Can you solve the impossible day of the week logic puzzle?
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- Опубліковано 6 кві 2024
- Can you solve for the day of the week Abby was born? What about Barry? This is an incredible logic riddle.
van Ditmarsch, Hans, Michael Ian Hartley, Barteld Kooi, Jonathan Welton, and Joseph BW Yeo. "Cheryl's Birthday." arXiv preprint arXiv:1708.02654 (2017).
arxiv.org/pdf/1708.02654.pdf
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Three logicians go into a bar.
The bartender asks, "Do you all want a beer?"
The first logician says, "I don't know."
The second logician says, "I don't know."
And the third logician says, "Yes."
@@verkuilb If either of the first two did not want a beer, they would know that ALL of them do not want beers. So the third logician knows that each of the first two wants a beer.
@@verkuilbThere is also a variant:
Three logicians are at that same bar, an hour later.
The bartender then asks: does any one of you want another drink?
The first one says: I don’t know. The second one says: I don’t know. The third one then says: No!
(None of them wanted another drink, and if either of the first two would have wanted a drink, they could have answered ‘yes’.)
And that's exactly how any() and all() work in languages like Python and Ruby :)
@@verkuilb The difference between logical and linguistic pedantry is logicians don't get kicked out of the bar.
@@verkuilb Sorry, but the bartender does not ask them whether they want to share a beer. Quite the opposite. If he asked them what you suggested to be correct, he would ask each of them whether they want more than one beer each.
If the bartender asked "Do you want a beer?" then he would be asking to give them a beer shared between them, because he offered the beer to a group. By adding the 'all' to the phrase, he asked each of them individually whether they want one beer. It does not define the total number of beers in particular.
Imagine this. There are three people looking at the sky when multiple falling stars are visible. Someone asked the three "Have you all seen a falling star?". Going by your logic, none of them could answer this question, unless they huddle up and determine whether there was any falling star seen by all three of them. But that's just not the case. If one saw a small star, one saw a large star and one have seen none, then the first person will say 'I don't know', the second person 'I don't know' and the third person 'No'. But if he also saw ANY falling star, he would say 'Yes'. Why? Because the condition was an 'A falling star'. Not a specific falling star.
Likewise, in this little bartender story, the beer is not defined. What is defined is whether each of them wants a single beer. But single for each of them individually, NOT for all of them collectively. Each of them can get a SIP of the beer, a LITER of the beer, a KEG of the beer...but 'a beer'. The volume does not matter as long as it is in a container (and thus is countable, thus fulfilling the condition for 'a' to appear') and each person will get no more than one container with beer. Whether it's the same container for each of them or a different one for each of them (or any combination thereof) is irrelevant.
A "perfect logicians" puzzle always makes me think that at the end it's going to be "Sorry, no, that's wrong, the other person messed up a couple of turns back"
Well no kidding: Uh, no, you cannot say what Abby said to begin with. Just because one scenario for sunday and tuesday are not true does not mean sun/sat and tues/wed is not true. What a load of bunk.... I know after all these years host of vid is scrapping the side of the barrel for good questions, but this one is just pure bunk.
@@w8stral The problem is solvable, though I don't think the given one is the clearest. See other comments for other ways of working through it.
@@w8stral Let's start with an example with the first step.
Her saying no means that, purely from knowing that Barry isn't monday, she doesn't have enough information to know his birthday.
Now if Abby was a tuesday or sunday, she would have known that the only possible in that case for Barry would be wednesday and saturday respectively (because it can't be monday) and so she wouldn't have said no.
Her saying no means that it's not a tuesday or a sunday. The logic used in the sun/sat tues/wed thing is basically the exact same.
I don't know about his other questions but this question, is in fact, not pure bunk.
@@lox7182Exactly, the problem is intentionally worded in a way where the information seems vague, but it's not.
For me I could see at least one of them figuring it out right away. If this is a logic test between the 2 of them then logically they should have an equal chance to get it right. A "perfect logician" would realize the logical solution will be the last option they both would have, here she has 1 piece of information he doesn't so she could logically do what he did here without the repeated asking if they figured it out. And since it's an equal chance he could easily figure out she wasn't born on Sunday or Tuesday and figure it out too.
Funny thing is that after Barry says yes, Abby would still say no, because she still cannot conclude whether Barry was born on Sunday or Tuesday.
I had a different strategy... I noticed that everything is symmetric around Monday, in that any logic that can eliminate e.g. Tuesday must necessarily also eliminate Sunday, and so on. The only day that doesn't get eliminated in a pair is Monday itself, so if you can end up with exactly one day Abby could be born on, it must be Monday, regardless of what kind of logic the two actually used to get there. For the same reason it can't be possible to determine which day adjacent to Monday Barry was born on.
Same here, i tried to align the possibilities around monday and they got clipped leaving the center
This isn't right,
1) you can determine that Barry was born on Tuesday in the puzzle
2) it's a coincidence Abby is born on Monday. Depending on the number of nos you can get any day of the week. 0 nos means Abby is born Sunday, 1/2 no's means Abby is born Friday, 3/4 no's means Abby is born Wednesday, 5/6=Monday, 7/8=Sa, 9/10=Th, 11=Tu.
@@dinhotheone How are you getting this? The problem is symmetric under time reversal.
Yeah I think the puzzle was supposed to keep it ambiguous if it was even possible to deduce Abby's birthday. The question as it's given in the video implies that Abby's day can be deduced, which gives this extra bit of information (the fact that it resolves to a single day that we can solve for).
If the question was "Can you solve for Abby's birthday?" then you would have to solve it as in the video. But your shortcut works because we can make the valid assumption that Abby's birthday is in fact deducible.
@@violetfactorial6806 The facts of the puzzle give that Barry knows Abby's birthday by the end. You don't have to infer from the wording of the question.
The post of mohitrawat5225 reminds me of a joke...
A mathematician, a physicist, and an engineer are riding a train through Scotland.
The engineer looks out the window, sees a black sheep, and exclaims, "Hey! They've got black sheep in Scotland!"
The physicist looks out the window and corrects the engineer, "Strictly speaking, all we know is that there's at least one black sheep in Scotland."
The mathematician looks out the window and corrects the physicist, " Strictly speaking, all we know is that there is at least one sheep with at least one black side in Scotland."
Good one
Similar to the Vsauce joke
Idk why but the last one is funny😂😅
That joke is VERY old. But it is also very good, so thanks for keeping it alive 😀.
Meanwhile me : " Strictly speaking, there's atleast one sheep in Scotland who's one side *appears* to be black "
@@thuyvannguyenthi1459 it's a joke and _is_ supposed to be funny
Well, that was a pleasant surprise. The accreditation was unexpected and very gracious of you. Thank you Presh.
Awesome riddle man!
I saw this puzzle decades ago in a book (maybe the famous Moscow puzzles?). Did you write it originally, or did you find it somewhere?
@@Misteribel Original as far as I’m aware. Kordemsky’s Moscow Puzzles has the familiar 3 foreheads puzzle, but not this. Hans van Ditmarsch sent me a draft paper describing a method for solving many puzzles of this type, I noticed the modulo case was missing and proposed this.
Once a mathematician, a biologist, a physicist and a chemist were sitting together in a coffee shop. They saw 2 people going in a house and after some time 3 people came from the same house. The biologist said " There must be reproduction happened in the house". The physicist said " There must be a wormhole inside the house". The chemist said " The house must had a nuclear fission reaction in it". The mathematician then said " If one more person will enter the house, the house would be empty". Now the question is who among them was right?
I wonder what an engineer would say 😅😂
@@GaurangAgrawal2 there was a person already at the house
they could all be left
@@hugobartha6824 that's exactly what came up in my mind
yes
Perhaps it's easier to deduce if you order the combos differently, like in a circle.
So Sunday/Monday, Monday/Tuesday, Tuesday/Wednesday, etc.
This way you can go along the circle, eliminating options. As you eliminate in both directions you end up at the other side of the circle with the Monday/Sunday and Monday/Tuesday options.
This
Except you CANNOT eliminate in both directions. The language does not allow it. Sun/Sat nor Tues/Wed by A cannot be crossed off eliminating any scenario where B can deduce anything of substance after the fact.
@@w8stral
It's exactly what he does in the video, except ordered. As soon as you eliminate one step in both directions the only other combinations with both of those two days are right next to them...
@@teambellavsteamalice No, you are PRESUMING if you eliminate reverse consecutive in one direction then you can eliminate reverse consecutive in ALL instances. You are PRESUMING if you eliminate consecutive going forward you can eliminate consecutive going forward in all other instances and there is no IF/THEN statement in the problem as stated in which you can make that logical jump. THAT is the problem. You make that PRESUMPTION because you made a PREVIOUS presumption: you and Presh and many others PRESUMED there is a logical solution to begin with. Many problems there is NO solutions. This is where Failure happens.
@@w8stral
I'm just proposing an easier way to graphically represent the problem by ordering the A/B pairings as you can eliminate them in order.
Note Sun/Sat isn't the same as Sat/Sun. Perhaps you'd prefer two separate circles, one for Sun/Mon and one for Tue/Mon?
The fun and trick of this problem is there is an IF THEN logic.
Without the two .../Mon pairs both Sun/... and Tue/... now have single solutions.
Sun/Sat and Tue/Wed are then eliminated by the first No.
This makes two other pairs .../Sat and .../Wed unique pairings for their day.
So the next No eliminates these.
If there was a Yes now, you'd have a Fri/Sat or Thu/Wed as solutions but wouldn't know the day for either of them.
The fact that this loops around to Mon/... gives the solution for A, even though B is still unknown.
Solved it mentally, and dude, it's insanely hard to keep track of my thought
Gotta agree. It's a simple method, but it's like stacking dominoes in a staircase with no supports. After a point it just wants to tip over lol
Yeah. I wanted to grab a pen and paper, but I was laying down in bed
It's not really that hard, you just remove the days around monday in pairs and you end up with monday for abby, and the other one is easy, just can't figure out his day. He took 7 minutes to manually reason every half of pairs when it's clearly a process repeating itself
@@sanamite Yeah, it's indeed simple. The problem is I keep losing my train of thought all the time, having to recall my memory over and over
@@sanamite As space Mario said. It is indeed simple, but mentally keeping track of all of it is the issue. It's alongside the idea of multiplying large numbers: It's just multiplication, but if you don't keep track of each part properly, it is easy to screw up
I think this is a lot easier to grasp visually, with a radial arrangement.
Mon
b
Sun Tue
1a 1a
Sat 2b 5a 5a 2b Wed
4b 4b
3a 3a
Fri Th
Notation:
a = Abby known to NOT be born on indicated day
b = Barry known to NOT be born on indicated day
preceding number = the number of "no" responses, i.e. the step
Awesome, had a similar idea but you showed it perfectly!
I put it in a spreadsheet to solve
biblically accurate logician
@@titouanboulanger6877 Be not afraid
Talent that how he got them in this shape
Abigail Grundy, born on a Monday, christened on Tuesday, and married on Wednesday. On Thursday, she fell sick, and the illness got worse on Friday, and she died on Saturday.
And buried on Sunday ??
@@agytjaxNo, that was when she rose from the dead.
I love these types of puzzles so much!! I'm running a math club and I always like to propose these puzzles on the members, thank you so much, please do more of these :D!
Write out all the days of the week in circle. M for monday, T for tuesday,... Su for sunday.
Now we define !B to mean Barry cannot be born on that day and !A for Abby.
Notice that we start with !B on M.
Every turn, when Abby says No, that tells barry that she cannot be adjacent to any days with a !B (for otherwise, she would know it must be the other day). Thus, on any turn where she says no, add a !A to any days adjacent to the !B days.
The same is done with adding a !B to any days adjacent to !A days when Barry says no.
So after doing this process, all the days end up having a !A on them except Monday.
also, all the days end up having a !B on them except Sunday and tuesday.
Therefore, Abby must be born on Monday and Barry can be born on Tuesday or Sunday.
Note that this method can be generalized quite neatly if you want to consider a number of cycle days more than 7.
This is the first one of your riddles I solved as I was hearing the beginning part of it! I am getting better at these logician puzzles
Finally, I managed to solve one of these tricky logic puzzles correctly before watching the solution. Took a while.
I used check marks next to the days of the week under two columns: one for Abby and one for Barry. I paused after your pairs to check and got the same result, and also to see if I could figure out the day Barry was born on.
Seems like the trick to solving these questions is, for every step, if X happens, think about what are the possible scenarios that must be true the opposite of X were to happen, and rule out those scenarios. For the next step, rinse and repeat with the pre-condition that the scenarios you ruled out remain ruled out. Eventually you'll come to a conclusion that only contains one possibility.
Great puzzle. It seems impossible at first but with a little logic, persistence, and a pencil and paper and you can do it!
I used square "days of week" by "days of week" grid. Then I started putting X in each cell where combination of days of week could NOT happen. It allowed me easily solve the puzzle
Same 🙂
Exactly what I did!
I sent the entire video distracted by whatever’s going on with barry’s ankle
Finally the first puzzle I could solve on my own
I solved it by myself too. I think this was easy.
I just took a wild guess and assumed that since Barry and Abbey weren't born on the same day, the fact that Barry wasn't born on Monday increases the likelihood that she was. So I guessed Sun, Mon or Mon, Tues.
i solved this puzzle by drawing 1-7 dots around a circle (1 as monday, 2 as Tuesday etc. then each time they answer, i can either slash it ( to eliminate Abby's day possibility) or circle it (to eliminate Barry's day possibility) it would then comes down to 1 being circled, 7 and 2 slashed. So Abby on Monday, and Barry on Tuesday or Sunday.
Got this, but only using a 2x7 grid: A, B over the top row and Mon thru Sun on the left side . Start off with an X0 in the B, Mon square, then put an X1 in the A,Sun and A,Tue squares as impossible days for A(bby) and B(arry) to be born. Continuing gets the answer rapidly.
Wow, I solved it the same way (after a while)! The table makes the pattern clear, much more so than with Presh's method.
Finnaly, I got this kind of puzzle without watching the solution, even though I only got Monday and Sun and forget about Mon day and tuesday since I didn't write.
If I was in this situation, I would just do something like this:
Abby: no (I wasn’t born on Monday)
Barry: no (I wasn’t born on Monday)
And so on. Using this logic, Barry was born on Wednesday and Abby was born on Thursday
Got it right and a good amount of satisfaction ... Thanks
My little brain found it easier to make three columns. I used a shorthand, but the column headers spelled out would have been: "Day of the Week", "Not Their Birthday", and "If/Then Notes". Next to Monday, the 2nd column got a B in it--because it's not Barry's birthday.
Then I walked through each of them saying "no" and did quick if/then notes for the deductions that could be made each round by the other person regarding whose birthday it was not on certain days. It was straightforward from there if you are good seeing patterns, but I went step by step.
Using pairs of days totally makes sense, but visually I found it easier to wrap my brain around what was essentially a week calendar with notes on it. Doing this without a visual to look at would have probably been impossible for me. Kudos to anyone who didn't need to open up a spreadsheet or notepad :)
The puzzle should include the party host stating that the two of them are perfect logicians. Otherwise neither can deduce the answer.
I'd love to see this work in real life. SOOOO much context needed for this to actually work. But frankly I think people are more logical when contexts exist, than when taken out in isolation like this. At least they should be, but people have gotten especially dull as of late. But it's like seeing someone you know from work at the mall, and you're just not sure who it is.
So I wrote this down myself and thought for sure that I got it right-
"So He can't have been born on Monday.
Abby- "No" She can't have been born on TUESDAY, or she'd know for certain that he was born on Wednesday.
Barry- "No" He can't have been born on WEDNESDAY, or he'd know for certain that she was born on Thursday.
Abby- "No" She can't have been born on THURSDAY, or she'd know for certain that he was born on Friday
Barry- "No" He can't have been born on FRIDAY, or he'd know she was born on Saturday
Abby- "No" She can't have been born on SATURDAY, or she'd know he was born on Sunday.
Barry- "Yes!" He was born on Sunday, and since he knows she wasn't born on Saturday, he knows she was born on Monday"
And then realized that I only did half of the riddle.
This was a fun one to solve. However, it is odd that from the start, both A and B already can eliminate five days by knowing their own birthdays, so I think the wording of the solution should be more careful to take this into account, for example by talking about an outsider's viewpoint.
For the sake of example, lets pretend B was born Tuesday.
You're absolutely right that he knows right from the outset that A must be born Monday or Wednesday, but...
B *doesn't* know that [A knows that B was born Sunday or Tuesday]
because from B's perspective its possible that it could instead be the case that [A knows that B was born Tuesday or Thursday].
For B to learn information from A's "No" answers, he needs to situate that answer from within his incomplete knowledge of A's own knowledge-base.
This kind of '2nd-degree' knowledge, (what person X knows that person Y knows), is what's missing at the start, and is what is being developed iteratively over each round of consecutive "No"s.
Some logic puzzles require extending this to '3rd-degree' knowledge (What X knows that Y knows that Z knows(!)), and higher.
When Party Host says in their mutual hearing that B wasn't born Monday, this becomes infinite-degree knowledge, a.k.a. "common knowledge" (en.wikipedia.org/wiki/Common_knowledge_(logic)).
@@rowanhabel7239Ah yes, it's like the "100 dragons with green eyes" puzzle
Fun to note is that it crumbles IF Abby doesn't figure it out before Barry. Very reminiscent of the Unexpected Hanging Paradox.
Mind blowing yet mind opening
Wow, one of the first ones I’ve actually gotten right for the right reason
Wow, just wow, I don't think I've ever heard Presh talk so much in giving a solution. The ratio of talk to writing stuff down in solving this problem is really, really high. I actually got the right answer but I had a different approach. Read below how i got the right answer. PLEASE DO NOT SCROLL DOWN IF YOU WANT TO FIGURE THIS ONE OUT ON YOUR OWN ...... !!
I constructed a table. Rows Mon, Tues, Wed, Thurs, Fri, Sat, Sun and columns Abby | Barry. Note that each column represents what the *other* person knows because each is going to know the day they were born. I put an X which indicates the day of the week that person could not have been born,
There are 6 questions Q1 to Q6. So after each question I marked off days that person could not have been born with a subscript. X0 is the initial condition (Barry not born on Monday), X1 from the first question goes under Tues and Sat for Abby Remember, Abby's answer gives clues to Barry so the X1's have to go under the column marked Abby. Next the X2's go under Wed and Sat for the Barry Column. You work it back and forth for Q3 to Q5 for the X3 to X5 and so when you arrive at Q6, there's only day left under the Abby Column, so Barry' knows the answer. I also got the second part right since there were no further questions, there were still two blanks under the Barry Column, meaning Barry could still be born under two possible days and therefore the answer was one of two.
These are tricky logic puzzles. It took me a while to figure this one out.
This has the same problem that most problems like this have which is that an arbitrary decision is taken in unison without communication and is taken as a given. There's absolutely no way whatsoever to know if the starting point is monday or sunday.
The entire point of the solution is that it's not arbitrary though. Abby can 100% say "Yes" if her birthday was Tuesday or Sunday but she has to say "No" because her birthday is not either of those days. There's nothing random about that.
Its intended to be a thought exercise with a pre-setup solution. Their answers themselves to the question tell us what we need to know (IE, if Abby doesn't know what day Barry was born on, it means Abby wasn't born on Sunday or Tuesday, because if she was born on either, she'd know when Barry was born) and then logic just goes from there. Will say though the situation is kinda fucked because it's rigged so Abby can never accurately conclude what Barry's birthday is
I solved it with a series of charts! I only needed one, but I wanted to make a new one for each answer.
1 problem: how would they know what the other person answers? If they're using their own birthdays to eliminate possibilities, then they can't figure out what the other person answers.
When they say yes or no, they give information. The same logic that we're using, they're using.
@@arandombard1197 I think I figured it out. If they are asked the question again, they know the other person said no.
They're in the same room at a party when the party host poses the question. Neither of them are deaf
@@lisajones1438 I thought they were in different rooms ok
It's very sad that I couldn't figure it out myself
I’m going to choose to believe Barry was born on a Sunday
This kind of riddle reminds me of ted-ed riddles, albeit easier. Nice one 👍
Repeatedly going through already eliminated options makes the solution a lot more cumbersome than it would have to be.
They know the day they're born on, and that the other is born on the previous OR next day. So if they can eliminate one of those, they'd know the other was born on the remaining day. Therefore, since Barry was not born on a monday, Abby would answer 'yes' if she were born on a Sunday (which'd leave Saturday) or on a Tuesday (which would leave Wednesday). She says no, therefore she's not born on either of those days.
Written down: (abby first, barry second)
XmXwufa sXtwufa
Barry, able to eliminate those two days, would answer YES if he were born on a Saturday or a Wednesday. He says NO, so he wasn't
XmXwufa sXtXufX
Abby would then know if she were born on a Friday or Thursday, but she says NO, so she wasn't
XmXwXXa sXtXufX
Barry would then know if he were born on a Friday or Thursday, but he says no, so he wasn't
XmXwXXa sXtXXXX
Abby would then know if she were born on a Wednesday or Saturday, but she says no, so she wasn't
XmXXXXX sXtXXXX
Barry therefore knows she was born on a Monday. he however can be born on a Sunday or a Tuesday; we have no way of knowing. This is because the info circles around both directions, skipping one 'domino' with each answer.
this is one of the first puzzles I solved on my own. It was very similar to your version but a little more visual. I created 14 boxes representing each day of the week for each person. Then I created a list for each person "if Barry = Tuesday then Abby = Monday or Wednesday" rinse and repeat for all valid options. removing days of the week after each no. It was pretty much the same process you went through to find Abby. I tried pretty hard to figure out Barry but couldn't figure it out. So I watched the rest of the video just to discover Barry was Tuesday OR Sunday 🤦😂
Am I the only one that noticed the images are AI generated?
Nah, it's pretty obvious. Too many imperfections.
Not the point of the video, but ok.
"Am I the only one-"
You never are
Oh god yeah they are
Man that sucks… 3 mil subs and the y use AI? Oof…
Bonus deduction, the only case when it's not possible to work out both birthdays is when the given exclusion overlaps with the other birthday. Anything else breaks the symmetry and lets us know both. The case we can't know both is also the longest possible sequence of deductions.
Great puzzle!
I did this with a table (columns are the days and rows are Abby and Barry) where I crossed out the possible days and where it follows from the logic that two crosses can not be diagonal to each other (this seemed more intuitive to me).
I did this with Rows as days and columns as Abby, Barry. Carefully crossing out after each turn fetches the answer.
I had a sneaking suspicion the solution had to be Abby being Mon.
Reminds me of a riddle involving bottles that uses green to designate the right neighbor being wrong, but doesn't state they're something to suspect, another clue eliminates one of the green bottles, but green bottle#2 is clear of all suspicion.
Interestingly, I misread the question as there being one weekday between their birthdays and still had the same logical exchange with Abby ending up being born on Monday (Barry on Saturday or Wednesday in this case, obviously). Now I wonder whether the host needs to exclude Abby's birthday as a possible birthday for Barry regardless of how many days they are apart. If they are born on the same day of the week or with three days between them, there is no deduction necessary.
2 minutes to solve correctly.
Just had a circle with 7 days of the week, starting on Monday each "No" eliminated both adjacent weekdays; until the "Yes" left only the Monday as remainder.
You need not A and not B rather than an absolute No
Real life. Abby: No. Barry: No. Abby: I said no, stop looking at me, creep.
I tried.. I failed miserably... LOL. But it was a good one! Thank you.
I solved this problem using the thumbnail in less than 60 seconds, but only because I've seen this type of problem before (except it was with numbers)
That’s fucked. I got the answer to Abby’s straight away, but when it said “can you deduce Barry’s day, I sat here for 10 minutes trying different options thinking “if they asked, there MUST be a way.”
If yes and no are only allowed: This could have been solved much simpler by the person just saying yes or no if they were born on the day going in calendar order.
i got the answer in less than 5 seconds
Barry wasn't born on a Monday
So Abby starts with Tuesday saying "No", she wasn't born on Tuesday
Barry says NO for Wednesday
Abby says NO for Thursday
Barry says NO for Friday
Abby says NO for Saturday
Barry says YES for Sunday
Since Abby isn't born on Saturday, Abby is born on Monday.
You can't tell what day Barry was born on, as the riddle goes in both directions. Barry could be born on Tuesday or Sunday.
I wish I could wrap my head around this stuff 😭
Immediate thoughts: abby knows barry isn't monday, therefore after the first no barry knows Abby isn't sunday or Tuesday. At this point abby can be any day except those two, so if barry was wednesday or Saturday he'd know which day abby was (thur/fri respectively), or if he was sunday or Tuesday himself then abby must be monday. Hes not sure though so says no, menaing hes not sunday or tuesday. Abby then knows if she was Saturday or wednesday that barry would be the adjacent day still available, but she doesn't so she can't be those two days either. Now Barry could be Thursday or friday, Abby could be Thursday or friday, and therefore barry knows whichever abby is is the one of those two that he's not and vice versa.
Edit1 halfway through vid: I wrongly assumed on step 2 that if barry was sun/tue then hed know which abby was, but abby could still be mon or sat/mon or wed meaning Barry would still be unsure, and from there my dominos were falling at a part where they shouldn't and ended up going the wrong direction leading to a faulty solution.
I got this one. Pleased with that.
The question is good. But I don't approve your solution technique. You should have used a circular layout instead of listing all possibilities. I solved it much easier that way. Thanks!
So if Abby was born on Monday, she would know that Barry wasn’t born on Monday given they are born on consecutive days. They could have worked this out without that statement, but Barry needs to know that Abby knows he isn’t born on Monday. Just seemed like an odd part to add given the solution, apart from to help guide the riddle
If you have the logic necessary to prove that Abby and Barry have common knowledge of the fact Barry's birthday is not Monday, knowing only that their birthdays are on consecutive days, and therefore don't need "Barry was not born on a Monday" announced, you're more than welcome to provide it.
All you've established is that Abby and Barry have mutual knowledge. i.e. that Abby and Barry individually know Barry's birthday can't be Monday. You haven't shown that Abby knows Barry knows Abby knows Barry knows Abby knows Barry knows Abby knows, ad infinitum, that Barry's birthday can't be on Monday, and vice versa.
We started by elimating Monday as an option for Barry, and then it turned out to be the answer for Abby. Coincidence?
What if we are told Barry wasn't born on Friday, which is equally true. Would Abby still be born on Monday?
'Two people fail to have a normal conversation and make it other people's problem' is the other way of looking at this question.
If the were perfect logicians they'd just ask each other if they were interested. 😁
Oh for frick sake.. I had the answer just based on the thumbnail. Thought I was all smart.. Then I click on the video and listen to the narrator and realize my dyslexia acted up and made me read “You were born two days apart” instead of “you two were born a day apart”… -_-
Fun fact if it were two days apart would take just as much time and the answer would be Abby was born of monday and Barry was born on saturday. Now I am going to redo all of my calculations.
Did the calculations again. Coincidentally Abby was born on Monday no matter was. Barry was born on either Tuesday or Sunday, either works.
I’m curious if they figured it out the same way I did.
A graphical representation of the possibilities (in a grid or ring) would be better than a list of ordered pairs
Yeah, I got same, quite similar (equivalent) logic procedure:
"Barry was not born on Monday, and you
two were born a day apart. Do you know
which day the other person was born?"
Abby: "No."
Barry: "No."
Abby: "No."
Barry: "No."
Abby: "No."
Barry: "Yes!"
Let's do A for Abby, B for Barry,
and 0 through 7 for respectively Sunday through Friday.
We presume each knows the day of the week they were born,
but not which day of the week the other was born, and that we presume
each answers truthfully based on the data available to them.
We also presume the regular sequence of days of the week (e.g. exclude
any jumps for Julian to Gregorian switch, or timezone change that would
cause such discontinuity, etc.).
We abbreviate the response sequence to (N for No, Y for Yes):
AN BN AN BN AN BY
Let's start with our basic initial conditions, and add information as
we go along. They're born one day apart, so for possible days and
correlations, and subtracting out that Barry's not born on Monday, we
have:
A B
16 0
13 2
24 3
35 4
46 5
05 6
Then we start adding:
>AN< BN AN BN AN BY
Since B isn't 1, if A were 0 or 2, A would be Y (by elimination of B 1),
So that eliminates A 0 and A 2:
A B
16 0
13 2
4 3
35 4
46 5
5 6
B herd and knows the above, then B responds:
AN >BN< AN BN AN BY
That eliminates some more possibilities, notably where B would've known
and answered Y
We eliminate B3 and B6, as were those the case, B would've known A and
responded Y, so now have:
A B
16 0
13 2
35 4
46 5
A heard and knows the above, then A responds:
AN BN >AN< BN AN BY
A B
16 0
13 2
35 4
46 5
That then eliminates A4 and A5, as with either of those, A would've
known B and given Y, so now we have:
A B
16 0
13 2
3 4
6 5
B heard and knows the above, then B responds:
AN BN AN >BN< AN BY
That eliminates B4 and B5, as if those were the case, B would know A and
respond Y, thus leaving:
A B
16 0
13 2
A heard and knows the above, then A responds:
AN BN AN BN >AN< BY
Now, if A were 3 or 6, A would then know B and respond Y, but didn't,
so we eliminate A3 and A6
A B
1 0
1 2
B heard and knows the above, then B responds:
AN BN AN BN AN >BY<
because B knows only 1 remains for A,
thus we have:
Abby: Monday
We don't have B, but know it must be 0 or 2, so we have:
Barry: Sunday or Tuesday
i did it in 2m or so no flex. i just clicked on that video to see if i was right. yep i was
I just guessed Monday cuz they told us he wasn’t. So I was like, “imagine if it’s Monday.” And turns out it was :)
If you were to say that Barry wasn’t born on Tuesday, wouldn’t that mean Abby was? If so intentional or not it’s a neat trick question that makes you over think it
Mathematicians will give you a beautiful solution for a problem you hadn't had before meeting them
if the other aint x and you dont know then you aint x+1 and x-1 so you have two lists denoting the day a and b arent born on starting ( ),(m) and at each step you put the day before and after in the other list for each day plugged in one list the step before.
Actually, the problem is MUCH easier for them, because they know which day they are born on, so instead of the 14 initial possibilities, they know there are only 2
Abby knowing that Barry's birthday could only be Sunday or Tuesday, or Barry knowing Abby's birthday is either Monday or some other day (depending on if he was born Tuesday or Sunday) doesn't mean one of them can deduce the other's birthday faster. They need to go through all of those "No" responses before one of them can possibly say "Yes".
@@rioc2802 not faster but in an easier way, because instead of having to cross out the 14 possibilities, they really only need to cross out 1, since they know their own birthday, they only need to eliminate either the day prior or the following day. I know the logic remains but it's much more practical to keep up with
Took a pause at 0:57
I think barry was born on either a Sunday or Tuesday and then abby on a Monday for sure
This is a famous puzzle, I've seen it in print a long time ago, where from its it originally?
Took me two subway rides to figure out, but I did ;)
Is that AI art?
sadly, yes
My intuitive guess is Monday, because otherwise Abby would be able to somehow pinpoint the day earlier. But that is just intuitive.
I guess intuitive also counts when solving puzzles but most people doubt themselves so much that they don't take the shortcut. I also have that intuition but in my head it sounds like "since it says barry is not born on monday that means abby is the one that was born on monday because the puzzle wants the solution to be as long as possible" i wanted to figure out barry's. At half way, i realized that is impossible because barry is the one answered. Wasted a lot of time but it's a good one.
1:24 It was great playing with days of week, after using elimination method, Abby is born on Monday.
Wish you had asked "Is it possible to deduce Barry's day?" I spent a while trying to figure out which of the two it was and find the trick.
Did not think of any of this logic as my brain straight up went to the logic that since bary cannot be born on Monday, Abby must have been born on a Monday.
Pausing @1:23 for my thoughts: So here are the seven days of the week UMTWRFS. We know that Barry was not born on a Monday. So that leaves UTWRFS. Abby says "No" so Abby cannot be born on U or T, because if she was she would know that Barry would then be S or W respectively. This leaves MWRFS for Abby. Barry says "No" so he cannot be S or W, because if he was then he would know Abby is F or R respectively. This leaves UTRF for Barry. Abby says "No" this eliminates R and F for her because she would then know Barry was F or R respectively. This leaves MWS for Abby. Barry says "No" this eliminates R and F for him because if he was then he would know she was W or S respectively. This leaves UT. Abby says "No" this eliminates W and S because otherwise she would know that he was born on T or U respectively. So by process of elimination, Abby was born on M, Monday. However there is not enough information to deduce Barry's birthday.
Hey Presh,
I'm one of your subscribers and I think UA-cam should rank your channel differently.
Coz many a times I see the question in the thumbnail and if I'm able to solve it, I drop a like and move one with the day. Hope YT's algo doesn't count them as fake likes.
Keep up the good work.
I took the "Can you solve for Barry?" question as a challenge. I figured out when Abby was born and spent far too long trying to figure out Barry's birthday before I gave up to look for the solution. I feel silly now...
I kinda just guessed that Abby was born on a Monday. I have no logical reasoning but I thought, oh Barry wasnt born on a Monday but Abby was. So uh my random guess wasn't so random after all
It was easy
Since Tuesday is the day of the week on which most babies are born, and that Sunday is the day of the week on which the least amount of babies are born, and that Abby is born on Monday, we can say with certanty that: Barry was born on a Tuesday, most likely.
Probabilities don’t confirm anything. Winning the lottery is rare for any one person but it still happens.
@@Ultranger 1. Joke
and
2. "Most likely"
This video would have been easier to follow if the immediately previously eliminated cases were highlighted when the next person is performing their deduction.
Almost solved. Made a mistake on the final step of the solution
I did find out on my own that Abby was born on Monday but could not find out the day Barry was born
The person setting the puzzle revealed too much information to Abby and Barry. The riddler said to them both that Barry wasn’t born on Monday, and you’re born on consecutive days.
Barry knows he wasn’t born on a Monday already. And Abby knows that she was. So by telling her they’re consecutive days, she already knows he wasn’t born on a Monday
Can we solve Abby's birthday without that information though?
If the host hadn’t said “Barry wasn’t born Monday,” then Barry could not have inferred any information from Abby’s first “no.”
@@q-tuber7034 So even though "Barry was not born on Monday" is not new information to Barry or Abby, the fact that it is now common knowledge starts the deduction process like in "100 green eyed dragons" puzzle.
I had copied down the problem incorrectly and missed the last no by Abby - and put down Abby saying Yes after 4 no’s. In that case we would know both Abby and Barry’s birthdays
I have recognised mathematician have way too much free time.
Just by the thumbnail assume each no is a confirmation of a day sunday to Saturday
A=7 b=6 because b /= 1 so once we reach Friday the logical conclusion can be made, to lazy to think more
Answer is Mon, Sun
Lol I tried to solve it from the thumbnail and thought a day apart meant something like wednesday-friday for example. I still got that abby was born on monday but got that barry was born on wednesday or saturday.
Why are they making me Abby? They could keep it third person, but weirdly chose not to.
Very easy, almost did it without paper....
So only Barry has enough information to solve the puzzle as presented? Barry and Abby do not start from the same information; he has more than her.
i don't understand the "no, no, no, etc" part. how did you deduce the days that she said no to? or was that just a random decision?
WAIT I JUST GOT IT LOL