12}, B e-of {2,4,6}. But b has 4 and a has 8, that shows that 4 is the answer

[@codebloke2200]

@@letsgoloca1846 The solution was that A had 4 not B had 4. I still think the solution is non-determinate given the logic parameters.

[@Mythraen]

@@codebloke2200 There's nothing wrong with the solution. People assuming A wouldn't ask a question (questions have no truth value) which provides A with information is where the problem (usually) lies, and that problem is in their brains, not in the logic puzzle.

[@AzureKyle]

Typing this all at once, but before the solution of each puzzle. Puzzle 1: So first, I wrote down each incorrect code given, then I wrote down the numbers 0-9, crossing incorrect numbers as I went along. For the solution, I first looked to the 4th code, where nothing was correct, and crossed out 0, 5, 6, and 7 from every code. Then I looked at the 1st and 3rd codes, which both had a 2 in the second position. However, one was correct number, incorrect position, and the other was correct number and position, which means it couldn't be 2, so I crossed it out from every code. This only left 1 in the fourth position for code 3, meaning it had to be correct number and position, so I circled it in every code and wrote it down in the fourth slot. This also left 8 and 4 in the last code, which had two correct numbers but incorrect positions, meaning 8 and 4 were part of the code. This also takes me back to the first code, with one correct number and incorrect position, and contained 8 and 9. Since I already proved 8 correct, this removed 9, which also left me with 1 and 3 in the second code, which was the same as the last code. Also, with both the first and last codes containing 8 in the wrong position, this meant 8 was 2nd. And since 3 in the third position was wrong, it had to be 4, leaving 3 in the first position, and giving the code 3841. Puzzle 2: So, first we look at A's first question and B's answer. If B had an odd number, he would know it's not double hers, so his number must be even. He then asked the same question and gets the same answer. This not only tells him that her number is also even, but also a multiple of 4, since they both know his number is even, and double an even number is a multiple of 4. She then asks if his number is half hers, which he doesn't know. This tells her it can't be more than 14, because otherwise he would say no, since 16 doubled is 32, which would be too high. He then asks the same thing and gets the same answer, this tells him her number. Out of his possible numbers: 2, 4, 6, 8, 10, and 14, half of them would be 1, 2, 3, 4, 5, 6, and 7. It couldn't be any of the odd numbers, because they were already ruled out, leaving 2, 4, and 6. However, he also ruled out 2 and 6, because he already knew her number was a multiple of 4, meaning her number had to be 4.

[@heyfling]

I think the 1-30 puzzle has a problem that you are overlooking. If A asks B, is your number double mine, it means A has to have a number between 1-15. Bs pool of numbers is still even. But after B asks is your number double mine, because As answer, the pool of numbers A has would be 4, 8 and 12, the only numbers divisible by 4 and below 15 and B should logically have 2, 4 and 6, the only numbers divisible by 2 that is half 15. Assuming this is the case and A having 4 is the correct answer, Bs number pool would be down to 2 and 6, and A asking B if his number is half mine would make sense because he is trying to determine if B has 2 or 6. But B asking if As number is half his doesn't make sense because in zero scenarios does A have a number half of Bs.

[@Icemann89]

Yeah, Presh completely overlooked the information person A gave us by asking the first question (B therefore knows A didn't choose any number higher than 15). Also (as you have suggested) B didn't have to ask the last question, he should already knew that A's number is 4.

[@rinosanchez2150]

​@@Icemann89 You're assuming an intent behind A's question which is not stated in the problem. We're not told that A is trying to figure out B's number at all, or that they're competing in any way As far as we know, this is just an abstract intellectual exercise.

[@gtf5392]

Both A and B could have picked 4. The rules don’t say anything about them having to pick different numbers. Other than that, your other points are valid.

[@tinnderbox3410]

Why would that be true? A can have 17, and still ask that same question. A gets the info whether B's number is even or odd. But I do agree the question could have been better, like: "is it possible that your number is double mine". And B's answer would have been "yes".

[@graeme1818]

A can ask whatever he wants. He could ask “Is your number a banana?”

[@kittybeans8192]

By solving the second puzzle, I also figured out that a logician would ask a question they know the answer to, if the way the question is answered would yield some information. That is, the questions asked are not tells about who knows what. Which is fair, I often ask questions I already know (or think I know) the answers to IRL. But then again, it's *also* fair to assume what someone knows or doesn't know based on the questions they're asking, something I also do IRL. I'm not totally sure but I think I've encountered other logic puzzles where the questions asked reveal information, so I dunno, I give this one an A-. (I'll update later if I can remember such a puzzle) (if you're stumped on what I'm rambling about still, here's a hint: When A asks "Is your number double mine?", it does *not* mean that her number is definitely less than 16.)

[@Phlebas]

As someone who grew up with the game "Mastermind" in the house, the first one felt pretty familiar. Second one was a bit difficult because I assumed either A or B asking "is your number double mine" implied that both numbers were below 15. That can mess with the logic of the puzzle. That said, if we assume that only answers give us information and that the questions are information-neutral, it seems like a pretty straightforward solution through process of elimination.

[@msshortty2u112]

I usually like puzzles, but that second one was just annoying, there were so many different ways to interpret the puzzle, but you could only interpret it one way for you to get the right answer.

[@Mythraen]

@@msshortty2u112 There's nothing wrong with the puzzle. The problem is with thinking that a logician would jump to conclusions. Logician A acquired information by asking Logician B if Logician B's number was double Logician A's, even though both Logician A and Logician B are aware that Logician B does not know Logician A's number _and_ are aware that Logician A knows this. So, A gets information by asking the question. If A gets information by asking, there's no reason for A not to ask, regardless of A's number. And, if there's no reason for A not to ask, then B has no reason to jump to conclusions about A's number.

[@nzeches]

B can also infer about A when A asks the question. If A asks « is your number double mine » then A must be less than 16, even before B answers… otherwise A (a logician) would not ask that question in the first place, assuming A wants to find B number…

[@autonomousstardust2]

​@@nzeches_unless_ they also don't want to give away their own number (if they're trying to guess first). This stipulation would've improved the puzzle immensely.

[@Mythraen]

@@nzeches No, B cannot infer about A. A and B both knew that both A and B did not know each other's number. It's ridiculous, then, to think that two logicians would ASSUME anything about each other's number based on questions, not answers. Especially since, in logic, questions have no truth value. You cannot have a true question and you cannot have a false one.

[@Fluxxdog]

Problem 2: From the first question, A and B learn something about each other's numbers. If A asks, "Is your number double mine?" then B knows A's number MUST be 15 or less. If it was greater than 15, A would already know B's number couldn't be double, therefore they wouldn't ask such a question. So A's pool of numbers is now 1-15. Then B answers "I don't know," and B's pool is reduced to even numbers. On the second question, when B asks "Is your number double mine?" A would also know that B is now only looking at A's number to be less than 15. So in order for A's number to possibly be double B's, B's number must be less than 7.5. The only even numbers less than that are 2, 4, or 6, one of which must be B's number. A answers, "I don't know" meaning that indeed their number must be a multiple of four, specifically 4, 8, or 12. So at this point, both A and B know that the potential pool of numbers are A: 4, 8, 12 B: 2, 4, 6 We now have a problem. A's next question would NOT be "Is your number half of mine?" A already knows that answer. Whether B's number is 2, 4, or 6, B would answer "I don't know" because B knows A's number is either 4, 8, or 12 and B's number, no matter which one it is, is half of one of those numbers. Likewise, B would not ask "Is your number half mine?" because none of the possibilities for A are half his possibilities, so B would know that A would answer "No." It seems multiple people in the linked Reddit thread pointed out this problem. Essentially, information that is given by someone asking those questions was ignored in the solution.

[@legendgames128]

tl;dr A and B play a number guessing game. A cheats. B can't win. B unfriends A. A is lonely.

[@theybuck_]

Yeah I ran into this too when solving this puzzle myself, normally I'm not so great at these kind of things, so I honestly assumed I was doing something wrong when I kept getting the sets of A: 4, 8, 12 and B: 2, 4, 6. Good to know I wasn't actually wrong!!

[@stephenkeen6044]

Except that, being a logician, they know that asking that will help the sequence of knowledge progress, so they ask it anyway... simple logic.

[@neoncat6820]

​​@@theybuck_if you wanna actually try solving it, make sure to think of it like this: the logicians cannot lie, but they can ask questions even if they know what the answer is. They are logicians, so the smartest thing to do is whatever finds the answer the fastest. That can involve asking things that you don't actually need to know.

[@pogmothoin288]

I fell into this trap at first but I didn't like any of the explanations as to why they ask the questions like that. My head cannon is they want to solve the puzzle first so they wouldn't want to give any information away with their own questions to help the other person. They could have said is your number even or a multiple of 4 or half one of the numbers we haven't eliminated yet yada yada yada. I have a similar puzzle that illustrates how annoying these can be. Same setup except 1-32. A: Is your number double mine? B: IDK. Is your number double mine? A: IDK. Is your number double mine? B: IDK. Is your number double mine? A: IDK. Is your number double mine? B: IDK A: I KNOW YOUR NUMBER!

[@SwordHunter37]

Fascinating! I solved both puzzles, but taking a different route than demonstrated here. I love how our minds all work differently.

[@Filip-ko8wl]

Nice I also managed to get them, the first pretty similar to the way in the video, The second I think I got my logic a bit wrong so it was more of an educated guess but happy to see 4 was correct

[@tinypixiekitten7806]

Me too!

[@Drteslacoiler]

el how did you solve the second

[@kittylina36]

Here’s my thought process: When A asks B if his number is double hers, he says he doesn’t know. If B’s number was odd, he would say “no”, since it would not be possible for an odd number to be double another whole number, which means B’s number must be even. B asks A if her number is double his. A knows B’s number must be even, she answers that she does not know if hers is double his. This eliminates all odd numbers and numbers that are double odd numbers, since she would have answered “no” in those cases, as it would not be possible for her number to be double his in those cases. This leaves the available options as 4, 8, 12, 16, 20, 24, and 28 A asks B if his number is half hers. He does not know. A knows B’s number cannot be above 15, as in that case he would know for sure that his number could not be half of another number within the 1-30 range. B asks A if her number is half his. A does not know. This eliminates all numbers above 15 for A as well, leaving the options as 4, 8 and 12. If A’s number was 8 or 12, she would know for sure that her number was not half of his, since she’s already established that B’s number is under 15. Which means her number must’ve been 4, as it’s the last available option I typed all of this before watching the video I just saw the thumbnail I will go watch soon

[@Michauuu666]

I've solved both problems. First inside of my head, second using pen and paper. Great puzzles, second especially.

[@nathanmorlonski1265]

took me long to find out the second one but it was really fun to solve 😆

[@Bismarck-S]

I did both in my head. Took like 2 minutes

[@davidbielsa5188]

Respect. I cant the second, even with the solution i dont see it

[@tvmy121]

The 2 problems were very nice to solve by head. In the second one 8 made the statement with the "double" assumptions that A and B had numbers inferiors to 15. It changed the game Thanks, Julien

[@Fluxxdog]

@@davidbielsa5188 The second problem is flawed. It ignores that fact that if one person asks if the other's number is double theirs, then the first person's number must be less than half the maximum.

[@lol101lol101lol10199]

Round 1: B reveals he has an even number. Round 2: A reveals she has an even number which is the product of another even number and 2. Round 3: B reveals his number is not higher than 14. Round 4: A reveals her number is not higher than 6. Four shall be the number thou shalt count, and the number of the counting shall be four. Two shalt thou not count, neither count thou six (neither of those being double any other even number). 1, 3 and 5 are right out.

[@tinnderbox3410]

And my favourite colour is blue. No! Red! Aaarghhhhh!!!!

[@cheweh842]

Both these puzzles have possible ambiguity in their wording--which I think could mean that they are more interesting than if they were more clear. In number 1, "one number is correct" does not explicitly say "exactly one." I did assume that it meant "exactly one" (which it did mean) but maybe this could be a mechanic in a different puzzle. In number 2, I first assumed A would not ask "2*a = b?" if A > 15

[@samstrange7958]

same, that's why i couldn't solve the 2nd one

[@tiemen9095]

From A's point of view, the first question makes perfect sense even if their number is above 15. Regardless of A's number, the only answers A could get from B are "no" (if B is odd) or "I don't know" if B is even. That outcome is completely independent from A. Therefore it is illogical to assume A would not ask the question if their number A>15. There is nothing wrong with the wording there, only with your logic.

[@kmarasin]

@@MrSlothJunior If you include the last question and answer, there is no possible solution. A must answer "no".

[@MrSlothJunior]

I made the same assumption for the second puzzle, that a logician would not ask "Is your number double mine?", if it is literally impossible for the number to be double theirs. I thought I had a solution, but I found out that I had made a mistake... Anyway, here is my attempt: A: "Is your number double mine?" B now knows that A's number is between 1 and 15 inclusive. B: "I don't know. Is your number double mine?" From the "I don't know", A knows that B's number is even. From the question, A knows that B's number is between 1 and 15 inclusive -> A knows that B's number is 2, 4, 6, 8, 10, 12, or 14. A: "I don't know. Is your number half mine?" From the "I don't know", B knows that A's number is even, and double of 2, 4, or 6, so 4, 8, or 12. B: "I don't know. Is your number half mine?" From the "I don't know", A knows that B's number is 2, 4, or 6. Unfortunately, this question makes no sense, given the assumption that B wouldn't ask it, if it is impossible for A's number to be half theirs... And that's where the train of logic ends. Confused A: "I don't know (I think you made a mistake.)"

[@MrSlothJunior]

@@kmarasin I don't count that as a mistake, but there was a different mistake in my "solution", so I removed the comment (and later I replaced it)...

[@GabrielBrooks-k6x]

The first puzzle was pretty straightforward and was pretty easy to solve. The second one on the other hand was much more difficult. I thought there was no possible way you could get enough information from that to generate a conclusion. Glad to see I was proved wrong. Anyway, great video! You did a great job explaining both puzzles.

[@ytadventurer9170]

Actually, there was too MUCH information. The puzzle itself is a failure, because "the solution" fails to take into account the questions. A asking "Is your number double mine?" SHOULD have eliminated all numbers above 15 from A's side, since A would already know from the start that B couldn't have anything larger than 30. When B asks "I don't know. Is your number double mine?", we should then be able to eliminate all numbers except 2,4 and 6 from B's side, since B's number is even AND B knows A's number is less than 15. When A then asks if B's number is half, that should mean A's numbers can only be 4, 8 , or 12. At that point B's question "Is yours half mine?" is no longer a logical question because there is no possible way it could be since none of A's potential numbers (4,8,12) are small enough to be half B's potential numbers (2,4,6)

[@Tensquaremetreworkshop]

@@ytadventurer9170 Agree totally! I worked this out and the answer to the last question should have been 'no', not 'dont know'.

[@Mythraen]

Don't mind them. I respect someone who acknowledges that they weren't able to solve the puzzle far more than I do people who falsely claim there's something wrong with it because they're bad at logic.

[@jlehm]

⁠@@MythraenThe people who “are bad at logic” have far more credible responses than yours…

[@Mythraen]

@@jlehm It's unfortunate that you didn't believe me, but I actually do respect the OP more than the other two.

[@dre3951]

For the second problem, it would be much clearer and more correct to explicitly say that the answers given are correct. But the questions themselves should not be assumed to contain information (i.e., not chosen carefully by the questioner). So when A asks if B's # is double, if we were to use the information in the question itself, we could deduce that A's # cannot be 16-30, otherwise A would be asking a question with the answer known (B would say "no" or "don't know" and the answer would be guaranteed to be "no"). And being a "logician," they should know better. I mean it's not like they are a "professor of logic" (google that for a laugh). So one way to solve the problem would be to remove 16-30 from A's candidates list. The other way is to not do that, and is the answer presented in the video. I know both ways are valid, but clear specification would be appreciated. One thing I hate about puzzles is trying to figure out details like this. I know people who never get them right don't notice or care, but some people do, and don't like wasting time solving the problem of how the problem was inaccurately specified.

[@libu6189]

I also started out using the inference that A's cannot be 16 - 30 because of the question itself. If you continue on as in the video you get to a point where there is no viable answer.

[@rohangeorge712]

at this point, the readers have to realize that the logicians have restrictions to how they ask their questions. (we have to assume that the logicians are not allowed to ask questions that obviously have a yes or no answer, otherwise they would have asked "Could your number possibly be greater than mine?" or "is your number even?" which yield the same answers. they should have mentioned that the logicians are not allowed to ask questions that will definitely yield a yes or no answer, to make it clearer for us. then it makes sense for the logician to ask a question they already know the answer to in this scenario, as they cant find a better wording for the question as they are not allowed to ask yes or no questions.

[@nh_999]

@@rohangeorge712 also that assumption cannot hold in the first place as numbers like “4” cannot be deduced from any number of half or double questions without accidentally eliminating your own number.

[@JohnnyFedora1]

Why do you assume that a logician wouldn't ask a question to which they already know the answer? B's answer, whether it's "No" or "I don't know" will provide A with valuable information. A knows that B does not know her number, meaning the only possible answers B can give are "No" and "I don't know". B *can't* know if his number is double A's without knowing A's number, so the only point in asking the question is to determine if B's number is even or odd.

[@rohangeorge712]

a perfect logician would phrase the question better. but there probably was some rule or something that prevented them from wording that way, (because the people who made the question wanted it to be phrased that way). so yea ur right a logician can ask a question they already know the answer to gain information, and B shouldnt assume anything about A's number from the question.

[@AlgodooGuard]

I did Riddle #2 much differently. So because I don’t know means they are likely trying to hide the fact that “you are getting there,” I noticed that there are 2 double-questions and 2 half-questions. Because of this, we know that A’s number cannot be an odd number because halving odd numbers gives us a decimal, which breaks the rules. Therefore, we can eliminate all odd numbers. Also, if B says “I don’t know” to A’s question of B’s number being double of A’s, we can easily eliminate 16-30 because multiplying any of those numbers by 2 is > 30. Now, we remain with 2, 4, 6, 8, 10, 12, 14. The number should be able to be halved and doubled 2 times without any decimals and still be remaining within the inclusive range. Also, the RESULTING number from the process can be an odd number because the resulting number is not the original number. Ergo, we can easily determine the number by halving and doubling any of the first group of numbers in the first sentence. Here is the process shown below, applied to each number, and the first time the process applied onto the number breaks the rule, an X will be marked at the end of it: 14 * 2 = 28. 28 * 2 = 56, ❌ 12 * 2 = 24, 24 * 2 = 48, ❌ 10 * 2 = 20, 20 * 2 = 40, ❌ 8 * 2 = 16, 16 * 2 = 32, ❌ 6 * 2 = 12, 12 * 2 = 24, 6 / 2 = 3, 3 / 2 = 1.5, ❌ 4 * 2 = 8, 8 * 2 = 16, 4 / 2 = 2, 2 / 2 = 1, ✅ 2 * 2 = 4, 4 * 2 = 8, 2 / 2 = 1, 1 / 2 = 0.5, ❌ With that, our answer to the 2nd riddle is equal to 4 as it is the only number that doesn’t break the rules when the process is applied.

[@michaelweiske702]

Initial guess for problem #1: 3841 Initial guess for problem #2: A's number is 4. Basically, from what I can tell, both of them must have a multiple of 4 and all have to be less than half of the pool, so they could have 4, 8, or 12. If A had 8 or 12, they would know that their number is not half of B's number, so because they don't know, their number must be 4, since 4 is half of 8 but not half of 12. Post answer: I got them both right, though my reasoning was a little different for the second one. I don't know if that means there are multiple ways of solving it or if I just got lucky.

[@michalkloucek473]

I solved problem 1 with a very interesting way. I took a look at all the clues. Correct numbers appeared exactly six times. Because all numbers are shown, at least two numbers from the correct numbers appeared only once. It can't be six so it has to be 3 and 4. The rest of the soloution was very similar to yours.

[@TikeMyson69]

Nice one!

[@megarural3000]

Finally got one of the puzzles your listed, the first one, not the exact same path, but the correct answer. That second one, damn, time to get my logic up.

[@hailmary7283]

So for problem 2, I thought that the fact that A even asked the question "Is your number double mine?" Meant A could only have a number between 1-15, because why would A ask that question if A's number was greater than 15. Then, the fact that B said "I don't know, is your number double mine?" means that B's number could only be even as you pointed out. But also, we know it has to be 2, 4, or 6, because if it was 8 or greater, then B would not have asked the question "is your number double mine?" because B would know that 8 doubled is 16 and A only has a number between 1 and 15. Then when A says "I don't know, is your number half mine?" since both know that B's number is 2, 4, or 6, then A's number would have to be 4, 8, or 12, because If it was anything else, A would know that their number is not double B's number. Then when B says "I don't know is your number half mine?" This question is redundant because at this point because both know that the numbers for A could be 4, 8, or 12, AND the numbers for B could be 2, 4, or 6. So then A of course says "I don't know." But then on the next step B somehow knows the number.

[@Bismarck-S]

Your logic is flawed. A question can be asked regardless of what information is already known. The first question is essentially just an eliminator of half the numbers, and is not based on what number the asker is thinking of. Think of it like this; I could ask my friend “Do we have a test this week?” even if I know if we do or not, to gather information on how well they have listened during class.

[@Bismarck-S]

When asking the question with a number above 15, you only know that they cannot answer “yes”, which they could not have anyways, because they do not know your number. You are only ever looking for “no” or “I don’t know” as an answer, because that essentially tells you odd or even.

[@legendgames128]

@@Bismarck-S No matter if you logic is flawed, B doesn't like A cheating.

[@Bismarck-S]

@@legendgames128 he's not cheating, because when B asks their questions, they will find out that A's number in fact can't be above 15.

[@aleksejsivanovs9355]

Spent some time writing a long comment about the second puzzle, argumenting that puzzle itself is flawed - numbers 16 to 30 are eliminated from A with the first question, and at the end there's no solution that suits all data. Then checked comments and saw that other people came up with the same conclusion.

[@thebush6379]

From what i found with what each person knows from their responses and quesitons: First question reveals A's number is between 1-15 B's response to the first question reveals B's number is even and between 2-30. Second question, B reveals his number to be between 2-14 but since hes asking A, who's number is 1-15, B's number is even and between 2-6. A's response reveals his number to also be in the same range, even and between 2-6. Third question reveals A's number can be halved, 1 is out of the possibilites, 3 is not an even number. his number is 4. The fourth question was unnecessary

[@nicholaschin8804]

An alternative solution for the 1st problem: After eliminating 6,5,0,7 from the 4th clue, we may also proceed to the 3rd clue, where 5 and 0 are cancelled and we're left with 2,1. By the 3rd clue, the correct number among these two also has the correct position. Now suppose 2 is the correct one. Then 2 must also be the correct number in the 1st clue, and 2 is in the 2nd position, but the 1st clue says that the correct number is in wrong position, so 2 cannot be in the 2nd position. We get a contradiction. So the correct number in the 3rd clue is not 2, but 1, and this 1 is in the 4th position. Since 2 is not a correct number, we turn to the 5th clue and see that only 8 and 4 are left. This 5th clue says that there are two correct numbers, so we can now be sure that both 8 and 4 are correct numbers. Meanwhile in the 1st clue, 2 and 5 are eliminated and we're left with 9 and 8, but since now we know that 8 is a correct number, we can eliminate 9 (1st rule says that only one number is correct) and so the 9 in the 2nd rule can also be eliminated. Since the 2nd rule has two correct numbers, the remaining 3 must also be a correct number. At this point, we've figured out all of the correct numbers: 1,8,4,3, and we also know that 1 is in the 4th position: XXX1 But we're almost done: From the 5th rule, the correct number 8 is not in the 1st position; from the 1st rule, the number 8 is not in the 3rd position, so it must be in the 2nd position: X8X1. From the 2nd rule, the correct number 3 cannot be in the 3rd position, so it must be in the 1st position: 38X1. Now we're done: 3841.

[@ps.2]

Yep that's basically how I did it.

[@kathybee8653]

I got 4891 for the 1st problem

[@tlefevre2918]

me too@@kathybee8653

[@nikitakashirin2117]

​@@kathybee8653​ This result would be right if first row had 2 correct number in wrong positions. But... there supposed to be just one :)

[@juanacosta4351]

​@@kathybee8653 I got that same number, now I realise thanks to op why it was wrong.

[@pesgameplay3665]

After first two dialogues both logicians knew that the other have a even number which is also less than 15.

[@rinosanchez2150]

Nope, we can't assume anything from the questions themselves, only from the responses. After the first two questions, we only know that B's number is even, and that A's number is a multiple of 4.

[@quackduckquack]

​@@rinosanchez2150you can. Cause if you number is greater than 15, then you can't have a double of that since they only chose number from 1-30

[@Drteslacoiler]

@@rinosanchez2150 you are wrong totally!

[@christianbarnay2499]

@@rinosanchez2150 Unless there is a rule limiting the type of questions asked, the questions do convey information. If you consider that the first question A asks B is strictly equivalent to "Is your number odd?" Then why did A use a different wording? Since we don't know of a specific rule forbidding A from directly asking B if their number is odd, then we must assume that A's choice of question is consistent with his knowledge of his own number and that B's number is 30 max.

[@Yggdr4zyl]

​​@@rinosanchez2150is completely right, sorry guys ! If you are deducing anything from the *questions*, then you don't understand how logic statements work. One guy could absolutely ask "is you number double mine ?" even if his number is 27. Nothing wrong with that. It's a logic puzzle, not a real-life situation.

[@Khetroid]

The second puzzle has a serious problem. Their questions themselves give information that is not being considered in the given solution. A asking the initial question implies that their number is less than 15 (otherwise B could not double it). B asking their first question similarly places B's number as less than 7. (In both cases we get the even rule as well) So A could have 2, 4, 6, 8, 10, 12, 14 and B could have 2, 4, 6. The next question, is B's number half of A's, restricts A to being 4, 8, 12 (since A knows B is either 2, 4, or 6 they would only ask this question if their own number were 4, 8, or 12). The following question is then impossible since there is no way for B to expect that A's number could be half of B's as there is no way for this to be possible with the questions and answers thus far given.

[@JohnnyFedora1]

You are incorrect. A's initial question reveals nothing about her own number, because B doesn't know what A's number is. If A's number was >15, and B knew it, the answer to the question would be a definitive "No", but B doesn't know A's number, and so must answer "I don't know".

[@Khetroid]

@@JohnnyFedora1 if A's number was 20, asking if B's number was double it would be nonsensical since it would require it to be 40, which is outside the range. So by asking the question it is known that A's number must be less than 15 or else they wouldn't have asked it.

[@JohnnyFedora1]

@@Khetroid It is not nonsensical to ask, because the purpose of the question is to determine whether B's number is even or odd. B does not know what A's number is. B knows that in order for his number to be double A's, it must be even. If his number was odd, he has to answer "no". Because his number is even, he answers "I don't know", because his number *could* be double A's, but he has no way of knowing if it *is*, because he doesn't know A's number. If A's number is >15, B cannot answer "Yes" to the question - but without knowing A's number, B can never answer "Yes" anyway. This is A's question. A is not trying to determine what A's number is; A is trying to determine what B's number is. If A's number was >15, and B knew it, the answer to her question would be a simple "No". B does not know if A's number is >15. A knows that B does not know if A's number is >15. If A's number was 20, it would still be a good question to ask B, because B doesn't know that A's number is 20. Even if A knows that the answer to her question is a simple "no", the question still provides valuable information about B's number, which is what A is trying to figure out.

[@CiscoWes]

I believe there could be multiple answers which are unknown because in literally every question… A ¯\_(ツ)_/¯ B ¯\_(ツ)_/¯ You have to have at least one thing to hang your hat on to solve everything else. There is no exchange of information when each question gets ¯\_(ツ)_/¯

[@noway2525]

@@CiscoWes Your logic is just totally flawed lmao. I'll explain : A : "Is your number double mine?" B does not know A's number. So B cannot answer Yes. But B can answer No if B's number is odd. Because if B's number is odd, it cannot be the double of ANY number. If B's number even, B will answer "I don't know". Because B does not know A's number but it is possible that B's number is double A's number. So yes, by the "I don't know" you can easily infere that B's number is odd.

[@luckydust4375]

Solved both in around 10 minutes, that's the kind of puzzles I like. For those who says that the first problem is flawed, I get your point but you're wrong. I thought of it when trying to solve it and I will explain my reasoning. The game have 3 rules for sure. 1. Each player chose a number from 1 to 30 2. Each player will alternatively ask a question about the other player's number 3. Each player have to answer honestly the questions considering all the informations they got so far (otherwise, no deduction could be made since both player could just lie or just not think about it and answer randomly) Your idea is that when B asked "is your number double mine?", B gave to A the information about his number not being over 14. I thought about it, but it doesn't work. You can't deduce that from the rules. B could very well ask a question that doesn't give him information, even if you could think it's not in B's interest (and the worst thing is, it's in B's interest since it will give him the same amount of information no matter the number he chose, I'll develop that later) it's clearly not making the game impossible so we don't have as much reason to put "each player must always ask questions that would give them informations" in the obvious rules as we had for "each player must answer honestly considering all the informations he have". Therefore, you did a mistake by adding a rule that can't be deduced logically, and that made you consider as an information something that isn't. Just consider informations you get when you get your questions answered, that's the only reliables ones for sure. And to add to that, A don't know B's number. Therefore, when B asks "Is your number double mine?", the information A will give him is the same whatever number B chose. He could have took 28, 24 or 6, A will still have to answer either "no" if his number is the double of an odd number (or an odd number), or "i don't know" if his number is the double of an even number. Therefore, you can't deduce anything on B's number from just that question since no rules forces B to think "Well there is no number that is the double of mine so I can't ask this question", even more when this question would actually give him so much informations. Such a rule would force you to take even numbers in the center of the pool to have the possibility to ask more important questions. I get that it's frustrating to fail because of that but it's instructive and you will end up developping an instinct for that kind of "traps". Sorry if I made English mistakes or wasn't clear btw I'm French

[@Purriah]

I didn’t even bother with the first one. I got the second one correct really fast, knew it, and had to skip forward immediately. This channel is growing my brain!

[@einSteppenwolf]

Second problem. By asking "Is your number double mine?" Alice conveys that her number is at most 15. By asking "Is your number double mine?" Bob conveys that his number is less than 8, i.e. 2, 4, or 6. By asking "Is your number half mine?" Alice conveys that her number is 4, 8, or 12. The subsequent questions and answers convey no additional information, i.e. there is no solution.

[@yoav613]

Exactly!

[@Salimji1]

I had the same issue with this problem

Isn't though? Since A knows B has 2, 4, or 6 and ask if B has half of A, she must have a value of 1, 2 or 3. B then asks the same, meaning he has 2.

[@RexxSchneider]

I don't think that a logician like Alice actually does convey that her number is at most 15. She is only asking whether Bob knows that his number is twice Alice's. At that point, Alice could have chosen a number from 16 to 30 and, although she would know that Bob's number can't be twice hers, Bob doesn't know that, so he can't make any inference from the question.

[@kseliascryser5259]

@@RexxSchneider fair point.

[@Tyrian3k]

Hope I didn't make a mistake, but I want to post my result for problem 1 before watching on. First of all, thanks to set 4, we know that it cannot be any 6,5,0 or 7. That leaves us with 2 and 1 in set 3. Since the position is correct and 2 is in the same position in set 1, it must be the 1. In set 5, 5 and 2 are ruled out and that means it must be 8 and 4. Since 8 is a correct number, it is the only correct number in set 1, meaning 9 is wrong. This only leaves 3 as a correct number in set 2. Correct numbers are therefore 8,1,3,4. As for the order, the 1 is in the right position, so position number four. 8 cannot be in position 1 or 3 and position 4 is taken, so it must be position 2. 3 cannot go in position 3 and position 2 and 4 are taken, so it must be position 1. 4 therefore goes in position 3. Result: 3841

[@syedhussainali2989]

I really appreciate your effort man. How much time did it take for you

[@Tyrian3k]

@@syedhussainali2989 About 15 minutes. Couldn't really get a reading on the second problem, though.

[@Phantom_User]

I got the same answer!

[@DeadlyOre]

I got both of these! I’m so proud of myself, thank you for these videos!

[@CiscoWes]

The first one is understandable, but I’m not sure about the second one. The answer “I don’t know” doesn’t convey any information. So I am only led to believe there can be multiple answers.

[@DeadlyOre]

@@CiscoWes there isn’t, since there are certain numbers they can have where they could say “no” instead of “I don’t know” which conveys enough info to solve it

[@CiscoWes]

@@DeadlyOre usually on these logic questions, there has to be at least one answer though. Something to build on. A and B just ¯\_(ツ)_/¯ at each other doesn't convey any information. Not really anything to go on.

[@letsgoloca1846]

Same bro !!!

[@DeadlyOre]

@@CiscoWes it does, if you watch the solution you’ll see how

[@martingrds]

Two Logicians: A's number is 4. Steps: 1. After A:"Is your number double mine?"->B:"I don't know.", A knows that B's number is even (otherwise he would have answered "No." 2. After B:"Is your number double mine?"->A:"I don't know.", B knows that A's number is 4,8,12,16,20,24 or 28 (Double of an even number. Otherwise A would have answered "No", since he knows that B's number is even.) 3. After A:"Is your number half mine?"->B:"I don't know.", A knows that B's number is 2,4,6,8,10,12 or 14 (an even number below 15. Where it bigger, B would have answered "No.". Alternative reasoning: It must be one of the halved values of the possibilities for A's number listed in step 2.) 4. After B:"Is your number half mine?"->A:"I don't know.", B knows that A's number must be 4, since from A's perspective B's number could be 2,4,6,8,10,12 or 14 (step 3). For A not to answer with "No", A's number must be half the value of one of those possible numbers for B. Those half values would be 1,2,3,4,5,6 or 7. The only of those on the list of possible numbers for A from step 2 (4,8,12,16,20,24 or 28) is 4. Therefore, B knows that A's number must be 4. 🙂

[@lukebradford]

I didn't get problem 2 because I assumed there wasn't enough information, but the solution made complete sense. What people are getting wrong is that they think it's the questions giving the information, when really the logicians are getting information from the ANSWERS. No, it IS NOT flawed. Some people are just idiots. And we're looking for A's number, not B's, which is another thing I've seen people in the comments getting wrong. B's number doesn't matter here. The problem only asks for A's. And one last thing: Presh clearly states that ALL statements are true. A: Is your number double mine? B: I don't know. So A knows B's number must be even, because not only would B say no if it was odd, the result of a number being doubled can never be odd. So this leaves the multiples of 2. B asks the same question and A says I don't know. The same logic applies to A's number. A: Is your number half mine? B: I don't know. B's number can't be higher than 14, because A's maximum value is 28. Because B says 'I don't know', A now knows that B's number is a maximum of 14. B asks the same question, A says I don't know. B knows that A's number is even and possibly half of his. 14, 10, 6 and 2 all result in odd numbers when halved, so they are eliminated. So A's number is either 4, 8 or 12. 4 is the only number that is half of a remaining possible answer, therefore A's number is 4. Ergo, not flawed in the slightest.

[@Hortondlfn1]

My reasoning was flawless! Except for the fact it was wrong.

[@ricciardisimone]

Solved both! Thank you for the brain workout! ❤

[@mikehigham23]

FWIW, this is OpenAI's ChatGPT answer: This logic puzzle requires careful analysis of the information exchanged between the two logicians, A and B. Let's break down the conversation and analyze each statement to deduce A's number and how B figured it out. A asks B: "Is your number double mine?" This implies that A's number is not greater than 15, because if it were, it couldn't be doubled and still be within the 1 to 30 range. B replies: "I don't know. Is your number double mine?" Since B doesn't know, B's number cannot be less than 8 because any number less than 8 doubled would still be within the 1 to 30 range, and B would know the answer. B's question implies B's number is not greater than 15, because if it were, it couldn't be doubled and still be within the 1 to 30 range. A replies: "I don't know. Is your number half mine?" A's response of "I don't know" means A's number is not less than 16, because if A's number were less than 16, halving it would always result in a number less than 8, and A would know that B's number is not half of A's. A's question implies that A's number is even. B replies: "I don't know. Is your number half mine?" B's response of "I don't know" means B's number is not even, because if B's number were even, halving it would result in a whole number, and B would know if A's number is half of B's. B's question suggests B's number could be even. A replies: "I don't know." This implies that A's number being half of B's number is still a possibility, which suggests A's number is an even number less than or equal to 15 (as previously deduced). B replies: "I know your number." At this point, B has enough information to deduce A's number. Considering the restrictions: A's number is less than or equal to 15 and even (from A's second and third statements). B's number is greater than or equal to 8 and not even (from B's second and fourth statements). The possible pairs of numbers that satisfy these conditions are limited. By examining each pair, B can deduce A's number based on the information exchanged. After examining the possibilities, the only pair that fits all the criteria is: A's number is 10, and B's number is 15. If A's number were 10 and B's number were 15, all the statements would be true, and B would be able to deduce A's number after the final exchange. So, A's number is 10, and B knows this because it's the only number that fits all the criteria based on their conversation.

[@m_chupon5131]

ChatGPT: "A's response of "I don't know" means A's number is not less than 16" Also ChatGPT: "A's number is 10" ChatGPT you are making my head hurt.

[@starryk79]

Chat GPT is not made for solving logical puzzles, it is great in generating text that sounds plausible but isn't necessarily.

[@borntoyeet1320]

Normally with these puzzles I'll just wait for the explanation, but for some reason I decided to try both of these and I'm happy to say that I got them both right. 3841 for the combination, and 4 for A's number!

[@RickyBobby-ty7nc]

Good puzzles! Anyone else get tripped up by the second puzzle. I thought that when A said their first line ''Is your number double mine', A had to have a number that could be doubled. So A's number was 1-15.

[@se6369]

There weren't any rules about nonsense questions

[@RedFloyd469]

Yep. The question makes no sense if the logicians were consistently logical. As they weren't, the questions are arbitrarily illogical. Bad logic puzzle. It demands that the one solving the puzzle knows prematurely which question is asked with a logical mindset and which isn't. This is impossible information to infer, therefore the puzzle makes no sense.

[@BeenThrDunThat]

The first puzzle is a similar/simpler version of an older game called super master mind that was around in the seventies, maybe still is in some form. Was a tad harder because it was colors and 5 slots (instead of 4) and allowed for blanks and duplicates along with the various other possible combinations but each guess would be scored the same "right color in right spot" or "right color in wrong spot" or no match at all. Parents used the game to keep me busy while they played bridge with their friends. Only peaked/cheated once that I remember!

[@caspergotlost]

I used to have this as an app, or at least incredibly similar- I think it was called code breaker

[@IbrahimQasim-sb5kr]

In my childhood we had a similar game but instead of using numbers we used letters of a password and it has to have a meaning. One player makes the password and the others play it in turn to guess it. The player who won that round would be the one making the password in the next one.

[@rhaining]

Great puzzles, and fantastic video walking through methods to solve!

[@Godithseeker]

Issue I always have with puzzle 2 is that I often forget you have to assume both people are perfectly logical. If either was just a normal person the question would not be solvable.

[@gamingnamehere1560]

true cause if they dont know they just dont know

[@AryanAgrawal-777]

So, in the second one, the first statement tells us that A's number ranges from 1-15. The second statement tells us that B's number ranges from 1-7. The third statement tells us that A's number is in the set {2,4,6,8,10,12,14}. The fifth statement tells us that B's number is in the set {2,4,6}. The sixth statement tells us that since A is already an even number and is possibly even half of the possible numbers that B has, that only leaves us with A's number = 2. There, you have it.

[@wdywkhuh]

By Basic Mathematics We have, 1-30 Look from first two statements : Any number after 15 gives its double more than 30 which is not possible according to the given condition that the numbers should lie between 1-30. We are left with 1-15 According to the other two statements the numbers can't be odd since the half of odd numbers gives fractional value which contradicts the condition which says the no. Should be whole number. We got 2 4 6 8 10 12 14 Now the halves of 2, 6, 10, 14 are odd no.s of B which is again contradictory to given condition. We are now left with 4, 8, 12 For 8: Half of 8 is 4 which is even✅ But double of 8 is 16❌. Since 16 is greater than 15 which is not possible. For 12: Half of 12 is 6✅ But here also double of 12 is 24❌ For 4: Half of 4 is 2✅ (2 is even & 1

[@BigMac4459]

For the second problem i was operating off the assumption if someone asks if their number could be doubled that they would only ask it if that were even possible which would exclude 16-30. Thoughts on this?

[@yurenchu]

Why would they only ask if it's possible (i.e. if they can expect "Yes" as an answer)? Would "No" not be acceptable as a possible answer?

[@struful]

​@@yurenchu because you can get the same information from "is your number divisible by 2?" Why would I ask a question that could lead my partner down the wrong thinking path? Would be better to constrain me to only asking questions that convey no information about my number.

[@yurenchu]

@@struful Why would the "partner" (in this case, B) be led down a wrong thinking path? Or why would A think that B would be led down a wrong thinking path? A and B are both logicians, they both know better than to blindly assume things that are not necessarily true.

[@BigMac4459]

@@yurenchu This is true it's just a question of is it logically sound or even valid to ask a question that you know is a negative. In this case it would be to get information of your partner's number which is acceptable but it's logically vague. Is your number double mine and I have a 16 I know logically that it is not because 32 was not an option. It's a matter of them asking questions regardless of it is possible but to convey information to the other.

[@se6369]

It was never stated it would function like this

[@bennmurhaaya8518]

I've approached the second problem differently and I can't seem to find where my logic is wrong. - If A asks: Is your number double mine, that means that A's number is max 15. If he had 16+ he could not be asking the B about B's number being possibly double. That cuts down the A's options to (1 - 15). - B, having just narrowed down A's choices to 1 - 15 does not know if B's (his own) number is double of A. That would cut the possible Bs numbers to even numbers from 2 - 30 including. If B had an odd number it would have answered No it's not double of yours. - But B goes and asks the same question if A's number is double of B. A does not know if A's number is a double of B so that first rules out odd numbers as a possibility for A. It rules out 2 because B can have even from and should leave the A with (4,8,12) as double the options of B below 15 (multiples of four below 15). - A asks is your number half of mine? That is either: 2, 4, 6? B does not know which narrows down the B's numbers to these 2, 4, 6 otherwise the answer would have been different. - B asks is your number half of mine? Which I don't really get, because it's like asking: Is your number either 1, 2 or 3? even though it has been established that none of their options can be odd and 2 is not even and option A has.

[@bennmurhaaya8518]

I think my problem lays with the fact that I deduced some information about A's set just from him positing the question and not only from B's answers. My aproach cut down the A's possible numbers to half which in turn cut down all the posibilities and left me with B asking for 1,2,3 instead of 1,2,3,4,5,6,7 leaving the 4 as the only common number. Let's imagine that A's number is 19 and he asks B: Is your number double of mine? Why would he be asking such question if he knew the answer lays outside of the boundaries?

[@rioc2802]

@@bennmurhaaya8518 "A's number is 19" and "A asks B 'is your number double mine'" aren't related events and you can't related them by the fact that A is a logician. A's number is 4: - If B picked an odd number they would say "No", because then A's number wouldn't be a whole number. - If B picked an even number, and knows that the possible numbers A could've picked includes at least 2 even numbers, they respond "I don't know". - If B picked an even number, and knows what A's number is, they would respond "Yes". A's number is 19: - If B picked an odd number they would say "No", because then A's number wouldn't be a whole number. - If B picked an even number, and knows that the possible numbers A could've picked includes at least 2 even numbers, they respond "I don't know". - If B picked an even number, and knows what A's number is, they would respond "Yes". When you assume that A wouldn't ask "is your number double mine" just because they picked a number greater than 15, you're introducing an element into the puzzle that was never stated and making assumptions about what a logician would do, but you can't guarantee that. The problem wouldn't change for example if A and B both asked each other if the other's number is 67 before asking the questions presented in the video.

[@asdfqwerty14587]

It doesn't make any difference what number A has. A already knows that the answer can't be yes no matter what number they have. If you're saying that "A can't ask a question that will never be yes", then that would be basically saying that A can't ever ask that question.. because it was never possible for B to answer yes to that question no matter what number A had. Further, we don't know anything about what questions they are or aren't allowed to ask, or even if they have any motivation to be trying to figure out what the other person's number is. All we know is that those questions were in fact asked, and that nobody knew what the other person's number is until the last step, which is only possible if A had the number 4 (otherwise one of them would need to have answered differently at some point during the puzzle). Speculating on why they asked the questions they did makes no sense when we don't even know what motivations they have or if they have a choice of what questions to ask to begin with.

[@chubbyclub2502]

I got lost on the last one. I felt proud though for being able to correctly reduce the possibilities to 4, 8 and 12.

[@tvmy121]

You can aluminate 8 and 12 because if you double it is more than 15.

[@chubbyclub2502]

@@tvmy121 Yeah I didn't catch that part.

[@oknelphil]

a better version of the second puzzle would be: A: "Is your number double mine?" B: "I dont know. Is your number double mine?" A: "I dont know. Is your number equal to mine?" B: "Yes" What is their Number?

[@phluidsph6269]

true! thats awesome!!

[@Wither_Strike]

For the second problem i got 2 A: is your number double mine? (This implies its possible, therefore A

[@g-rexsaurus794]

This is fine when you assume both parties are making genuine questions based on their own knowledge like real people, but the problem doesn't use such people and doesnt clarify a few pressupositions and rules.

[@Wither_Strike]

@g-rexsaurus794 in that case what's to stop them from answering falsely as well? At that point both could be any number

[@g-rexsaurus794]

@@Wither_Strike I mean, you are completely right as the rules dont even explictly state that A and B know about the veradicity of each other's responses

[@Yusso]

As soon as A asks "Is your number double mine?" you can eliminate 16 to 30 of A's numbers because for those numbers A wouldn't need to ask.

[@justinharper6909]

The statements are always true, the questions don´t have to be. You make an assumption that is not in the question.

[@_P2M_]

"A wouldn't need to ask." So? That doesn't prevent A from asking anyway.

[@DmitDmit1]

@@justinharper6909 there was also a statement that they are logicians. Fair to assume they ask reasonable questions

[@MCTrapsandTutorials]

​​@@DmitDmit1Reasonable question does not mean that it cant be an always false question. The point of asking the question is to learn whay the other knows. I think there would be less confusion if you mentally add a "Do you know if..." to the start of their questions

[@DmitDmit1]

@@MCTrapsandTutorials As a logician, what are you trying to achieve by asking "is your number double my number"? In your interpretation the point is figuring out if the opponent's number is odd or even. Why not ask directly this question and avoid possible confusion. Clearly the author of the puzzle tried to be fancy but didn't think it through

[@Maple38]

Great puzzles! Solved the first one (albeit it definitely took longer than your solution), and needed a tiny bit of guidance from the solution for the second problem, but managed to get the answer for that too.

[@Pengalen]

The second puzzle is dependent on a large number of assumptions.

[@gizmophoto3577]

Years ago, I wrote a program for an HP-11C to generate 4-digit number puzzles, then score the guesses. My notation was x.y, with x being the number of correct digits in the correct location, and y as the number of correct digits incorrectly placed, 4.0 being the solution. I used that same notation to solve this one. I still have that program listing somewhere.

[@eragon78]

So my thoughts before watching. B does not know if their number if double A's, this must mean its possible for it to be double. All numbers which are double an integer must be an even number. Therefore B must have an even number between 1 and 30. A now knows B has an even number 1-30. They do not know if their number is double B's, this must mean its possible to be double. A number that is double any multiple of 2 must be a multiple of 4. Thus B must have a number between 1 and 30 which is a multiple of 4. B now knows A has a number that is a multiple of 4 between 1 and 30. B does not know if their number is half A's number, which means it must be possible for it to be. This must mean B has a number between 1 and 15 since any number 16 or greater would be larger than 30 if doubled. Thus B has an even number between 1 and 15. A now knows B has an even number between 1 and 15. A does not know if their number is half of B's number, which must mean that it has the potential to be. This must mean A has a number between 1 and 7, since any number 8 or greater would larger than 15 when doubled. A's number must also have a factor of 4 due to previous logic. Therefore A must have a number between 1 and 7 which has a factor of 4, of which only one integer number exists which is the number 4. Therefore A must have the number 4. (And B must have one of the numbers 2/4/6/8/10/12/14)

[@christianwetzel1862]

My thought process on problem 2: Already with A's first question ("Is your number double mine?"), B could eliminate numbers 15-30 from A's possible numbers, and the same vice versa with B's first question. After the next round it is then clear that A's number must be 1) double of an even number smaller than 15, as well as 2) half of another even number smaller than 15, leaving 4 as the only possible answer.

[@colcob]

This assumes there is a rule that states no-one will ask a question they already know the answer to. This is not stated in the problem, so you cannot presume that limitation on questioning. Albeit you still got the correct answer!

[@renedekker9806]

​@@colcob _"This is not stated in the problem"_ - it is not stated in the problem either that they are both perfect in logic. Yet both are reasonable assumptions to make in a puzzle like this. By the way, when you make that assumption, you won't reach the conclusion of 4. The puzzle doesn't have an answer.

[@christianwetzel1862]

​@@colcob Both are stated to be logicians, so I would assume that each subsequent question would be informed by the previous answers and questions, and each one knowing that the _other one_ knows what _they_ should know up to the respective point.

[@taflo1981]

@@christianwetzel1862 Even if A chose a number larger than 15, asking whether B's number is double A's number is still sensible. The purpose of the question would not be to figure out what the correct answer is (A would already know that it's "no"), but to figure out if B knows the answer. Any question whose answer can give you new information is reasonable.

[@tiemen9095]

​@@taflo1981exactly!

[@NitinRathod-ws3qy]

Yeah I solved both, I really like it I love logic puzzles and God's grace I'm pretty good at solving those idk how from technical wordings like yours but i can solve them in my head like these two (yeah I did em in my head) and then watched the vid to see if answers matched and they did 🎉 , really love your vids pls keep them coming! ❤

[@kurticusmaximus]

I like these kind of puzzles. Ones that don’t surprise you with “all you need to do is apply Fermat’s Last Theorem from 1637 to solve it!” Simple logic and reasoning anyone can walk through.

[@vitriolicAmaranth]

who hurt you?

[@Eye-vp5de]

Usually such puzzles (ones with Fermat's last theorem) don't appear on youtube, since people use it for entertainment and such puzzles don't get many views (bc dislikes exist)

[@Bell2323]

The number in the second puzzle can be deduced quicker, since when A asks if his number doubles hers, she's saying that her number is between 1 and 15, which eliminates a step.

[@rioc2802]

A's first question to B does not imply that their number must be between 1 and 15. You can't pull that kind of information from a question being asked without evidence to back it up.

[@jnam23]

@@rioc2802They both know that both of them picked a number between 1 and 30. They are logicians. If your number was 16, you wouldn’t ask if they had a number that was double yours because that’s impossible. That wouldn’t be logical for YOU.

[@victorpaesplinio2865]

My reasoning for the code puzzle is a little different. Consider each statement in order. The "nothing is correct" is the 4th. Consider the 3rd and the 1st. From the 4th we know that 5 and 0 are incorrect, so either 2 or 1 must be in the correct place on the 3rd. But the 1st says the correct digit is in the wrong place, and it can't be the 2 the correct digit since it would contradict the 3rd. Hence the number 1 is correct and the code is ---1. We also know that either 9 or 8 is correct. The 5th statement shows us that 8 and 4 are correct digits since 5 and 2 aren't. Since 8 is correct it means the correct digit in the 1st must be it. Then it can't be on the first nor in the third position, meaning it must be in the second. The code is -8-1 and we still have to fit the 4. The 2nd shows us that 1 and 3 are correct digits in wrong places. Hence 3 must be the first digit and 4 will fit in the third position. The code must be 3841.

[@taflo1981]

Since the comment section seems to be flooded with comments asking why in Problem 2, the very first question of A doesn't reveal that her number is at most 15, I try to explain in this separate comment why this isn't the case. The discussion between A and B can be thought of as each of them interrogating the other and I agree that as logicians, each question should have the purpose to gain information. (Although technically even that is an additional assumption that's not in the statement of the problem.) However, even if you already know the answer to a question, if you don't know whether the other person *also knows*, then asking the question will be sensible, because the answer will give you new information (assuming that no lying is involved, which was part of the setting of the problem). A question only becomes pointless if you already know for sure what the other person will answer. Thus, none of the questions themselves reveal any information, just the answers.

[@BederikStorm]

No, I think that Presh just missed that first question was not only revealing even numbers but also limited numbers with 15 at most. It does not contradict anything as he did the same elimination after.

[@Bismarck-S]

Yes this is the beautiful thing about questions. Another example of this occurrence is in police interrogations. They might ask the suspect where they were at a given time, to gather information about the suspect and the crime in general, even though they know exactly where the suspect was at the time given.

[@taflo1981]

@@BederikStorm Well, I tried to explain why A's question does *not* reveal anything about her number. If "every question is only asked if the person asking doesn't already know the correct answer" were a rule (to be clear, I'm positive it isn't a rule), the puzzle would not work: - The first question of A would reduce her possible numbers to 1-15. - B's answer would then reduce his possible numbers to even numbers. - B's first question would now eliminate all numbers greater than 15, only leaving 2,4,6,8,10,12,14 for his numbers. - A's answer would reveal that her number is double one of B's possible numbers at that point in time, only leavingt 4,8,12 for A. - A's second question would not convey any new information. - B's answer would show that he has 2,4 or 6. But then B's second answer would contradict the "rules", because he knows that A's number can't be half of his. (B even knows that A knows the same.) Meaning that if this were a rule, then it was broken by B with his second question. Not to mention that A would also have lied by claiming that she doesn't know.

[@taflo1981]

@@Bismarck-S Exactly. The same holds for exams (checking knowledge of the examinee), hiring committees (also to see the reaction to the question, the way they answer it and how they behave), or even things like debates.

[@yurenchu]

​@@BederikStorm Presh didn't "miss" anything, he's not the author of these riddles. If anything, Presh possibly noticed that this riddle has a potential to go viral due to its controversial logic element, and hence thought it would be very suitable for his youtube channel.

[@Someone-tn8ur]

Here is the problem with the second puzzle: Once A asks if B's number is double hers, B can conclude that A does not have a number above 15. If he reasons this, the rest of the questions do not follow with the ambiguities of "I don't know"

[@Meager02]

B is a logician, so he would not conclude such an idiotic thing.

[@hahahasan]

Each logician can only gather information from questions they ask not from ones they answer. If A had 4 or if A had 20, B would answer the question the same way because he doesn't know what A has.

[@momom6197]

Logicians famously like to know if their interlocutor are aware of some tautologies. In this case, if A has 20 and asks "Is your number double mine?", she knows the answer cannot be positive, but it will still give her information about what B knows of her number. Of course, she's not trying to figure out her own number, but asking the question allows her to deduce facts about the hypotheticals entertained by her interlocutor. In fact, if you calculate the possible outcomes of her move, it's an incredibly effective question from the perspective of information theory: 1- If B answers "yes", they both know which number the other has. (Under the assumption that all the statements they utter are valid.) 2- If B answers "no", considering that she knows that B doesn't know her number, she can deduce that his number is odd. 3- If B answers "I don't know", as shown in the video, she knows that B's number is even. Outcome 1 is unfeasible under the initialization of the problem, thus in all feasible cases she divides her candidate pool by half, which is the optimal result of a binary question. Ask a closed question, get 1 bit of information: she couldn't do better at trying to guess B's number.

[@momom6197]

(Although the question is not optimal for the whole game of both trying to guess each other's number. If she considered that B is optimizing his questions too, and that they are cooperating to find the truth, then she could divide the candidate space by nine with an optimal question, but at the cost of quadrupling the initial candidate space.)

[@Someone-tn8ur]

​@@Meager02what an idiotic response.

[@narancs5]

I went with a different approach for the second riddle, did not come to the same result because of my logical flaws at the last steps but implementing this idea could improve your solution. So for the first question A would only ask if B's number is double if that was possible -> A's number must be 15 or below When B replies I don't know that means -> B's number is not 1 As soon as he askes is you number double mine knowing A's number is 15 or below it is clear that -> B's number must be 7 or below. When A replies I don't know that means -> A's number cannot be 1 The rest is where I went wrong and got the wrong result but you get the idea.

[@kamehapa]

If you are to assume that the logicians cannot ask questions where the results will either be "I don't know" or "No" then it actually makes the second problem not have a solution; fortunately the logicians know that they can still get information even if the answer to the question can't be yes. If it was a rule that they could only ask questions where yes was a possibility the logic would be as follows: Q1: Possible A: 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15 Possible B: 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30 Player A would not ask the question if double their result would be outside the set. Player B has confirmed they are even. Q2: Possible A: 4,8,12 Possible B: 2,4,6 Player B knows Players A's set is between 1-15, therefore to ask this question their number must be less than 7. Player A has confirmed they are a multiple of 4. Q3: Possible A: 4,8,12 Possible B: 2,4,6 Player A and Player B reveal no new additional information about themselves. Q4: !Paradox Player B asks if Player A's results would be half of theirs, which would mean they imagine options 1,2,3 being in A's possibilities which they know they are not.

[@muhammadsyafiiq7203]

The phrasing of 2nd puzzle is a bit weird to me at first. Should've been clearer if they say: "Could your number be double mine?" (but i can still understand "is your number...") And "Probably" instead of "I don't know". it only makes sense to me when i remember that they are concealing each other's number.

[@Lcsmu]

By using the "the first question makes A number be 15 or below" logic, can I shorten the puzzle? A - is your number double mine? B - IDK, is your number double mine? A - IDK. Do we have the same number? B - Yes. Question: what is the number?

[@mikicoal]

A piece of logic missing from the second puzzle is that when A asks the first question, B can establish that A's number is 15 or lower, and when B asks the same question, A can do likewise.

[@marekgnutek251]

Not necessary. Even if A's number is 30, the first question is valid.

[@noodle_fc]

You are right, and that actually breaks the puzzle. When B asks the question knowing that A ≤ 15, then his own number must be ≤ 7. Later, when B knows that A's number is a multiple of 4, he would only ask if her number were half his if he had 8 or more, but we already know from his first question that he doesn't. He wouldn't ask that.

[@Tom-jw7ii]

I started solving the puzzle that way too, but I reconsidered when I realized it was a dead end. It’s kind of like the Pinocchio’s green hats puzzle in that what could be construed as dishonest in normal human behavior is still valid mathematically. Even if A knows that B’s number is not double their own, it’s B’s answer to that question they actually care about, and the true value of A’s number doesn’t prohibit them from asking that question. Therefore B cannot conclude that A’s number must be such that the answer could possibly be yes.

[@noodle_fc]

@@marekgnutek251 How is it a valid question if A's number is 30? 30 is the maximum. No logician is going to ask whether their partner's number is greater than the maximum. What's the point? EDIT: after reading Tom-jw7ii's comment, I understand why A could still usefully ask that question. I don't like it, but I understand it.

[@noodle_fc]

@@Tom-jw7ii Okay, I see what you're saying. But if the information A can glean is limited to whether B's number is even or odd, and asking in another form conveys nothing to B, why not ask directly about parity to begin with? The only reason not to do so is for our benefit, where we have to make the logical inference that an answer of "I don't know" implies an even number. If you want the reader to make that leap, write the puzzle with constraints such that A must ask it that way.

[@quantheory]

These logician puzzles are always weird, because the answer depends on the logicians' "theory of mind", each one's internal model of how the other logician thinks. The puzzle only works if each logician is infinitely quick to deduce all implications of the data present, and also completely truthful, and also has an inerrant theory of mind about all other logicians. That's very different from how real people work! Thus there a number of unstated assumptions in the puzzle that would not usually be true in real life, e.g. both logicians not only believe the other person is inerrant and telling the truth, but also both logicians have to know, for certain, that "I don't know" means "I can't possibly figure it out" rather than "I don't know because I couldn't be bothered to think about it". That is, they have some value system or objective that compels them to give an answer that is not just true, but deeply considered. I think this is why so many people think that the first question should eliminate the possibility that A has a number >15. If both people are so cooperative that they are expending so much effort to give each other answers that are as accurate as possible, then it seems like they *must* both be trying to bring the game to a conclusion as quickly as possible. Hence that they must be using the questions to communicate as much information as possible. Unfortunately, such an assumption breaks the puzzle. To get the "correct" answer, you sort of have to assume that both logicians place a high value on communicating as much information as possible through answers, but at the same time intend their questions to communicate no meaningful information whatsoever. (Also notable: many comments have described A and B as "opponents". But nowhere in the puzzle is it stated that this is a competition! It could equally well be a cooperative exercise, or just an experiment by two bored academics. In real life, this wouldn't make much sense as a competition, since one could always try to lie, or simply plug one's ears during the other person's question and then truthfully answer "I don't know" every time.)

[@Lila-ie1eo]

A lot of people are mad at the second riddle, but it doesn't state that they are cooperating. It only says that "all statements are true". A question is not a statement, and they can ask whatever they want regardless of their number. To simplify, if the only numbers were 1 and 2, and you have 2, if would still make sense to ask "is your number bigger than mine?" even though you know it can't be, because if they say "no", it means they have 1, which can be either smaller or equal, while if they say "idk" it means they have 2, which is either bigger or equal, but they don't know which one.

[@JackPullen-Paradox]

I created a program that would solve the Master Mind puzzle many years ago. The method of the program was to keep track of the "Boolean" equations representing the positions and colors of the colored pegs. I don't recall all the details at this point, but it was pretty simple to program. I do remember that each equation equaled 1 for true, and that the equations were multiplied together at each step. I would say that the 4-digit code problem can be solved by a closed form computer program in a similar way. It might be interesting to make this a challenge.

[@NoteGames380]

Better version of riddle 2 where the two logicians are actually logicians. Whole numbers 1-130 A: Is your number double mine? B: Idk, is your number double mine? A: Idk, is your number less than mine? B: Idk, is your number half mine? A: Idk, is your number greater than mine? B: Idk, is your number greater than mine? A: Yes, and I know your number! What are A and B’s numbers?

[@unerror]

I think the logicians in the second puzzle are missing a crucial inference that they can make, making the result faulty (what I mean is, the conversation should've ended earlier, and they should've figured out the number earlier). As soon as A asks the first question "Is your number double mine?", B immediately knows that A's number must be less than or equal to 15 (otherwise there's no way that B's number = 2 * A, and assuming A wouldn't be asking a question to which she already knows the answer is definitely NO).

[@rioc2802]

I don't think you can necessarily assume that though. The only information given is that A and B both individually picked numbers between 1 and 30 and they asked questions and said "I don't know" truthfully several times before B truthfully said they knew A's number. A can ask the question "Is your number double mine" even if their number is 16 or more as the result from B is the same; they would've said "No" if they picked an odd number, and they don't definitive know A's number otherwise, so they have to respond "I don't know".

[@rohangeorge712]

thats why the question is bad from a perfect logician, its all to do with semantics. to avoid this issue, A should ask "could your number possibly be double of mine" (just to make it clearer for us that b cant assume that A's number is 1-15). because a perfect logicial wouldnt ask "is your answer double mine" if they know thats not the case, and that would cause B to assume that A's number is 1-15. its sort of confusing that that point.

[@unerror]

@@rioc2802 That still doesn't make sense to me - why should A or B make inferences just from the replies to their questions, but not from the questions asked to them? If A had a number greater than 15, why would she risk such an ambiguity by asking "is your number double mine?"; instead of directly asking "is your number even?". The fact that a number in an interval being 2 times of another conveys more information than just oddness/evenness test, should compel the other to deduce, it is deliberately asked that way, and not the other. There's no way either A or B could answer "Yes" to the question. They can answer "IDK" if it's even, or "No" if it's odd. So, why not directly ask whether it's even?

[@unerror]

@@rohangeorge712 yes exactly! otherwise the rules should explicitly state; either to make inferences just from the replies not from the questions, or that the logicians may ask questions of which they already know the actual truth value.

[@rioc2802]

​@@unerror All B knows, when A first asks a question is that: - A picked a number between 1 and 30. - A asked B "Is your number double mine?" As B, you don't know what A's exact intent is. You're assuming "A wouldn't ask this question if they picked a number between 16 and 30" without explaining why. A picking 30 and asking whether B's number is double their's is a completely valid hypothetical scenario, thus, B has no reason to discard it. It doesn't matter if you personally wouldn't pick that question, or if "is your number odd/even?" produces a similar result in a less convoluted fashion because none of those are elements in the riddle itself.

[@Yeah-I-am-Me]

B: is your number 4? A: yes the end

[@tanaysingh7913]

Wait what!?

[@northernbear13]

Yes, as others noted, when A asks "is your number double mine" that should eliminate A having any numbers over 15. And the logic seems to break down after that.

[@rinosanchez2150]

You're assuming an intent behind A's question which is not stated in the problem. We're not told that A is trying to figure out B's number at all, or that they're competing in any way As far as we know, this is just an abstract intellectual exercise.

[@nidadursunoglu6663]

Guys! Why is everybody eliminating numbers above 16? Its okay to ask theirs is double yours even like that. Because their answer will tell you if their number is odd or not! You gain info from the question still. Its askable.

[@MCTrapsandTutorials]

Everyone seems confused about the second question and is assuming it can eliminate 16-30. This isnt true. Asking a question can be useful even if you know the answer. Why? Because you learn what the other knows, which is ultimately the goal. Lets make a shitty easy riddle to show how. Say you and 2 friends (A and B) are made to play a game where each of you gets a token that only you see. One is white and two are black. You have to then ask A one question to find who has the white one, but you arent allowed to ask them any question about their token. You look at you token and see its black. You ask A "Is my token white" despite knowing it is not. If A answers no then you know A has white, if "I dont know" then B has white. Thus you solved the riddle by asking a question you know the answer too.

[@legendgames128]

This is why the riddle should be A: Is your number odd? B: No, is your number doubly even? A: Yes, is your number half mine? B: I dunno, is your number half mine? A: I dunno. B: Your number is ____

[@MisuVir]

Yes, the problem here is with *assumptions*. People are assuming that B can infer something about A's number from A's question, but that is not *necessarily* a correct assumption. In a logic puzzle, you should not make an assumption unless it's certainly a true assumption.

[@illiil9052]

Shouldn't A's first question implies A's number is at most 15? Why would A ask if B's number is double when A got a number greater than 15?

[@leonfu3883]

At the beginning, when A asked B "Is your number double mine?", it already means A's number is no more than 15. Otherwise, A should not ask this question. Then after 2nd Q&A, it means B's number is even number that no more than 15. Otherwise, B should not ask this question. So A's number has to be x4 number that no more than 7 because A said "I don't know". So only 2 Q&As can get the result - A's number is 4.

[@nh_999]

That’s not actually true. You’ll find that the restriction to only asking questions you don’t know the answer to will force all the question, and lead to unsolvable situations E.g. for the first question A must ask “is your number double mine” as asking the latter eliminates 4: A -> 1-15 B -> even B must ask “is your number double mine” for the same reasons A-> 4, 8, 12 B -> 2, 4, 6 Now we’re stuck. A must ask “is your number half mine” because otherwise 4 and 12 gets eliminated, and B must ask “is your number double mine” because otherwise 2 and 4 is eliminated. Both results in “I don’t know” and leads to no progression

[@rolandfisher]

So satisfying. It took me just the right amount of time and brain power to solve them with full engagement. Not too easy, not too hard. Juuuust goldylocks

[@13xPetra]

I'm quite happy to have known that I had solved the 2nd puzzle within 5 minutes! I did not think I got it right, but there was no other option!

[@OctopussInPants10min]

I got to the right answer in my head on the second one by virtue of needing a number that could be halved twice and doubled twice and still be between 0 and 30, and the only number which can do that is 4!

[@FinalDisnerd]

This is an old puzzle, and it's been echoed a hundred times before, but I want to clarify my own confusion and WHY the first question in part 2 is faulty. As perfect logicians, if A's number is above 15, then they know the answer is No either way, but with the added knowledge of B doesn't know that part, so while B's answer of "No" means their number is odd, and an answer of "I don't know" means their answer is "Even", that doesn't give B any information, and can in fact be misinterpreted, as shown by a great many of us in the comments. They could have simply asked "Is your number even" and gotten the same results, but with less ambiguation. The fact that they worded their question the way they did, as perfect logicians, implies that they're trying to relay information as much as they are gathering information. TLDR: As a perfect logician, A's first question is perfectly fine for themselves, but does nothing to help B, which would work better if this is a competition to see who can guess first.

[@joosh_rocks]

I got both of these correct before the solution without writing anything down, they were super fun, especially the second one where I had to go back and draw more information out of the deductions I already made.

[@dale3478]

I almost got the second problem correct. I managed to get that B knows A's number is multiply of 4, and after asking the last question the possible number would be 1 to 7, but because I did it all inside my head, I lost track about which are which

[@DimensionParadox]

The first puzzle is a game that a classmate of mine and I used to play regularly in class. It's called "bulls and cows". Everyone comes up with a four-digit number that only they know. Then one gives a random four-digit number to the other, and he must answer how many cows and bulls are in that number according to the number he has secretly thought up. A "bull" is a correct number in the correct place. "Cow" is a correct number in the incorrect place. After he has given an answer, it is his turn to ask. And so we take turns until someone guesses the correct four-digit number and wins the game. We usually gave the answer on the fifth or sixth try, just like in the puzzle example. It was such a pleasure to recall the game and guess the answer because I hadn't played that game in 25 years.

[@ajitsdeshpande]

In the final question which B asks A "Is your number of half of mine", A can and should answer Yes, because of the deduction and elimination which is common knowledge to both, A can say yes. And then B can say A's number is 4.

[@BlitzPSH]

Question 1: If B answers "I don't know", their number is 2x some number from 1 to 30. B answers "I don't know" so they know B is one of (2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30). Question 2: If A answers "I don't know", their number is 2x one of B's numbers. A says "I don't know" so they know A is one of (4, 8, 12, 16, 20, 24, 28). Question 3: If B answers "I don't know", their number is in the intersection of B's previous options and (2, 4, 6, 8, 10, 12, 14) B says "I don't know" so they know B is one of (2, 4, 6, 8, 10, 12, 14). Question 4: If A answers "I don't know", their number is in the intersection of A's previous options and (1, 2, 3, 4, 5, 6, 7). A says "I don't know". The only number of A's between 1 and 7 was 4. So A's number is 4.

[@taylorcombs1519]

I sat here and did both and did them right. I'm proud of myself.

[@drew3030]

The 1st question to the second puzzle was not "is your number exactly double mine", it was just "is your number double mine". So rather than ruling out the odd numbers, this rules out B having a number greater than 15. If B had a number higher than 15, B would have to answer no because 2*x>30 for x = 16, 17... 30. By answering idk B implies that it is possible to double his/her number and for it to be double A's. If you also change the question to it being exactly double, you are only left with B possibly having 2, 4, 6, 8, 10, 12, 14. This makes the third question redundant!

[@handanyldzhan9232]

Q1. Take 1937 and 8524. Both have two correct digits each, and don't have any digits in common, so other digits (0, 6) don't exist at all. There's nothing wrong in 6507, so 193X and 8X24 have two correct digits (1, 9, 3, 8, 2, 4). In 5201, one digit is correct and in the right position (X2X1, 1 or 2). In 9285, one digit is correct and in the wrong position (928X, 9, 2 or 8), meaning 1, 3 and 4 exist. Given 5201, the only correct digit must be 1 as the 4th digit. 2 doesn't exist. 8524 -> 8X24 -> 8XX4 -> 8 and 4 exist but 8 isn't the 1st or 4th digit. 4 isn't the 4th either. 1937 -> 193X -> 9 doesn't exist. 1 isn't the 1st, 3 isn't the 3rd. Only 1, 3, 8 and 4 exist. 9285 -> 8 exists, not the 3rd. 8 -> 2nd 4 -> 1st, 2nd, 3rd 3 -> 1st, 2nd 3841. ---------------------- Q2. Just because a logician knows the answer to a question, it doesn't mean the other does. It can be a good way to help the other figure things out. A1. A asks if B's number is double hers. Her number can be over 15 or not. She wants to size things up. B1. B doesn't know the answer, which can only mean his number is even. Then he asks if her number is double his. A2. From B's answer, A realizes B has an even number. She can't give a concrete answer herself, because hers is actually divisible by 4. Then she asks if his number is half hers. B2. B has an even number, and realizes A's is a multiple of 4. He can't give a concrete answer, because his number is below 16. Then he asks if her number is half his. A3. A's number is divisible by 4. She realizes B's number is even and below 16. She can't give a concrete answer because hers is below 8. B3. B realizes A has 4.

[@BWeManX]

Question 1 was pretty straightforward Question 2, it's pretty clear that B wasn't actually listening and spent the conversation searching his phone history and determined A's number. They still text sometimes.

[@wherearetheturtles3963]

B is even A is even Both numbers could be doubled, otherwise they wouldn’t ask, so both numbers are between 2-14 A’s number is even when halved, so she must have 4, 8, or 12 B doesn’t know if his number is half of A’s, so he must have 2, 4 or 6 Considering this, the following questions and answers don’t make any sense B knows that A’s number can’t be half of his, and A knows this too

[@Anonymous-jo2no]

For the first puzzle, after reading nothing is correct, I just started crossing all the 5s, 0s, and 7s from the other clues, and then my attention were brought to clue no. 3 and 1. On clue no. 3, we know 5 and 0 are wrong so the correct answer must be either 2 or 1; but 2 can't be the correct answer because then the location is a contradiction with clue 1. My movement then goes to clue 5 where we know that 8 and 4 are the correct numbers, then to clue 1 to figure out that 9 is wrong, and then to clue 2 to figure out 1 and 3 are the correct numbers. How I figured out the location is the same as how you do it. Second puzzle took me a while before the gears in my brain start turning. Basically same thought process.

[@anime_enjoyer5507]

i answered the first one easily but couldnt answer the second one, probably bcuz im a skeptical person.. 'i dont know' is a very easy thing to say and i usually dont overthink if people said it because there's million ways it can go about it..

[@danielkelsosmith]

The first one was easy. Second one, the wording got me 🤷‍♂️😂