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"

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."

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.

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."

Solved it mentally, and dude, it's insanely hard to keep track of my thought

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.

Well, that was a pleasant surprise. The accreditation was unexpected and very gracious of you. Thank you Presh.

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 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

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.

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.

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.

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

I sent the entire video distracted by whatever’s going on with barry’s ankle

Great puzzle. It seems impossible at first but with a little logic, persistence, and a pencil and paper and you can do it!

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'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.

Finally the first puzzle I could solve on my own

Got it right and a good amount of satisfaction ... Thanks

Fun to note is that it crumbles IF Abby doesn't figure it out before Barry. Very reminiscent of the Unexpected Hanging Paradox.

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.

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.

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.

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).

Am I the only one that noticed the images are AI generated?

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.

Wow, one of the first ones I’ve actually gotten right for the right reason

The puzzle should include the party host stating that the two of them are perfect logicians. Otherwise neither can deduce the answer.

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.

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 :)

I solved it with a series of charts! I only needed one, but I wanted to make a new one for each answer.

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.

A graphical representation of the possibilities (in a grid or ring) would be better than a list of ordered pairs

Repeatedly going through already eliminated options makes the solution a lot more cumbersome than it would have to be.

This kind of riddle reminds me of ted-ed riddles, albeit easier. Nice one 👍

Mind blowing yet mind opening

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.

It's very sad that I couldn't figure it out myself

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.

I wish I could wrap my head around this stuff 😭

I’m going to choose to believe Barry was born on a Sunday

I got this one. Pleased with that.

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

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?

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.

This is a famous puzzle, I've seen it in print a long time ago, where from its it originally?

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 🤦😂

I tried.. I failed miserably... LOL. But it was a good one! Thank you.

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.”

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)

Since Tuesday is the day of the week on which most babies are born, and that Sunday is the day of the week that 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.

Is that AI art?

Took me two subway rides to figure out, but I did ;)

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.

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.

Hey Presh, I'm one of your subscribers and I think KZfaq 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.

Just curious: Is there a generally accepted “technical” term for this type/class of puzzle? (Thank you for posting this. I love this type of puzzler. That said, I can virtually never actually solve them, but it’s great to watch the logic unfold.)

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.

Mathematicians will give you a beautiful solution for a problem you hadn't had before meeting them

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

emm... that do make me wondered :how can abby win?( for both barry and abby make no wrong and wile guess)

How complex a problem does it have to be for a logician to be named Zachary?

I did find out on my own that Abby was born on Monday but could not find out the day Barry was born

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.

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.

This reminds me of the blue-eyed islanders puzzle

I have recognised mathematician have way too much free time.

Real life. Abby: No. Barry: No. Abby: I said no, stop looking at me, creep.

1:24 It was great playing with days of week, after using elimination method, Abby is born on Monday.

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

My intuitive guess is Monday, because otherwise Abby would be able to somehow pinpoint the day earlier. But that is just intuitive.

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

Very easy, almost did it without paper....

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.

It was easy

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 :)

'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. 😁

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.

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

i did it in 2m or so no flex. i just clicked on that video to see if i was right. yep i was

Why is it bothering me so much that the 14 options were not put in 2 even columns of 7

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 got just monday/tuesday, i think i rushed to the conclusion it was only 1 answer but yeah, i used the same method of thinking

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

When "no" actualy means "yes"!😇

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 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...

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.

Somehow I came up with Abby, Thursday and Barry, Friday. I eliminated Monday for Abby, and now I’m not sure why, whoops

I just guessed and got it right.

Not me having to redo the entire riddle bc I read it as “two days apart” instead of one day 🤦‍♀️

Almost solved. Made a mistake on the final step of the solution

Why are they making me Abby? They could keep it third person, but weirdly chose not to.

This took some thought but I eventually got (hidden for spoilers) Monday

i figured this one out good puzzle would be bad if i couldn't tho