Can You Solve This Tricky Multiple Choice Question?
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- Опубліковано 12 гру 2024
- This logic test has 6 options and you need to find the correct answer. But each option refers to other options. So which one is correct?
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I think this is one of the only questions I was actually able to solve on his channel
Yeah me too
Well, this is the second question that I solved in this channel in less than 30 second
Me too haha
I solved it about 1 second after all the answers were shown, truth be told. That was one of the only ones though.
Same
I would love to see more of these logic problems. This was fun to figure out.
Pretty clever little logic problem, but I didn’t think it was too hard. Just used process of elimination. This was fun, thanks for sharing!
at 3:26, can't you just say; because 1,2,3 and 4 are false, 5 is true. Because 5 is true 6 is false.
This. Not sure why he evaluated 6 before 5, other than to add some unneeded complexity.
That’s what I thought.
I guess to make the answer the last one and build up the reveal
It think 6 is right
I thought 5.
simple but nice.
I guess many people here are not criticizing easy problems per se. they are against easy problems presented as super hard just to attract viewers
JWentu Dem Math Meanies™ are jealous.
This is University level Maths( first year first term of an Analysis course)
dalek1099 The question may appear on a college level question, but the difficulty actually is fairly easy.
JWentu Yeah, I’m not even in high school yet but solved this in 15 seconds.
@@angelmendez-rivera351 I'd love to agree with you, but as someone who is aware of general human intelligence I can not.
I got it right by considering "true/false" values for the statements, but then I stopped to ponder whether "answer to this question" is logically the same as "true", but I gave up on that train of thought once I realized there is very little difference.
That's a perfectly clear explanation! Thanks for sharing.
I think you should stop with the reminders every video of how smart we are for watching you. It gives me a r/iamverysmart vibe
Shantanu Modak Careful not to become a Math Meanie!
It's sarcasm
Math meanie alert!!!
The "math meanies" comment makes him seem like such a twat.
An*
OMG! The first one I managed to solve completely on my own! I've been close many times, but this was the first one that was actually correct, and with the correct steps to get there too.
The teacher: "The test is easy its multiple choice."
The test:
Teacher wasnt lying then
Damn, u have easy teachers then, when my teachers say that it’s not easy or multiple choice
if I had only tests like this in school I would have PhD now
I like like the content of your videos, but lately they have been getting too focused on “math meanies”. Don’t focus on the negative comments. You can’t please all of the people all of the time. Focus of the message, you don’t need to tell people to like your videos, and you don’t need to keep telling everyone how many views you have had. Just make the video and people who like them will stay and people who don’t will go away.
Views and likes means ratings, and therefore ad revenue (assuming adpocalypse hasn't hit).
FlagDUDE08 ,but telling people that they should like something is rather infuriating. I can make my own mind up thank you. Telling me to press the thumbs up actually make me more likely not to conform and press thumbs down. I don’t know how other people react to this tactic but if they act like me then telling people to like a video could be counterproductive.
To be fair, unfairly hateful and negative comments can really lower the confidnence of doing something like this. Saying that once or twice can help ppl stay positive even when that happens.
The thing i would change is instead of “Subscribe to help us out” say “If you liked the video or what we do, you can subscribe to help us out”. The former is a command whilst the latter is a suggestion.
Note: Criticism if its right doesnt count as unfairly hateful.
Then do what you want. The guy can say what he wants, and it has been explained the ramifications for doing such a thing. At this point, it looks like over 1100 users disagree with you, which is a heck of a lot more than the at most 60.
FlagDUDE08 Thanks for your permission to do what I want. Not sure I needed it.
You seemed to have made an assumption that I have pressed the thumbs down button!
Is it just me or "my videos will make you so smart" sounds patronizing? Might as well go full "Oh look, you've drawn 2+2=4, you are so smart, let me put this drawing on the fridge with drawings of other smart kids"
It does, and these videos (although fun to watch) will probably not make anyone smarter than what they already are.
Very irritating to hear that, and quite pushed me away from his videos.
He even ramps it up a notch by saying he's received "overwhelmingly positive" feedback for his snide comments. (See his response to the criticism)
Yeah, that sounds like "oh look how good and useful my videos are, people are smart thanks to me and if I wasn't there they wouldn't be, I am such a great person"
Yeah but *fridge* made me spit my coffee.
No you are smart. Since i tell you and i know how smart you are ;)
I’ve been a subscriber for a long time, and I’ve always enjoyed your upbeat attitude and fun math videos! :)
There are two things I watch at those questions: 1. Can there be more than one answer true? 2. Are answers contradictory? If there is only one answer that can be true, it's easy to find out, cause you can strike the ones that say something positive like "one of the above/all of below/above" cuz it means there have to be 2 correct answers in that case. Then you only need to rule out the negative statements and watch for contradictorys.
This exact question appeared on AQA's Computer Science Paper 1 A level today I kid you not
here to check my answer from it xD
An alternative thought process: the question asks you to choose "the" correct statement implying that there is only one correct answer. This implies that any question that suggests more than one answer are correct must be false, so we can provisionally exclude 1 and 3. [redacted an incorrect conclusion]. Also, 1 and 2 can't both be right at the same time because they contradict each other, so that confirms 3 has to be false which, in turn, confirms that 1 is false. 2 might still be right, so we can check for additional right answers below. If 2 is correct, that would make 4 correct, but that contradicts the statement of 2, so we have to mark them both as wrong to avoid the contradiction. That makes 5 right since we've already eliminated 1-4 and if five is right, then 6 can't be right. The correct answer has to be 5.
You can take this further: because only one answer is correct, any answer that says one of the other answers is correct must be false, which eliminates 1, 3, and 4 immediately.
@@cwingate438
I think you two have clearer, simpler explanations than Presh.
At least twice he seemed to be over-complicating things, by missing some simpler logic.
This was actually easier than reading parking signs to find out when you can and can't park.
0:00 I’m gonna say: ”5 is correct.”. All the others lead to contradictions. 😎
*EDIT:* 4:15 Exactly 🎯!
Quit whining about "math meanies". Either ignore them or get harder problems.
Telogor _ Don't be such a Math Meanie™!
Some smart people get it in five seconds, but not me. No, Presh, I did not figure this out. However, after your clear and logical explanation, I understand the reasoning. And this time I do not need to watch the video twice to get it. Moreover, I can even explain it myself. Many thanks for your time!
Same
wait so couldn't solve it?
I got it after like 15 seconds of looking at thumbnail
@@Qui-Gon_Jinn69 and…?
@@taffles7498 and nothing
@@Qui-Gon_Jinn69 exactly so shush no one cares
I like how you went through the problem.
Most teachers I've had would start with one, explain how 2, 3, 4, 5, and 6 all relate to it. Then they'd go to 2, explain how 1, 3, 4, 5, and 6 relate to it, then move on to 3, 4, 5, and 6 and do the same thing, which yes, means they'll repeat themselves over and over until they've explained how every option relates to every other option multiple times, which is totally unnecessary, and the reason I'd just answer the question in my head and tune them out. If they called on me I'd just give them the answer and go back to ignoring them until they gave me a new question or set of questions to do.
That sounds so ridiculous that I have a hard time believing you're being accurate in your representation of what went on. Maybe ridiculous is the wrong word, but it feels like something is missing imo.
1st one of your videos I actually solved without explanation!
I have the following issue with this problem:
Yes, #5 is logically consistent in being the only non-contradictory one. Yet, it also needs to answer the original question to be correct, right?
But for me, this self-referential question doesn't even have answers in the traditional sense.
Therefore, none of the options is the answer to the question, not even #5 even though it's logically consistent.
Suppose 5 is false.
This implies that there exists a correct answer above, which is false.
@I Exist makes sense, even though 5 is correct, It isn't necessarily an answer
Another possible issue is that we don't seem to have excluded the possibility of statements being neither true nor false. In most ordinary contexts it's safe to assume that a contradiction from assuming "true" implies "false", but mutually referent logical statements is no ordinary context. (To elaborate, "This statement is false" can neither be true nor false. That's a simple case in which it's impossible to assign "true" or "false" to a statement. So why are we safe assuming that an even more complicated set has the exclusive true/false property?)
@@gremlinn7 Because they can. You just gave an example of a statement that is neither true nor false. All the statements in this question are either true or false.
Number 5 isn't just 'non-contradictory' as the narrator says, it's 'true'. So it does answer the question by virtue of being true.
Since the question asks for which "answer" (not "answers") is correct we can assume that's there's only one right answere, therefore 1, 3 and 4 must be wrong because they need another right answer to be right. 2 can't be right as well because it would make 4 right, so 1, 2, 3 and 4 are wrong and that makes 5 right, which then makes 6 wrong
Answer: 5
Are you trying to bait some of your viewers? At first it was “my problems will make you smart, you will even see commenters asking for harder problems!”, which was a complete misinterpretation of those criticisms, now this. You don’t have to publish videos on hard problems only; but it’s always good to maintain at least some standard, or level, of complexity.
Danil Dmitriev Math Meanies™ are attacking!
This is University level Mathematics( first year first term of Analysis course).
This is one of those that looks a mind bender, but is actually very straightforward.
I took a slightly different route:
- It can't be 3, as 1 and 2 clearly can't both be true
- Hence it can't be 1 (as then 3 would be true)
- Hence the truth of 4 would imply the truth of 2, contradicting the assertion that 4 is true; hence it's not 4
- The truth of 6 would imply the truth of 5, and assuming there's a unique solution it therefore can't be 6.
- So it's either 2 or 5
- But if 2 were true, then 4 would be false, contradicting the assertion that 2 is true.
- Hence it's 5, confirmed by checking consistency.
Nice problem.
To be honest, you actually elaborated my brain functioning when I was solving it in 10 seconds.
For me, he condensed the process of my brain functioning when I was solving it in half an hour.
I tend to over-think things because I want to make sure that I am absolutely correct before making a conclusion.
Starting from the bottom made more sense to me.
6 cannot be true, because 4 & 5 cannot both be true.
6 false, 5 true, and everything else false works, which solves the problem.
Raymond Smullyan would be proud of you.
OK, the easiest way to solve it is by eliminating answers that we know are false. Hopefully that will cascade to leave us with only one true answer.
(1) is only true if everything below it is true, but (4) is incompatible with (5), so (1) is false. That makes (3) false as well.
Having eliminated {1,3}, (4) can only be true if (2) is true, but (2) can only be true if (4) is false. This might seem like a setup for a Liar's Paradox, but in fact we have exactly one stable model, where (2) and (4) are both false.
Knowing {1,2,3,4} are false, we can now just read (5) as true, making (6) false.
So the answer is (5).
“I made my house a mess, which was making it clean, which made Squidward clean my yard, but that really means he was messing it up, but the opposite of clean is filth, which means filth is clean, which means Squidward was really making my yard a wreck, but normally i’d wreck my own yard which means Squidward is being the opposite of Squidward which means he’s Spongebob! Ah-ha! I understand everything now.”
Finally! Managed to answer you puzzle correctly!
I mean, 1 and 3 cant be true because only one statement is true, 2 is flase because of 4, 4 is false because 1 2 and 3 are false, and 6 is false because if it were true, then 5 would also be true since they fully overlap.
Fairly straightforward logic puzzle, but can be tricky if you’re not careful. I briefly second-guessed myself, though my original answer was correct anyway.
Nice to see problems that aren’t just playing with numbers on this channel!
I got 5 watching the vid now
Paused at 0:36 when I realized the answer has to be 5 because it can't be 6 because if 6 were true 5 would be as well but 6 says it's not. So if we rule out 6 that rules out 1 because 1 says 6 is true. If we rule out 1 that means we can rule out 3 because 3 says 1 is true. 4 can't be right because the only one we haven't ruled out above it is 2 which days 4 can't be true. If 4 is true then so is 2 but if 2 is true 4 can't be. This rules out both of those and we're left with 5 as the correct answer
After all this time watching your videos I decided to solve one myself and I succeded. I am so happy. Thank you a lot for making these videos!
me: only watch the thumbnail and know the answers
i am four parallel universes ahead of you
Presh, We love your videos. You do not need to prod us so hard to subscribe or to buy your books. We get it!! Perhaps you would consider going back to your earlier style of reming us to do these things, which was less obstrusive!
I appreciate your support and feedback. I've received overwhelmingly positive responses to the current format over previous iterations. Many people watch the videos for the first time, and you'd be surprised how many emails I get asking about my books and how to subscribe. If people want to share examples of how other UA-camrs promote their books successfully please do! I am always willing to learn from best practices.
At the very least, comments on this video are overwhelmingly negative about the current format. I love your puzzles and the answers you write for them, but, along with the ~hundred of people who wrote a comment about that here or liked one of these comments, I must agree that your unending talk about how great your own channel is ends up being pretty obnoxious. That matter is made even worse by the fact that the actual puzzle disappears from the screen for a long period of time before the timer starts. Finally, I'm also very perplex by the claim that people don't know how to subscribe; I find it pretty hard to believe.
MindYourDecisions the 5-second self-advertisement before the countdown is fine. But for God's sake, leave your math meanies text out (at least the one right after you told the problem) it destroys the flow of your video and is a little bit cringe tbh. And do your cross-promotion also after the solution, as it, again, destroys the flow and personally is only annoying and ends up with me skipping a minute within the video.
It's even so annoying for me that I consider unsubscribing in the long term (not that you have to care)
Stop being so fastidious. If the videos weren't good, he would not have 800k+ subscribers (and growing).
Ferdinand Kraft lol. You're kidding, right? If I look into my trending tab, I don't see quality = success. And just because someone is successful, it by no means means that they are immune against criticism and shouldn't be criticised.
Love your vids, I always try to work it out by myself before watching. Thanks for keeping this brain working.
2:50 "So if 4 is false that means none of the above is true". That is true knowing that 1 and 3 are false but you should say "So if 4 is false that means none of the above is true OR 2 OR 3 are true" and then continue logic with saying that since we know 1 and 3 are false then 2 is also false which is not possible because we assumed it was true. Just saying.
(2=true) implies (4=true) because 4 is a "one of the above", but (4=false), meaning NOT(4=true), so therefore 2 cannot be true
Why is 4 false? Well (4=true) implies (1=true) OR (2=true) OR (3=true). 1=false and 3=false, so (4=true) implies FALSE OR (2=true) OR FALSE which simplifies to (4=true) implies (2=true). However, (2=true) implies, among other things, (4=false).if (4=true) implies (2=true) and (2=true) implies (4=false), it simplifies to (4=true) implies (4=false), which is a contradictory statement. Therefore, 4 cannot be true, so it is therefore false.
sorry natnew, I stopped reading your comment after the start, because you wrote "(2=true) implies (4=true)", which is incorrect, if (2=true) then (4=false). And also to clarify, in my first comment I said that he should say "So if 4 is false that means none of the above is true OR 2 OR 3 are true" and those numbers in the sentence (2 and 3) are not indicating sentences number 2 and 3, I meant that two or three of the sentences are true (or all are false as i said earlier).
(2=true) doesn't directly imply (4=true).
However, if (2=true), then (4=true). 4 implies that either 1, 2, or 3 is true. if (2=true) is true, then (4=true) would imply a true statement, meaning (4=true) is true. That's what I meant by (2=true) implies (4=true).
BUTTT (2=true) implies (4=false) directly, meaning (2=true) implies (4=true) and (4=false), which is impossible, meaning (2=true) is false.
No man, that is wrong logic!!! We are checking each of the sentences individually! You can't say that "if (2=true), then (4=true)", because (as you said) (2=true) implies (4=false) directly. Now read this carefully:
We want to know if statement 2 is true or false. We start from assuming that (2=true). Ok, now we know that (2=true), let's read what the statement 2 is saying. It says that "none of the below statements are correct". We assumed that sentence 2 is true so of course it gives us information that "none of the below statements are correct". Statement 4 is below sentence 2. So the sentence 4 is not correct. Now we know that (4=false). We also know that (1=false) and (3=false) because of the reasons mentioned in the video. Now read what sentence 4 is saying. It is saying that "One of the above statements is correct". We know that (4=false), so we get the information that "either all(three) of the above statements are correct OR two of them are correct OR none of them is correct". Since we know that (1=false) and (3=false), then we must have that statement 2 is false (2=false). Thus statement 2 is self-contradictory and cannot be true.
I wrote way too much about that but it is to show you what is the correct logic process from whoch we get that (2=false). It is written at the right side of the video at around 3:08 minute mark, I just tried to make it clear so it took more writing for me. Pause the video at 3:08 and read it, this is the correct logic from which we get that (2=false).
Uhh... That's exactly what I said.
...We were saying the same thing, then correcting eachother over it, when we really agreed in the first place so this discussion shouldn't have happened...
...sorry about that.
4:17 okay that was one of the coolest text effects I’ve seen. 😯
Fun fact: The "people who solve the world's hardest problems" are also the ones who most commonly make the world's hardest questions. They then challenge themselves with the very hard questions made by the other people who are the world's best mathematicians. The "My videos will make you so smart that ..." is very narcissistic.
Except he gets problems from other places and cites where he got it from.
Thats not narcissistic
There is also another solution to the Which answer is correct... You notice that they ask which is 'CORRECT' not which is true, not even which is the right answer. it asks which is 'correct'... in that case its which ever one the test maker has chosen as the correct answer.
Your analogy actually explains people's frustration with very easy questions well. Marathon runners practise with 5k runs and not a leisurely jog to the shops. While solving easier problems can be a great form of practise and a way to warm up, they are only useful if they are still appropriately challenging and generally you also want them to be archetypal, in that they show a method you can use to attack harder problems that are fundamentally similar. You'll find that a lot of exams actually do this. They will ask you an easier version of the problem and then use this to help take you through the harder parts.
This question is fundamentally about a useful technique for hard multiple choice questions, where instead of finding the answer you eliminate all of the incorrect answers. This is only really useful for people who take multiple choice exams though and I suspect a lot of your demographic just does maths for fun. Given this method isn't considered to be very satisfying, it seems odd that you would feature it, but each to their own.
Practice logic riddles fit fir AIs of the 25th century, fail consistently, but learn from your errors and you will master logic riddles made for mere humans of the 21st century.
AQA Compsci 2022 makes me cry
This was the easiest one for me to solve. On my first read I got it.
Me, too, BUT I doubted myself.
(So maybe the videos alone do not build confidence? Back to my paper books! :)
Eliminating 1 through 4 was easy. Had to think about the last two a little bit longer to make sure it wasn't a trap or to make sure it made sense.
I’ve looked at this problem a lot, trying to find something that he missed, but the case is flawless, just as numbers are. You would have to start at 1, or there would be any progress. you need to skip over 2 because you haven’t read, proved, or disproved anything. 3 is wrong when you prove 1 is wrong, and 4 can’t be right because we haven’t proven or disproven 2. 6 is wrong because of the only one left(that isn’t a repeat), 2. 5 is wrong because of 2, yet again, so 2 is the last answer. I know one could argue that by proving 4 is right because 2 is right, causing some sort of confusion and proving them all wrong, but you then have to consider the next step, which would be proving 2 right. Some people would say this creates a loop, and it does, but we found an answer before it, so it doesn’t hold up. The case is rock solid, so scram, math meanies!
I think it is a cool problem, though, and would like to see more of things like this.
When one item contradicts another item, it's not "self-contradictory".
the item is self-contradictory because the item itself (when true) forces the other item to be true/false, which contradicts it
@@pranaysoni8967 I'm going to self-contradict you and say you're wrong.
@@pranaysoni8967
7. Every odd one is false.
8. Everything below the fifth is false.
The above are self-contradictory, because they violate their own statement if true.
A paradox, by definition, is self-contradicting, like the one below.
9. The ninth is false.
It is different from the other two as it can neither be true _nor false_ because of itself, while the first two can be false.
I suggest just taking them in order and stop mixing it in weird ways:
1 - all of the bellow; cannot be true due to different statements in 2-6 -> False
2 - none of the bellow; since points 3-6 effectively cover all possibilities (all, at least one, none), one definitely should be true and this point is therefore False; but your argumentation does it well, too.
3 - all of the above; simply cannot be (same as 1) -> false
4 - one of the above; 1-3 already proven false, so -> False
5 - none of the above -> true
6 - none of the above -> false, cause 5 is true
contradictory 2 and 4 are nice, too, but I like to take things in order
For those who say this was easy, nice! Either you have natural talent or you have been training, which is one of Presh's points.
So extra challenge, write an explanation of the answer that's simpler than Presh's answer!
*Me after seeing this question* : Give me two seconds....
*Me after solving this question* : Nah, I didn't even need that.
Papai Pal What's that smell? I think I smell a... Math Meanie™!
That took me about an entire minute!
Admitting, however, when I saw 5 and 6 as the same, I thought it would kind of be a clue.
But I've done all the Smullyan books, so these are much like his material.
Thanks.
This was indeed fun! My reasoning:
1. contradicts 2, so it is false.
2. implies and contradicts 4, so it is false.
3. is false because 1 is false
4. is false because 1-3 are false
6. implies and contradicts 5, so it is false.
Missing number is five! And indeed, 5 being true and the other being false is the (only) consistent truth assignment.
This took me like 10 seconds and I’m confident enough to say it’s 5 before I see the answer.
Panda Chong Same. I took 15 seconds though, a bit longer.
Yes, of course I am going to watch and share every single Mindyourdecisions video ever uploaded!
I got 5.
If 1 was correct, then 6 would contradict 1.
If 2 was correct, then 4 would contradict 2.
If 3 was correct, then 2 would contradict 3.
Since 1, 2, and 3 aren't correct, that means that 4 is incorrect.
If 6 was correct, then 5 contradicts 6.
Therefore, 5 is correct.
You don't need to consider 6 before 5 - if 1, 2, 3 and 4 are incorrect, then "none of 1, 2, 3 and 4 is correct" is correct.
rmsgrey
It’s always good to double check if one of the remaining options isn’t a better answer. Some multiple choice tests are very straight forward and only have one proper answer, i.e. if you spot that it’s (a) you don’t even need to bother with (b)-(z). Other tests are tricker and want to catch you slipping and can have multiple plausible answers but instruct you to pick the best.
For example choice (6) could’ve read something along the lines of “two of the choices are correct.” Which would be a better answer than (5).
If 5 is your answer then youll leave 6 as an answer but 6 also means "none of the above", assuming that 5 is neither the answer
Kiko Baltazar
Huh? If you select (5) as your answer it simply means (1)-(4) are not solutions. They aren’t. Therefore (5) is true. It says nothing directly about (6).
I wonder what would be the time complexity of a general algorithm to solve this kind of questions. We can encode each possible answer as an integer, so the list of all answers is an array. A positive sign means the answer refers to higher indices (below), and negative refers to previous indices (above). To encode "none, one, two... all" we need to add an offset, because 0 doesn't have a sign, so "none of the above" would be -1, "none of below" is +1, "one of the above" is -2, 0 is none for both sides, and N+1 (N = answers available after or before the currently selected answer) would mean "all of the below or above" (depending on sign).
The answers in the video would be encoded as:
[+6, +1, -3, -2, -1, -1]
This representation is easier to work with using an algorithm, because it's just some arithmetic and conditional expressions in a loop. I still don't know what's the general algorithm, but seems easy to develop
Your brain is beautiful
@@exintrovert1337 Thanks, I guess lol
7. The question is a scam.. *SOLVED* 😎
Crash Twindicoot Math meanies trolled EPIC style
question : what's 9+10?
8. 21
9. 19
10. 20
11. 22
12. Blackjack
13. 666
vLinh dh , it’s number 9.
@@CaptainAlligator no its 69 you dumdum
I worked as a temporary math teacher in the school in my town tow years ago, I gave my students some of the puzzles you feature on the channel 😁
All the love from Syria 😘
First reaction: 5?
Edit: Aww yeah
Haven't seen the answer but here's my logic.
3 and 5 contradict, so 1 is false.
1 is false so 3 is also false.
2 cannot be true because that would make 4 true, therefore both are false.
As 1-4 are all false 5 is true which also contradicts 6.
5 is the correct answer.
EDIT: yeah, this is the same except for the reasoning of why 1 is false and the way the last two were deduced.
The actual logic problem here was interesting, although its question could have been phrased a little better, as others have pointed out.
The claims about what your videos have accomplished and how you are characterizing people who criticize them are less impressive.
That was fun! Took about 30 seconds of overthinking each point to get it right. I may check out the rest of the channel now.
Who are the “math meanies”?
In the "You Feature Me - I Feature You" section, the question asked is: "Can you guess the secret word in this brain teaser?" Yes, I can guess - that's easy. Pick a word at random, and I guessed the secret word. The question should have been: "Can you apply logic to determine the correct secret word?"
this one was really logical I could answer it. Thanks for this question
Cracked it bro!!
1-4 are contradicting, thus making 5 a correct answer, which means that 6 is false.
I peeked and looked at the logic for the first statement, but I got it right after that. Plus, when I peeked, it turned out I was already thinking exactly what you said.
I love logic puzzles. Logic and math are not the same, but they are cousins; with logic as the senior concept. Math relies on logic. The reverse is not necessarily true, although logic can usually be expressed in numeric or similarly-symbolic (e.g. Boolean) terms.
yeah i like to call it Math and Informatics are applied Logic and Physics is applied Math
I have seen that statement made primarily in the context of Boolean math.
Logic in and of itself is neither mathematics nor is it dependent upon mathematics. But there are SYSTEMS of "logic" which are mathematical in nature and form, not least that of Boole.
Pure maths at University is pretty much 100% logic so I'm not sure I'd consider logic and mathematics as distinct.
The type of logic here was studied at the start of my first year Analysis course because to prove many theorems you need this logic to eliminate all possibilities but one.
There is much pure maths that you can do from just carrying the logic from the theorems without any need to be able to calculate anything even if you didn't know 1+1=2 even.
As I said: Logic is the senior concept. Math could not exist without it.
The reverse is not true.
Hence, math may be a branch of logic; and some systems of logic may be branches of math; but logic -- fundamentally -- is not a branch of math.
JamesG What logic isn't Mathematics?
4:19 I did not actually, but after your explanation I was able to solve many similar questions. Thank you!
Before watching the solution, i believe #5 to be the correct answer to this. #1 being true would induce complicated contradictions, #2 being true would mean #4 was also true (contradicts with #2!). #3 would induce a contradiction between #2, #4 would either lead to a contradiction or leave us with nothing. And since there are only two instances of "none of the above" left, I'll take the former option (#5). Because #6 being true would also make #5 true (#5 excludes a subset of what #6 says is false) and thus contradict with itself(#6).
But #5 being true makes #6 false. Perfect path!
You can't imagine the happiness when I got it right in this channel
I agree 5 has no contradictions, but the question itself is self-referential, so I'd argue this whole thing doesn't make logical sense. If the question was phrased a little differently then this wouldn't be applicable. I've seen enough tricky math problems on the internet to be skeptical regardless. E.g. equations to be solved via substitution with pictures used in place of letters for variables.
Right. The problem is too self referential to have an answer.
This sentence contains five words.
Having shown that you get a contradiction if any of 1 through 4 are correct, you've concluded that none of 1-4 can be true/correct, so you have concluded that the thing that 5 says (that none of 1-4 are correct) is true.
Self-reference is risky (‘This sentence is false’) but it’s not always invalid or illogical. Consider the classic definition of factorial:
“0! = 1, and n! = n x (n-1)! for n>0”
This statement is self-referential but totally valid. Computers use it all the time with no errors or contradictions.
rmsgrey and hence also that 6 is false.
I found this problem quite elegant! Nicely composed I think.
The problem I have had with this channel is the insistence of going through all of the steps of puzzle even when the solution is far more easily deduced. You can say that logic requires this that and the other, but when the solution boils down to simple math, by going through a tedious process to arrive at an immediately obvious solution (if there are 20 socks in a drawer of 2 types, 10 of each, and you pull out 3 pairs, you're holding a matching pair by simple virtue that there are not three different types of socks in your drawer. The puzzle ends there. Part of logic is realizing that wasting time on a pointless exercise that can be bypassed is not logical), you're defeating logic.
This is not one of those cases. This is a difficult problem which actually does require that steady process. Here, the exercise is not pointless.
So which answer is correct?
A. All of the below.
This cannot be correct because it comes into immediate conflict with
B. None of the below
This cannot be correct because it comes into immediate conflict with
C. All of the above
This is immediately discounted because it cannot be resolved with B and A simultaneously and individually.
D. One of the Above
This is placed in conflict all three, none of which can be correct if D is correct.
E. None of the above
This does not conflict with any of the above and up to this point would be correct.
F. None of the Above
This isn't correct because that would mean E isn't correct, which it obviously is and would make this statement false.
The correct answer is E, or 5. I used letters when you used numbers. Sorry about that.
my method of solving it exactly.
B is disproved by D, not C.
@@nono7105 Sooo...you're saying that "C. All of the above" can be correct at same time as "B. None of the below"?
@@pianotm No, C is disproved by A being false. The fact that C is false does not disprove B. To disprove B you need to evaluate D, not C.
Edit: C is also contradicted by B (you don't need to 'evaluate' A to conclude C is false). But B is not contradicted by C. You actually need to evaluate the first 4 statements to conclude B is incorrect.
@@pianotm C being false does not mean that B is false though. If you took D out of the question altogether then the question would be ambiguous (either B or E could be correct but not both of them and there would be no way to tell which of the 2 it is).
B does contradict C, but C does not contradict B.
That question was so easy. I immediately realized 5 was true.
Can you solve this,, find the pattern in the numbers and what follows
45 65 19 77 7...
This isn't even hard. You just have to think about them one by one.
congratulations on your enormous IQ!
I narrowed it down to only 5 or 6 with one piece of logic. Answer 4 says “One of the above,” and the problem itself says “Choose which one is correct,” not “Choose which ones are correct,” stating there is only one correct answer. So if 1, 2, or 3 is true, then 4 is also must be true. As the problem says, there is only one answer, therefore making all 1, 2, 3, and 4 false
I got everything but what is the QUESTION
The question Is which is correct
What is the Matrix?
First time I could easly solve your riddle. I took my 6 minutes but I am still happy.
I think 5, but didn't start the video yet
New to the channel I love these kind of brain teasers
Before seeing the solution, I think it is 6.
After solution: I still think that 6 could be correct, but if not, oh well
Gy001 hey bro...after convincing the first four options to be false... Think of only 5&6... Option 5&6 says the same statement "none of the above is correct" ... But the positions of 5&6 make 6 wrong... 5 is above 6... 6says none of the above is correct, so 5 staying above 6, has to be wrong...if 5 has to be wrong, then 6 also has to be wrong cos 5&6 states the same statement... This means that the statement on 6 contradicts with exactly the same statement as itself on 5...so 6 has to be kick out... And the remaining option 5 doesnt have any contradictory view to the above four statement and its clone statement below it... So 5 has to be pick up
Let's assume that 6 is correct: none of 1, 2, 3, 4, or 5 are true, they are all false. Then 1, 2, 3, and 4 are all false, so 5 is true. Now 5 is both true and false, a contradiction, so our original assumption that 6 is correct is wrong. Thus, 6 is incorrect.
5 and 6 can't both be correct, so that means only 5 can be correct. If 5 isn't correct, then one of the above is the answer. 6 can never be the correct answer.
If 6 is correct, then 5 must be false. If 5 is false, then at least one of 1-4 must be true. But if any of 1-4 are true, then 6 is false. So, if 6 is correct, then 6 is false. RAA.
794613825a thanksss :))
I saw first that 6 and 5 could not be true at the same time because then 1-4 would contradict either of them, and thereby 6 unto 5. I assumed then that 5 would be true, but knew 6 was not possible. Working down I saw 1 and 2 also cannot be true simultaneously, and already having known 6 and 5 could not be true simultaneously, I canceled 1 and 2 out. Then with 3 and 4, both statements cancel each other directly in relation to no other numbers, leaving 5 to be the one that did not contradict any of the “above” possibilities.
The ship’s captain, large vs small dogs, and sheep questions were fun, too. Thanks!
I feel good about myself that I solved it in around a minuet and right!
1 minute is very long for this
Small mistake at 2:57: you don't need to say "since 1 and 3 are already known to be false". If 4 is false then 2 is false, because the opposite of "one of the above is true" is "all of the above are false". 1 and 2 and 3 are all independently required to be false by 4 being false; there's no need for "since".
Also at 3:27 there's no point in skipping statement 5; it can be directly evaluated at this point. It is true, so there's no point in even looking at statement 6.
No. 4 could be false if 2 or more of the above were true, as well as none of the above. So it does not logically require that 1, 2, & 3 be false.
Since 1 & 3 are false, that means that 2 being false would make 4 false, while it being true would make 4 true. But if it were true then 2 would become false, which means that 4 is also false.
If 1 were some different statement which happened to be true (such as 'at least one of the below'), then 4 _could_ be true, making 2 false. However, it could _also_ be false making 2 true (it being false by virtue of both 1 & 2 being true).
So you do need for 1 & 3 to be false to make 2 & 4 mutually exclusive.
As for 5 being true, yes, it is, but we don't stop our analysis there. 6 could also be true. We have to evaluate it to know. When we do evaluate it we see that it's false, leaving only 5 as a true statement. But there was nothing in statement 5 that precluded the possibility of it being true. It might have said 'one of the above' like 4 does. In which case it would be true. You don't know until you evaluate it.
Before watching answer my guess is 5
Edit: nice, got it correct
Either 5 or 6. There’s a 1/3 chance it’s one of those and if one’s right, they’re both right. Also it’s my first instinct to chose it, also it’s my best guess.
The question isn't "which of the following statements is true?" it's "which is the correct answer to this question?" The statement that is the answer has to be true, but that doesn't mean that if it's not the answer then it is false. "If P, then Q" does not imply "if not P, then not Q".
The reasoning is parallel with yours for 1 and 3. But then we skip to 4, where if 4 is the answer, then 2 must be the answer, but if 2 is the answer then 4 is not the answer, making 4 contradictory and not the answer. If 2 is true, then 5 and 6 are not the answer, making 2 the answer. If 6 is true, then 2 and 5 are not the answer, making 6 the answer. If 5 is true, then two is not an answer, but we do not yet know if 6 is true. If 6 is also true, then 5 cannot be the answer, making 6 the answer, but if 6 is false, then 5 is the answer. So we're left with not enough information to determine which statement is the answer, but it could be 2, 5, or 6.
The answer can't be 2.
For statement 2 to be correct/true, statement number 4 must not be true/correct.
But if number 2 is correct/true, the statement in number 4 is also correct/true (because its statement that one of the above is correct is satisfied).
And the answer can't be 6.
If statement 6 were correct, then 1-4 would be incorrect as would statement 5. Taking it further, by statement 5 being incorrect, then at least one of statements 1-4 would be correct. And we arrive at a contradiction.
You are correct that P => Q does not imply NOT P => NOT Q, but it does imply NOT Q => NOT P, which is exactly how he proved the correct false statements are not answers. Since there is exactly one answer according to the question, it follows that the one true statement must be the answer. See? You completely misrepresented what was said in the video. This is why it's hard for me to take criticisms in YT comments seriously: it's always like this
Many of ur puzzles have stumped me, but this one I got in 10secs. Nice one
For some reason, this one was extremely easy for me to solve. I like it lol
It can be a lot simpler actually. The question implies that only one answer can be correct, therefore every answer that states that another answer is also correct is automatically false. So 1, 3 and 4 are out. And since 4 is out, so is 2.
Leaving only 5 and 6. And since 6 if true contradicts 5, only 5 can be correct.
i appreciate you trying to build a positive community of people who watch your videos. lets stay positive and overshadow the math meanies!
nathanisbored Math Meanies™ need to be stopped!
Are you seriously using the phrase "math meanies" without irony?
I got this one just fine on my own, but going out of order to explain which anwers were wrong seemed more complicated than it needed to be. "1 can't be true if 2 is true" is easier than jumping to 3 to invalidate 1.
Probably the most lame question on this channel. Did anyone not know it?
lightdark00 *cough* *cough* Math Meanie™ *cough*
This is University level Mathematics(first year first term Analysis).
dalek1099 LOLOLOLOL for a low expectations class. Simple logic, child's play, instant answer kind of question.
lightdark00 It's not an instant answer question unless you guess the answer or know the answer. Otherwise, it will take about a minute at least to properly rule out all the options with the correct logic.
It took me about a minute to complete this question and I am starting my study of Masters level Maths in Autumn at a World Top University(31st for employer reputation worldwide). For the maths courses in my first three years of the four year degree and masters combined I averaged 89%.
This sort of logic is essential for proving theorems in Mathematics.
dalek1099 I have a quantum mind then. Upon comprehending the words, it had to be 5 or 6 and then it was obvious. It didn't even take two seconds.
At a glance (5) stood out as instantly ruling out (6). They have a shared range, (5)'s falsity contradicts the rest of (6)'s assertion. A quick check if the above could all be false without contradiction and done.
There is a test-taking strategy that takes human nature into account. In a multiple choice test the writer rarely puts the correct answer first. They want you to read their creative falsehoods. Next to last is what they like best so you get the full dose of their brilliant foolers. Choosing blindly from choices a,b,c,d choose c. When taking a test check c first. If obviously false and you must choose blindly b works best. If there is an "all" or "none" of the above ( must be in that order if both) that is often a good place to start narrowing the options. If you're down to 2, look for the answer with the most qualifiers and quibbles. No loopholes.
So I started with (5). Which worked well.
I’m pretty sure it would be 5. none of the above by going through each answer and figuring out contradictions.
I found this to be pretty easy. Thanks Mr. Talwalkar.
nice, it is the first of your problems i got right. of some other ones i only knew some parts. thanks for challanging my brain so often i hope u continue to make such good videos.
Thank you man you brain teasers are really fun when you're hanging out with someone but has nothing to say