I actually wished the solution was that there were 5 statements, none of them guaranteed to be true: 1-3. the cat-hat ones 4. Exactly one of the (five) statements is true. 5. Exactly one cat contains a hat. With maybe an additional assumption that there's exactly 1 correct answer between a-e. In that case D could (potentially) be the correct answer. But unfortunately, the riddle was much simpler, and 4&5 were meant to be taken for granted.
*me:* feeling proud after finally solving the first problem in this channel, geez I'm getting smarter *everyone in the comments:* this is the dumbest problem this channel has ever seen *me:* cat in tears meme face
I thought it would have been better to work through hat one and get a contradiction, then hat two and get a valid answer, and THEN to still go on to consider hat three. If hat three had also been viable, many people might have stopped after hat two and given answer B instead of the (what would have been) correct answer of E.
I guessed it immediately, then altered some information in the brain tank, then thought it again and remembered my first assumption I tend to do this a lot (think it might be impulsiveness), anybody else?
I picked hat two because if statement three is the one that is true then one is wrong and two is wrong and if two is wrong then the cat is indeed in that hat
When I saw the thumbnail, I immediatly thought that the cat would be in hat 3, because there's no sentence that says "The cat is not in the hat 3"... And then, I saw the entire problem
I did it the other other way, assuming every statement was false and looking for the two where the evaluation is consistent. C = Cat, N = No Cat Statement 1 false, possible outcomes: NCN NNC Statement 2 false, possible outcomes: NCN Statement 3 false, possible outcomes: CNN Only the NCN case is consistent with two false statements, meaning the cat is in hat 2 and statement 3 was true.
I took a test online where the order of the answers to each question was randomized. One question went: Question? (a) All of the above (b) ... The correct answer was (a).
Our minds naturally want to logically arrive at an overall truth. This problem is unfortunately based on contradiction to truth by asking which condition (cat in hat 2) arrives at a single test being true. It's a tricky question, but useless for computer programming where "none of them" applies.
@@antoninjacob2232 people know the Joe Bloggs strategy so the last one is one that basically no one would pick. Plus, d and e are obviously trap answers so ahmad has a point.
@•• ha! will they be on the 2020 results? I assume Trump "calls" the election at midnight and declares a coup, embattled, stifled and sieged on all sides by … democracy …
@@brightymcbrightface Judging from all the enthusiasm I am seeing in favor of Trump, I don't think democracy will give him any trouble. But then, in 2016, media personalities were talking about how Trump wouldn't accept the results. And we all know how that turned out. You don't have to worry about Trump thinking the election was rigged. You have to worry about the possibility that half the country thinks the election was rigged. There better not be any anomalies with mysteriously "found" ballots.
@@zeldaadlez3377 you must be a very sad, sad person. It was a fun question, no need to try to make yourself feel better by calling everyone else retarded
My solution: Consider the statement of hat 1 and 3. These statements are opposite to each other. So 1 of them is true and other is false. So we can surely say the statement of hat 2 is false. Which forces that the cat is in hat 2. (Is it correct?)
we get so worried about the information given with the hats that we may not pay enough attention to what the problem actually says anyways, just squeeze the hats slightly to feel for the cat, or see which one is moving
Finally one I could solve. I just saw 1 and 3 contradicted each other so one had to be true and one false. Since only one statement could be true, the 2nd must be false, making the cat be in 2. Then I just double checked
That was even smarter than the routine way of solving it. I think the problem tried to hide the fact that question 1 and 3 were actually just the same question with opposite answer by putting each question under one of the hats, rather than putting the questions in a list.
Here is a spin-off puzzle with *TWO* cats: Hat 1: There is a cat in this Hat Hat 2: There is no cat in this Hat Hat 3: There is no cat in Hat 1 Exactly *TWO* of the above statements are true and each hat can only hold a maximum of one cat. Find the hat without the cat.
We will approach the problem in same way. Since first and third statement are contradictory,only one must be true. By this second statement will always be true and hence cat will not be there in box/hat 2.
No statement is made about hat 3. Since the statements under hats 1 & 3 contradict, and the statement under hat 2 confirms the cat is not in hat 2, why is it not correct to say that the cat is in hat 3?
Kenneth: Exactly ONE hat contains a cat - thus cats in other hats are not possible. Exactly one hat contains A cat - therefore no two-cat hats. Exactly ONE statement is true = only with a single cat in hat 2 is the problem solved. Rick: Because if a cat is present in hat three and there is only one cat-carrying hat, then both the statement under hat 2 and the statement under hat 3 would be true. There is exactly one true statement, exactly one (albeit unspecified) cat, and exactly one cat-containing hat. (Namely hat 2.)
@@kennethfisher7013 I guess any number of cats could at some point in the future (from the problem’s point of view) sneak in to any number of hats, but that is outside the scope of the problem since it only deals with the present at the time the problem describes.
There's a pretty fun consideration that can be made: Sentence 1 and sentence 3 can't both be true at the same time, but they can't also be both false, either. So it means that one of them has to be the true sentence, but it also means that sentence 2 needs to be one of the two false sentences, so if we make sentence 2 true, we find out that the cat has to be under hat 2!
That was easy. How I did was: First and Third statement were contradicting and one of them Had to be true, which means Middle one had to be False. If the middle one is indeed False (not in this hat), then that's the Hat the cat must be.
I used this fact aswell and combined it with the Information "there is only one True senstense" so i tried out True-False-False, skipped False-True-False and checked if False-False-True wich was the correct andere.
@@11FruitCake11 or they're people who take the "rules" of the question ("1 cat in 1 hat" & "1 statement is true") as statements as well (like many ppl in the comment section) With this their thought process will proceed as such: If "only 1 statement is true" is true, then all other statements must be false. However, statements 1&3 are contradictory and therefore cannot both be false. Thus, the statement "only 1 statement is true" must be false, we do not know how many of the remaining statements are true. Therefore, there is then not enough information to solve the puzzle, hence "wrongly" answering e) not enough information
You can also solve it without those three assumptions. Because the 1st and 3rd statement are opposite to each other (both about 1st hat, but have totally opposite results), then in any situation one of them will be true, and the other will be false. Because we need to have only one true statement (which we already nessiserely have in 1 or 3), then the 2nd one must be false to fulfill the condition (only one true). In that case if the 2nd statement lies while telling us that the cat is not there, ten the cat is there!) Such a beautiful solution 😊
@@think32 Of course it is not. If the option with no cat had also fulfilled the criteria of only one statement being true, then it would have been impossible to conclude which of the two would have been the correct one. Just because one alternative fulfills the criteria dos not mean it is the only one. And if there are multiple, then the correct answer is that there is not enough information. And if one option automatically set another option as not possible, then of course it should be explained and motivated why this is the case.
@@arvidbaarnhielm6095 Hi. Here's a very simplified example: What is 2 + 2? a. 3 b. 2 c. 4 d. all of the above e. none of the above If we already know that d and e cannot be correct alongside any other answer, then why explore them once we've found the correct answer, which would be C in this case? Another example: when taking a standardized test (ACT, SAT, or any test with multiple choice sections), would you encourage the students to always explore "all of the above" and "none of the above" regardless of whether they had found the correct answer? Even knowing that further exploration would have no impact on the result? I agree completely with "Just because one alternative fulfills the criteria dos not mean it is the only one." I was referring specifically to "contradicting answers," as I mentioned. Sorry if that was not clear. And sorry if I misunderstood your initial point.
@@think32 Haha, when rewatched the video I saw that it is clearly stated in the problem "exactly one hat contains a cat". This make option d) "None of them" false no matter what. This makes my first reply useless. If you want to, this acknowledgement can be enough to end the discussion with you being right, however, we can still discuss the hypothetical scenario that there might not be any hat with a cat, if you like. In your example, it should be clear to anyone that of course only one answer can be correct. However, I would like to present to you another example: There are three hats and not more than one cat. Exactly one of the statements below is true. Hat 1 has statement "There is a cat in this hat" Hat 2 has statement "There is a cat in Hat 1" Hat 3 has statement "There is no cat in Hat 2" If there is a cat in Hat 1, then both Hat 1, Hat 2 and Hat 3 would be true -> there is no cat in Hat 1 If there is a cat in Hat 2, then both Hat 1, Hat 2 and Hat 3 would be false -> there is no cat in Hat 2 If there is a cat in Hat 3, then both Hat 1 and Hat 2 are false, but Hat 3 is true -> there is a cat in Hat 3 I this example, even though the criteria would be fulfilled if the cat was in Hat 3, we can not say that this is the correct answer without exploring the possibility of there being no cats under any hat: If there is no cat in any hat, then both Hat 1 and Hat 2 are false, but Hat 3 is true -> there is no cat in any hat In this example, we found two options that both fulfills the criteria. It is not possible to find a single option to be true. This gives that the correct answer in this example would be "There is not enough information", even though we found a working set up where there is a cat under one of the hats. While constructing this example, I realised that I had a hard time to formulate the question in a way that the option of there being no cat is not totally obvious, but I'm not sure if that is a problem. Regarding your example on the ACT, SAT or any test with multiple choice questions. I'm not from USA, so I'm not familiar with the set up of those tests, but if it is only to mark the correct choice without argument, then I would say yes, you should always explore all options unless you can motivate for yourself why an option can not be true without exploring it. In the example in the video (excluding the fact that there is a clear statement that there is exactly one cat), the fact that the second option fulfills the condition does not in itself rule out the possibility of there being more options fulfilling the conditions. And if there are more than one, then the correct answer is "there is not enough information". This is important to consider in any test with multiple choices, like the ACT and SAT if they work as I assume, and that there could be questions where more than one condition fulfills the criteria. If that is stated to not be the case, then of course one true answer rules out the rest. But in my experience from doing similar tests, I have never seen a test that has stated that there can only be one option that fulfills the criteria. However, I just read the last lines of your reply again, and I believe I might have misunderstood what you mean by "contradicting answers". Could you elaborate on that one. Perhaps that is simply just the motivation I am asking for above, that if you can show that one option being true contradicts another from having the possibility to be true, then no further exploration is needed for that other option if you can see that the first is in fact true.
See, I went a bit differently about it. At the time that the question was asked, there was, in fact, one cat outline on all three hats. While the statements themselves talk about "the" cat, the problem itself doesn't explicitly state that there's only one cat; it only states that there are three hats and three statements. With that in mind, I went with answer A. Since you can see the cat in hat 2, then statement 2 is wrong and since you can see the cat in hat 1, then statement 3 is wrong. Edit: I think what went wrong is instead of answering the question "which hat contains the cat", I tried to see "which statement is accurate"
when i saw one of the answers being none of them i started to ever think things and started considering the fact that the fact there is one cat is possibly one of the true or false statements and if that wasnt even off limits whats to say that the fact only 1 is a true is even true
Next week: This is a question from a 2nd-grade oral exam in Taiwan. The students were given 3 minutes to solve this question. Tihim has a rectangle made of a number of identical square tiles. The rectangle is 2 tiles wide and at least two tiles long. Tihim then splits the tiles into two groups (of at least 2 tiles each) and tries to make those into rectangles, but he finds he cannot make either group on its own into a rectange that's more than 1 tile wide! What lengths could Tihim's original rectange be and what lengths can't it be, given this information?
An even number at least 4 or odd number that is 2 more than a prime. Btw you should require the 2 new rectangles to be at least 2 tiles long for this puzzle to work.
Maybe I overthought this, but aren't "Exactly one of the statements is true" and "Exactly one hat contains a cat" statements themselves? In which case the answer would be "e) Not enough information"?
Yes, you overthought it. "Exactly one of the statements is true" and "Exactly one hat contains a cat" are statements, of course. These statements should help you find the right answer. Why would two clear statements mean "not enough information"? Also, these kinds of riddles usually do have an answer, so the "not enough" or "all of them" is supposed to confuse you. :)
@@PrimoStracciatella It's overthinking, but it would be NEI under that. "Exactly one is true" would be false in any possible situation where those two are included as statements, so every statement could be either true or false with no way to determine.
JUST LOOKING AT THUMBNAIL If the cat is in hat 1, then: statement 1 is true, hat 2 is true, hat 3 is false. If the cat is in hat 2, then: hat 1 is false, hat 2 is false, hat 3 is true If the cat is under hat 3, then: hat 1 is false, hat 2 is true, hat 3 is true. REACHED 0:24 Now we know exactly one statement is true. Therefor, cat is in hat 2
@@ryannoonan5518 A lot of problems on this channel can be solved just by thumbnail. Sure, I couldn't fully solve the riddle without the extra info in the video itself, but I was able to determine those facts.
I thought the trick was that Exactly one statement is true and Exactly one hat contains a cat Were also statements that counted towards the problem. I didn't evaluate that, because I wanted to know if that was the case.
the correct answer is e). there are five statements given: 1. The cat is in hat 1. 2. The cat is not in hat 2. 3. The cat is not in hat 1. 4. Exactly one of these statements is true. 5. Exactly one hat contains a cat. It's trivial to show that statement #4 is false -- if it's true, then #1 and #3 must both be false (impossible). For the same reason, all 5 can't be true. So either 0, 2, 3, or 4 statements are true. But 0 statements can't be true, because that means #1 is false (and there is no cat in 1) which means #3 is true. So either 2, 3, or 4 statements are true. Given that, if 2 statements are true, we can use the solution you presented, which results in FFTFT. But if 2 statements are true, we can also have multiple cats. This makes 5 false, but if there are in fact 2 cats they would be in hat 1 and in hat 3, making TTFFF. Another possibility is that there are actually zero cats, in which case we get FTTFF. It's also possible for 3 statements to be true: the cat in hat 1 provides TTFFT. The cat in hat 3 gives FTTFT. It isn't possible for 4 of the statements to be true, since #1 and #3 cannot be simultaneously true, and under this circumstance #4 is also false. I note that you state "each hat has a statement" -- but nowhere is it stated that these are the only statements. Under the circumstances, I'm forced to assume there are five statements total, and proceed with the analysis above. It's possible to find a cat under any hat, and there's no hat that is guaranteed to have a cat under all possible scenarios. I need more information -- maybe something along the lines of "there are three statements -- each statement accompanies one hat. Additionally, you know two other facts for certain..." Without that, though, my answer is forced to be e).
If you have two of something then you have one plus another one. If you have one of something and acquire another then you have two. Proof enough for me.
@@qua7771 It's basically just that, but, mathematically, you must first define what is the "one", then define the "two", set the two groups of one, let it be clear that they are not the same thing, join them together as the group of two, and there it is.
How to make this puzzle more interesting; same set-up as before, but with an unknown number of true statements - however, you are told that knowing the number of true statements makes this perfectly solvable. Even if it’s the same answer with more steps (0 and 3 true statements are both impossible, 2 makes it unsolvable without more info, so it must be 1 true statement), it’s such a simple twist on the puzzle I’m wondering why it wasn’t included.
Statements one and three contradict, meaning at least one of the statements must be true. Therefore, the second statement must be false as only one of the three statements can be true. Since the second statement says that the cat is not under the second hat, then by contradiction it must be hat two.
That's actually a nicer method to arrive at the solution than the one used in the video. Sad to say, I also used the brute-force method from the video.
You could say the third Choice is correct also with all answers being true. As the first statement, "the cat is in this hat" does not refer to a specific hat, so linguistically we don't know which hat it's referencing, thus it could be referencing any of the hats including hat 3.
Me an intellectual : hats can't talk, and a cat wouldn't be able to fit in even one of them. So none of the hats have the cat inside of them. It's called logic.
And if you include “exactly one of the statements is true” and “exactly one hat contains a cat” as possibly true or false statements, I think that the true answer is e
After 15 years in software development, I am still in awe of how many people don't know what a truth table is -- to say nothing of how it is used to evaluate valid conditions.
Too simple. "The cat is in this hat" and "The cat is not in hat 1" are exclusive, i.e., one is true and the other is wrong. We know exactly one statement is true, so the second statement "The cat is not in this hat" is wrong, which means the cat is indeed in hat 2.
I git it right but I didn't use your approach. You started with "the cat is in hat 1, let's eval each statement". I did it as "let's assume statement 1 is true, and eval the rest.". It made finding cat in hat 2 easy.
I want more of these problems, but harder. Once you know that the hat isnt in hat 1, you just find out which hat it is knowing statement 3 is the correct one.
Due to the set of five possible answers - i.e. _d) "None of them"_ as it would be immediately excluded by _"Exactly one hat contains a cat"_ - this could also have been a trick question when you consider that there are not _three_ statements to be evaluated but _five_ . When two extra statements about _truthfulness of only one statement_ and that _there is only one cat_ may also be scrutinised then the answer would be _e) "Not enough information"_
Its much easier than that. Start by considering that the statement on the first hat is true. Now just follow the logic and remember all the conditions and you will reach the answer: Assume s-1 is true: Therefore s-2 also has to be true: Contradicts - "only one st. is true": Therefore s-1 is false: Therefore cat is not in hat 1: Therefore s-3 is true: Therefore s-2 can't be true since we already have a true st.: Therefore cat is in hat 2
Literally the question: Exacly one hat contains a cat
d: None of them
very smart u r.
I noticed that
Conspiracy theorists will pick d
I actually wished the solution was that there were 5 statements, none of them guaranteed to be true:
1-3. the cat-hat ones
4. Exactly one of the (five) statements is true.
5. Exactly one cat contains a hat.
With maybe an additional assumption that there's exactly 1 correct answer between a-e.
In that case D could (potentially) be the correct answer. But unfortunately, the riddle was much simpler, and 4&5 were meant to be taken for granted.
you failed. why ? you didnt consider that the cat was owned by Schrödinger.
"The cat is not in this hat."
*Sounds exactly like what a hat with a cat would say.*
Yes
Hat is sus. Vote hat.
Yes
This one was too easy.
Yeah I agee
Siap bang jago
Agreed. It is hat 2.
U can't do that I finally solved one question
Hmmm
*Everyone asking where is cat, but no one asking how is cat?*
Why is cat though?
I’ll top you “What is cat?”
Well "Who is cat tho?"
Which is cat?
????
*me:* feeling proud after finally solving the first problem in this channel, geez I'm getting smarter
*everyone in the comments:* this is the dumbest problem this channel has ever seen
*me:* cat in tears meme face
same
You could consider talking math classes to boost you abilities
Same, same 😀
I mean, you're in the 36% of people who can solve this
@@TheTutorialDude now imagine being in the 64%.
Once he skips to hat three: ok, we know the answer
So true lmao
Or, we knew beforehand?
I thought it would have been better to work through hat one and get a contradiction, then hat two and get a valid answer, and THEN to still go on to consider hat three. If hat three had also been viable, many people might have stopped after hat two and given answer B instead of the (what would have been) correct answer of E.
I guessed it immediately, then altered some information in the brain tank, then thought it again and remembered my first assumption
I tend to do this a lot (think it might be impulsiveness), anybody else?
True me too
This has got to be one of the dead easiest problems on your entire channel
I still don’t understand 😂😂
I thought that maybe there was another possible answer so that the puzzle would be unsolvable. But no, it was just really easy.
Tbh if I got this one wrong I'd be kinda embarrassed of myself
Believe me, there are some which are hell easy
I don't know what "dead" easy means.
Plot twist: _the survey was sent to grade 1 students_
Lol
@lux03 Seriously ??
@@codewithsmoil4098
there's only three choices and the win rate is 36%, they legit just guessed it
5 choices actually
@@atlas_hcr But it says there's exactly one cat so you can exclude 2 of them right away
If we are talking about Schroedinger's cat, the cat is in all the hats simultaneously
Well, turns out we are not. Schrodinger's cat was different.
actually it's in all of them at the same time and at the same time in none of them
@@GiantKush Let's say that it's a different type of Schrodinger's cat
@@PlanesAndGames732 Nope because you have the information given in the question, so you're sure of the position of the cat
what if it's the Schrodinger's neighbor's cat?
Everyone else :dumbest problem....grade 1 problem
Me: I know cat is in hat 3
No, it is simultaneously in and not in hat 1, it's Schrodinger's cat
I chose hat 3 because that was the only “true” hat that contradicts the answer to be hat 2
I picked hat two because if statement three is the one that is true then one is wrong and two is wrong and if two is wrong then the cat is indeed in that hat
You're not alone
When I saw the thumbnail, I immediatly thought that the cat would be in hat 3, because there's no sentence that says "The cat is not in the hat 3"...
And then, I saw the entire problem
I did it the other way, assuming each statement was correct in turn and looking for a contradiction in the evaluation.
Same
Same way
Same way
Same. Plus the confusion when the solution went by cats and got there one try earlier.
I did it the other other way, assuming every statement was false and looking for the two where the evaluation is consistent.
C = Cat, N = No Cat
Statement 1 false, possible outcomes:
NCN
NNC
Statement 2 false, possible outcomes:
NCN
Statement 3 false, possible outcomes:
CNN
Only the NCN case is consistent with two false statements, meaning the cat is in hat 2 and statement 3 was true.
I'm impressed by whoever dared and successfully managed to put a cat in a hat.
you can do anything when they fall asleep ...
@@heloxiii8894 yea but the hat gotta be big
The cat likes playing in the hat.
"Exactly one hat contains a cat".
My answer: d.
I took a test online where the order of the answers to each question was randomized. One question went:
Question?
(a) All of the above
(b) ...
The correct answer was (a).
My answer: Z, but Z is too small to see, so don't try, because you can't. ;)
Our minds naturally want to logically arrive at an overall truth. This problem is unfortunately based on contradiction to truth by asking which condition (cat in hat 2) arrives at a single test being true. It's a tricky question, but useless for computer programming where "none of them" applies.
@@pebble100c how is tricky lmao it LITTERALLY took me 3 seconds to find the answer
literally same-
plot twist, none of the people surveyed actually think. they just randomly guess. so 36% is logical , since 1/3 is close enough to 36%.
Not if we consider the 5 possible answers.
@@antoninjacob2232 people know the Joe Bloggs strategy so the last one is one that basically no one would pick. Plus, d and e are obviously trap answers so ahmad has a point.
If everyone just randomly guessed, it would be 20% as there were 5 options.
plot twist, the survey was only given to musk rats
@@antoninjacob2232 that would mean they didnt even read the question if they read the question its 33%
36%? where was this "survey" conducted?
Is this just an advertisement to link to brilliant.org?
4% of the people thought about it, the other 96% make a guess. 1/3 of 96% guessed right + 4% knew right hence 36% gave a right answer.
@@JaakJacobus BriLliAnT ruclips.net/video/P6Nfx5fT1V8/видео.html
@JaakJacobus There are 5 answer choices
@•• ha! will they be on the 2020 results?
I assume Trump "calls" the election at midnight and declares a coup, embattled, stifled and sieged on all sides by … democracy …
@@brightymcbrightface
Judging from all the enthusiasm I am seeing in favor of Trump, I don't think democracy will give him any trouble. But then, in 2016, media personalities were talking about how Trump wouldn't accept the results. And we all know how that turned out.
You don't have to worry about Trump thinking the election was rigged. You have to worry about the possibility that half the country thinks the election was rigged. There better not be any anomalies with mysteriously "found" ballots.
My ex gf would probably respond something like: there is a cat in each hat, I can see it
Tiktokers in a nutshell
I mean she's not wrong
I love these types of puzzles since they don't require the knowledge of any mathematical equations.
They also don't require any mental effort. This was probably a question to test for retardation, like the SAT.
@@zeldaadlez3377 you must be a very sad, sad person. It was a fun question, no need to try to make yourself feel better by calling everyone else retarded
*s a m e*
If you want this type of more content, then I will highly recommend you this channel #mathsandphysicsfun .
@@zeldaadlez3377 did you not do well on the SAT?
“I don’t know how, but you used the wrong formula and got the right answer” Not the first time for me
My solution:
Consider the statement of hat 1 and 3. These statements are opposite to each other. So 1 of them is true and other is false. So we can surely say the statement of hat 2 is false. Which forces that the cat is in hat 2.
(Is it correct?)
Wow..thats good 👌
I thought it too
we get so worried about the information given with the hats that we may not pay enough attention to what the problem actually says
anyways, just squeeze the hats slightly to feel for the cat, or see which one is moving
Finally one I could solve. I just saw 1 and 3 contradicted each other so one had to be true and one false. Since only one statement could be true, the 2nd must be false, making the cat be in 2. Then I just double checked
Exactly.
Solution in the movie is "by brutal force".
That was even smarter than the routine way of solving it. I think the problem tried to hide the fact that question 1 and 3 were actually just the same question with opposite answer by putting each question under one of the hats, rather than putting the questions in a list.
It's since* not "sense"
@@ameerkherbawi8466 thx I corrected it. Idk how I messed that up lol
@@dr.c5655 It happens lol
Everyone wondering "where is the cat?", but does anyone care to ask "how is the cat?"
Why is the cat!!?
When is the cat?
What is the cat?
Here is a spin-off puzzle with *TWO* cats:
Hat 1: There is a cat in this Hat
Hat 2: There is no cat in this Hat
Hat 3: There is no cat in Hat 1
Exactly *TWO* of the above statements are true and each hat can only hold a maximum of one cat. Find the hat without the cat.
Hat 2 will be empty then.
Hat 1 is empty
Edit: I get my error
We will approach the problem in same way. Since first and third statement are contradictory,only one must be true. By this second statement will always be true and hence cat will not be there in box/hat 2.
Hat 🎩 2
Still hat 2
this doesn't forbid a second cat from sneaking into hat 3
No statement is made about hat 3. Since the statements under hats 1 & 3 contradict, and the statement under hat 2 confirms the cat is not in hat 2, why is it not correct to say that the cat is in hat 3?
@@rickblackledge8948 that's not what I'm saying. it says 1 hat 1 cat, but there can be 2 cats in this scenario
Kenneth: Exactly ONE hat contains a cat - thus cats in other hats are not possible.
Exactly one hat contains A cat - therefore no two-cat hats.
Exactly ONE statement is true = only with a single cat in hat 2 is the problem solved.
Rick: Because if a cat is present in hat three and there is only one cat-carrying hat, then both the statement under hat 2 and the statement under hat 3 would be true. There is exactly one true statement, exactly one (albeit unspecified) cat, and exactly one cat-containing hat. (Namely hat 2.)
@@kennethfisher7013 I guess any number of cats could at some point in the future (from the problem’s point of view) sneak in to any number of hats, but that is outside the scope of the problem since it only deals with the present at the time the problem describes.
There's a pretty fun consideration that can be made: Sentence 1 and sentence 3 can't both be true at the same time, but they can't also be both false, either. So it means that one of them has to be the true sentence, but it also means that sentence 2 needs to be one of the two false sentences, so if we make sentence 2 true, we find out that the cat has to be under hat 2!
Exactly how I did it.
So if we make sentence 2 false**
But other than that nice
@@ryannoonan5518 He means, if we negate the statement, such that it will become true.
I found the Cat in Hat 2 when you skipped from Hat 1 to Hat 3...😂
That was easy. How I did was:
First and Third statement were contradicting and one of them Had to be true, which means Middle one had to be False. If the middle one is indeed False (not in this hat), then that's the Hat the cat must be.
I used this fact aswell and combined it with the Information "there is only one True senstense" so i tried out True-False-False, skipped False-True-False and checked if False-False-True wich was the correct andere.
Sometimes the problems we face are like those cats in those hats
Just like looking for my phone under the sofa 😂😂 . What you saying ?
@Raymond Albert I partake in that and it's really good , nice pin pointing there
So what are really tryna say most people don't know about or what ?
Anybody in this millennium in one way or the other has heard of it
That's why you need to relax and let a professional trade for you and you recieve profits just like a king
It was the easiest problem on your channel...but your all questions are interesting. So a big thanks 😊
Me: *Wondering how the heck a cat fits in a hat*
Someone: ...
The 2nd Hat: "The cat is NOT in this hat..."
Cats become zombies until you remove the hat.
I solved this in seconds just by trying all three cases in my head. I find it very hard to believe that only 36% of people got this right.
People are dumber than you think ;)
@@11FruitCake11 or they're people who take the "rules" of the question ("1 cat in 1 hat" & "1 statement is true") as statements as well (like many ppl in the comment section)
With this their thought process will proceed as such:
If "only 1 statement is true" is true, then all other statements must be false. However, statements 1&3 are contradictory and therefore cannot both be false. Thus, the statement "only 1 statement is true" must be false, we do not know how many of the remaining statements are true.
Therefore, there is then not enough information to solve the puzzle, hence "wrongly" answering e) not enough information
The cat would have died till the problem was solved back then ....easiest way was to check if cat was there or not by removing hat😂😂
Since statements 1 and 3 exactly contradict one another, one of them must be the true one. So statement 2 must be false.
I thought the sentences "Exactly one of the statements is true" and "Exactly one hat contains the cat" were also subject of being either true or false
I know right, i was so disappointed in the end tbh
All this shows is the sad state of people in general... it really wasn't difficult and yet nearly two thirds of people fail
You can also solve it without those three assumptions. Because the 1st and 3rd statement are opposite to each other (both about 1st hat, but have totally opposite results), then in any situation one of them will be true, and the other will be false. Because we need to have only one true statement (which we already nessiserely have in 1 or 3), then the 2nd one must be false to fulfill the condition (only one true). In that case if the 2nd statement lies while telling us that the cat is not there, ten the cat is there!) Such a beautiful solution 😊
"Exactly one of the statements is true".
That's the relevant rule to remember, then it's easy.
Personally I was thinking about Dr Seuss "Cat in a Hat".
You missed exploring option “None of them” to make sure it isn’t “Not enough information”
Exactly! Of course, if he had explored that option, the answer would still be Hat 2, but without exploring, this is not a complete answer.
@@arvidbaarnhielm6095 The correct answer automatically rules out the possibility of all contradicting answers. So yes, this is a complete answer :)
@@think32 Of course it is not. If the option with no cat had also fulfilled the criteria of only one statement being true, then it would have been impossible to conclude which of the two would have been the correct one.
Just because one alternative fulfills the criteria dos not mean it is the only one. And if there are multiple, then the correct answer is that there is not enough information.
And if one option automatically set another option as not possible, then of course it should be explained and motivated why this is the case.
@@arvidbaarnhielm6095 Hi. Here's a very simplified example:
What is 2 + 2?
a. 3
b. 2
c. 4
d. all of the above
e. none of the above
If we already know that d and e cannot be correct alongside any other answer, then why explore them once we've found the correct answer, which would be C in this case?
Another example: when taking a standardized test (ACT, SAT, or any test with multiple choice sections), would you encourage the students to always explore "all of the above" and "none of the above" regardless of whether they had found the correct answer? Even knowing that further exploration would have no impact on the result?
I agree completely with "Just because one alternative fulfills the criteria dos not mean it is the only one." I was referring specifically to "contradicting answers," as I mentioned. Sorry if that was not clear. And sorry if I misunderstood your initial point.
@@think32 Haha, when rewatched the video I saw that it is clearly stated in the problem "exactly one hat contains a cat". This make option d) "None of them" false no matter what. This makes my first reply useless.
If you want to, this acknowledgement
can be enough to end the discussion with you being right, however, we can still discuss the hypothetical scenario that there might not be any hat with a cat, if you like.
In your example, it should be clear to anyone that of course only one answer can be correct. However, I would like to present to you another example:
There are three hats and not more than one cat. Exactly one of the statements below is true.
Hat 1 has statement "There is a cat in this hat"
Hat 2 has statement "There is a cat in Hat 1"
Hat 3 has statement "There is no cat in Hat 2"
If there is a cat in Hat 1, then both Hat 1, Hat 2 and Hat 3 would be true -> there is no cat in Hat 1
If there is a cat in Hat 2, then both Hat 1, Hat 2 and Hat 3 would be false -> there is no cat in Hat 2
If there is a cat in Hat 3, then both Hat 1 and Hat 2 are false, but Hat 3 is true -> there is a cat in Hat 3
I this example, even though the criteria would be fulfilled if the cat was in Hat 3, we can not say that this is the correct answer without exploring the possibility of there being no cats under any hat:
If there is no cat in any hat, then both Hat 1 and Hat 2 are false, but Hat 3 is true -> there is no cat in any hat
In this example, we found two options that both fulfills the criteria. It is not possible to find a single option to be true. This gives that the correct answer in this example would be "There is not enough information", even though we found a working set up where there is a cat under one of the hats.
While constructing this example, I realised that I had a hard time to formulate the question in a way that the option of there being no cat is not totally obvious, but I'm not sure if that is a problem.
Regarding your example on the ACT, SAT or any test with multiple choice questions. I'm not from USA, so I'm not familiar with the set up of those tests, but if it is only to mark the correct choice without argument, then I would say yes, you should always explore all options unless you can motivate for yourself why an option can not be true without exploring it. In the example in the video (excluding the fact that there is a clear statement that there is exactly one cat), the fact that the second option fulfills the condition does not in itself rule out the possibility of there being more options fulfilling the conditions. And if there are more than one, then the correct answer is "there is not enough information".
This is important to consider in any test with multiple choices, like the ACT and SAT if they work as I assume, and that there could be questions where more than one condition fulfills the criteria. If that is stated to not be the case, then of course one true answer rules out the rest. But in my experience from doing similar tests, I have never seen a test that has stated that there can only be one option that fulfills the criteria.
However, I just read the last lines of your reply again, and I believe I might have misunderstood what you mean by "contradicting answers". Could you elaborate on that one. Perhaps that is simply just the motivation I am asking for above, that if you can show that one option being true contradicts another from having the possibility to be true, then no further exploration is needed for that other option if you can see that the first is in fact true.
Without looking at the answer. ... the cat is in the hat that is moving along the floor
It also has strange noises coming from it.
I’m overthinking these questions too much when the answer is so simple lol
Wrongthink. Not overthinking.
just remove the damn hats, cat is in none. cat could be under one
See, I went a bit differently about it. At the time that the question was asked, there was, in fact, one cat outline on all three hats. While the statements themselves talk about "the" cat, the problem itself doesn't explicitly state that there's only one cat; it only states that there are three hats and three statements. With that in mind, I went with answer A. Since you can see the cat in hat 2, then statement 2 is wrong and since you can see the cat in hat 1, then statement 3 is wrong.
Edit: I think what went wrong is instead of answering the question "which hat contains the cat", I tried to see "which statement is accurate"
These problems are called “Knights and Knaves” but this has to be the easiest one
The only logical answer is that, "We don't have enough information."
Feh, to this video!
Yes, because of option d. which contradics the second information, meaning you can't trust the first information either
@@eigilhysvr2292 I think that the option d is for "this puzzle is unsolvable"
Agreed. With how things are set up It’s logical to make the lower sentences the 4th and 5th statements.
The “None of them” option seems particularly strange to include, considering one of the premises was “Exactly 1 hat contains a cat”
Every time a puzzle is to easy I think, there is an amazing trick, that totally changes the awnser
when i saw one of the answers being none of them i started to ever think things and started considering the fact that the fact there is one cat is possibly one of the true or false statements and if that wasnt even off limits whats to say that the fact only 1 is a true is even true
I legit solved it within 4hrs straight
And I realized that there is no f****** reward
I feel robbed
Well in real life, you'll know it if the hat moves 🤣
This is the first one I’ve ever gotten right on this channel and I’ve been watching for two years now
Next week:
This is a question from a 2nd-grade oral exam in Taiwan. The students were given 3 minutes to solve this question. Tihim has a rectangle made of a number of identical square tiles. The rectangle is 2 tiles wide and at least two tiles long. Tihim then splits the tiles into two groups (of at least 2 tiles each) and tries to make those into rectangles, but he finds he cannot make either group on its own into a rectange that's more than 1 tile wide! What lengths could Tihim's original rectange be and what lengths can't it be, given this information?
( My joke being that this is the Goldbach conjecture in disguise. )
An even number at least 4 or odd number that is 2 more than a prime. Btw you should require the 2 new rectangles to be at least 2 tiles long for this puzzle to work.
I see what you did there
I was too busy wondering why there is a cat under a hat...
Maybe I overthought this, but aren't "Exactly one of the statements is true" and "Exactly one hat contains a cat" statements themselves? In which case the answer would be "e) Not enough information"?
Yes, you overthought it. "Exactly one of the statements is true" and "Exactly one hat contains a cat" are statements, of course. These statements should help you find the right answer.
Why would two clear statements mean "not enough information"?
Also, these kinds of riddles usually do have an answer, so the "not enough" or "all of them" is supposed to confuse you. :)
@@PrimoStracciatella It's overthinking, but it would be NEI under that. "Exactly one is true" would be false in any possible situation where those two are included as statements, so every statement could be either true or false with no way to determine.
No the 2 aren't statements but Informations. So we had enough Informations.
Plot twist: the cat is simultaneously alive and dead
JUST LOOKING AT THUMBNAIL
If the cat is in hat 1, then:
statement 1 is true, hat 2 is true, hat 3 is false.
If the cat is in hat 2, then:
hat 1 is false, hat 2 is false, hat 3 is true
If the cat is under hat 3, then:
hat 1 is false, hat 2 is true, hat 3 is true.
REACHED 0:24
Now we know exactly one statement is true. Therefor, cat is in hat 2
You cant do it just looking at the thumbnail lol
@@ryannoonan5518 A lot of problems on this channel can be solved just by thumbnail.
Sure, I couldn't fully solve the riddle without the extra info in the video itself, but I was able to determine those facts.
@@ryannoonan5518 yes you can
F) the cat has knocked all three hats off the table and is now mad at you for putting them in a hat.
I thought the trick was that
Exactly one statement is true
and
Exactly one hat contains a cat
Were also statements that counted towards the problem.
I didn't evaluate that, because I wanted to know if that was the case.
Yea, I wished that was the riddle... unfortunately not. Also, no way 36% would solve that if that was the case.
That’s where I went too.
I like your intro - short, to the point and visually pleasing.
Finally . . . I thought of the right answer 🤩🤩🤩🤩👏👏👏👌😄
Thanks Presh. Love your videos.
If you want this type of more content, then I will highly recommend you this channel #mathsandphysicsfun .
I believe the cat is in all of the hats simultaneously, while at the same time the cat is not in any of the hats
I solved the problem... It means that even a new born kid can solve it
Lol on me
do you even have experience in communicating with a child over the age of 2?
the correct answer is e).
there are five statements given:
1. The cat is in hat 1.
2. The cat is not in hat 2.
3. The cat is not in hat 1.
4. Exactly one of these statements is true.
5. Exactly one hat contains a cat.
It's trivial to show that statement #4 is false -- if it's true, then #1 and #3 must both be false (impossible). For the same reason, all 5 can't be true. So either 0, 2, 3, or 4 statements are true. But 0 statements can't be true, because that means #1 is false (and there is no cat in 1) which means #3 is true. So either 2, 3, or 4 statements are true.
Given that, if 2 statements are true, we can use the solution you presented, which results in FFTFT.
But if 2 statements are true, we can also have multiple cats. This makes 5 false, but if there are in fact 2 cats they would be in hat 1 and in hat 3, making TTFFF. Another possibility is that there are actually zero cats, in which case we get FTTFF.
It's also possible for 3 statements to be true: the cat in hat 1 provides TTFFT. The cat in hat 3 gives FTTFT.
It isn't possible for 4 of the statements to be true, since #1 and #3 cannot be simultaneously true, and under this circumstance #4 is also false.
I note that you state "each hat has a statement" -- but nowhere is it stated that these are the only statements. Under the circumstances, I'm forced to assume there are five statements total, and proceed with the analysis above. It's possible to find a cat under any hat, and there's no hat that is guaranteed to have a cat under all possible scenarios. I need more information -- maybe something along the lines of "there are three statements -- each statement accompanies one hat. Additionally, you know two other facts for certain..."
Without that, though, my answer is forced to be e).
I love how your channel has problems ranging in difficulty from grade school to PhD in theoretical math.
@@SomeRandomGtaDude-zl3us Though some problems i solve easily, others i can´t even understand Presh´s solution!
So the difficulty for most people is that they can imagine a cat inside a hat, but they can't imagine a hat telling a lie?
Dr Seuss: THE CAT IS IN THE HAT
There is literaly not enough information to slove this mind game.
prove that 1+1=2
Just understand Peano Axioms and that's it.
e) "not enough information"
Actually Bertrand Russell wrote a proof of this, and is grindy as *
If you have two of something then you have one plus another one.
If you have one of something and acquire another then you have two.
Proof enough for me.
@@qua7771
It's basically just that, but, mathematically, you must first define what is the "one", then define the "two", set the two groups of one, let it be clear that they are not the same thing, join them together as the group of two, and there it is.
How to make this puzzle more interesting; same set-up as before, but with an unknown number of true statements - however, you are told that knowing the number of true statements makes this perfectly solvable. Even if it’s the same answer with more steps (0 and 3 true statements are both impossible, 2 makes it unsolvable without more info, so it must be 1 true statement), it’s such a simple twist on the puzzle I’m wondering why it wasn’t included.
Imagine that the sentence : "Exactly one of the statements is true" is considered as a statement. This problem becomes more interesting.
This channel has started solving 1st grade puzzles
Statements one and three contradict, meaning at least one of the statements must be true.
Therefore, the second statement must be false as only one of the three statements can be true.
Since the second statement says that the cat is not under the second hat, then by contradiction it must be hat two.
That's actually a nicer method to arrive at the solution than the one used in the video. Sad to say, I also used the brute-force method from the video.
Truly an underrated comment.
this is definitely the better solution.
A rare happy moment of mine when I finally get a puzzle from the channel done in 5s
Thank god Im in that 36%😂😂
You could say the third
Choice is correct also with all answers being true. As the first statement, "the cat is in this hat" does not refer to a specific hat, so linguistically we don't know which hat it's referencing, thus it could be referencing any of the hats including hat 3.
Yeah! Thnx presh. I love the logic problems
Me an intellectual : hats can't talk, and a cat wouldn't be able to fit in even one of them. So none of the hats have the cat inside of them. It's called logic.
I think the reason not many ppl got it is cuz of the option “not enough information.” If that wasn’t there then I think it would be extremely obvious.
yeah true
but the ability to look past the contradictions is what makes puzzles like this interesting
A great man once Said...
Logic can get you from A to B.
But.
Imagination can take you everywhere.
And if you include “exactly one of the statements is true” and “exactly one hat contains a cat” as possibly true or false statements, I think that the true answer is e
Yeah because it could be two or three because nothing proves three wrong
I wished that was the riddle when I saw it mention "statements".
This was puzzling until the full set of knowns was presented and then it was just working out the truth table.
Took me 10 seconds to figure out. I am an Asian newborn baby.
took me 5 second to figure it out and I am an Asian just conceived baby.
@@amaseaman by brother took 2 seconds and he is an unfertilized egg in Asia
@@The_Math_Enthusiast my sister gets it done in 1 second and if she ever exists her name would be Asia.
Everybody gangsta until the problem changes to all statements true
Plot Twist: The cat's name is Gougu. 😎
After 15 years in software development, I am still in awe of how many people don't know what a truth table is -- to say nothing of how it is used to evaluate valid conditions.
"Only 36% can solve it"
Me: I'm smarter than average. 😎
Also me: You fool. It was obviously a lie to make you feel smarter than average. ☹️
Too simple. "The cat is in this hat" and "The cat is not in hat 1" are exclusive, i.e., one is true and the other is wrong. We know exactly one statement is true, so the second statement "The cat is not in this hat" is wrong, which means the cat is indeed in hat 2.
First from brazil !!!
Primeiro a comentar em português!
@@MarcioSilva-mt3bp nada mais justo ! Hehhehe
The cat is already in your kitchen, gorging itself on the fish you meant to prepare for dinner.
When you finally solve a mind your decisions problem
I git it right but I didn't use your approach. You started with "the cat is in hat 1, let's eval each statement".
I did it as "let's assume statement 1 is true, and eval the rest.". It made finding cat in hat 2 easy.
I saw 3 hats with 3 cat emblems on them ... - World problems solved with cats in hats... Riiiiiiight. ;)
If u are good at minesweeper, u are good at this.
I want more of these problems, but harder. Once you know that the hat isnt in hat 1, you just find out which hat it is knowing statement 3 is the correct one.
Was waiting for a plot twist. Seemed easy to me.
It's very simple when you assume that each accompanying statement is false and narrow it down from there.
Due to the set of five possible answers - i.e. _d) "None of them"_ as it would be immediately excluded by _"Exactly one hat contains a cat"_ - this could also have been a trick question when you consider that there are not _three_ statements to be evaluated but _five_ . When two extra statements about _truthfulness of only one statement_ and that _there is only one cat_ may also be scrutinised then the answer would be _e) "Not enough information"_
Its much easier than that. Start by considering that the statement on the first hat is true. Now just follow the logic and remember all the conditions and you will reach the answer:
Assume s-1 is true: Therefore s-2 also has to be true: Contradicts - "only one st. is true": Therefore s-1 is false: Therefore cat is not in hat 1: Therefore s-3 is true: Therefore s-2 can't be true since we already have a true st.: Therefore cat is in hat 2
Yeah this one is easy compared to the mind blowing puzzles that this channel has to offer.