Prisoner Hat PUZZLE || 10 Prisoners || RED & BLUE Hats

Рет қаралды 358,425

7 жыл бұрын

A jailer lines up 10 prisoners facing one direction in the increasing height order and randomly places either red hat or blue hat on each prisoner's head. A prisoner can see the color of hats of the prisoners in front of him, but not his own or of the prisoners behind him.
Starting from the last prisoner in the line, the jailer is going to ask the prisoner the color of his own hat.
For correct answer, he will be saved, else he will be executed.
The Same Procedure will be repeated for all the prisoners.
The jailer announces that, if at least 9 prisoners answer their own hat color correctly, all of them will be released.
Before being lined up, the prisoners are allowed to discuss a strategy, to develop a plan for their survival.
PUZZLE : What would be their strategy to make sure that all of the them survive.
The video explains the Puzzle's solution and the Logic behind.
Please comment below your answers and suggestions. Also LIKE the video and SUBSCRIBE to my channel if you are new.

Пікірлер: 381

@sriramsubramanian1291 6 жыл бұрын

Great! I never thought about this logic. I was thinking the prisoner can see through the policeman's specs mirror and answer the color. Lol.

@LOGICALLYYOURS 6 жыл бұрын

Thanks Sriram :)

@lancerralseijoinedyourpart3633 6 жыл бұрын

thats the easy mode xd

@ourcreations9765 5 жыл бұрын

Super bro 😎

@ragunathjisankaran509 4 жыл бұрын

Awesome

@ragunathjisankaran509 4 жыл бұрын

But i think he is wearing cooling glass

@kratos952 6 жыл бұрын

IIT graduated prisoners

@warfyaa6143 5 жыл бұрын

LOOL

@ws_zilch 4 жыл бұрын

LooooL i was thinking he same. XD

@ritvikkaran967 4 жыл бұрын

and another iit graduated find a loophole in metro kzfaq.info/get/bejne/eqmfa9Jl1sWrfnU.html

@Rizwan1875 4 жыл бұрын

Hahaha 🤣

@yourdad5471 3 жыл бұрын

Underrated bro🤣🤣🤣

@ppmnox 3 жыл бұрын

I found the solution not only logical, but also compelling in the sense that I wondered if odd/even would play into the solution.

@hypercubemaster2729 4 жыл бұрын

I got it after leaving it alone for a day, lol. Very awesome line of logic and puzzle! Subscribed!

@brianaresendes966 4 жыл бұрын

I was really hoping the guard was wearing sunglasses/glasses and they could use their reflections, but this is cool too.

@mayukh_ 3 жыл бұрын

I hate this kind of answers.. If you guys are not serious, then don't answer.

@cool-aquarian 3 жыл бұрын

I’m just glad that I am attempting this puzzle sitting at home and not one of those prisoners. Solution idea is good, but implementation is 10x difficult. One moron prisoner in the line, and everyone in front of him is doomed.

@touristtam 2 жыл бұрын

think nodes and throwing a pool if the nodes cannot verify themselves. Not actual prisoners.

@sorsocksfake Жыл бұрын

Yes. This eventually led to the Goldenrock massacre in 2098 CE, where a foolish prisoner caused the Overlord to go to war with and exterminate Mexico. The world recoiled in horror, and henceforth, only logical mathematicians would be sent to jail. The subsequent shortage of logicians and mathematicians caused the re-election of Donald Trump, but fortunately he had calmed down a lot, having died 73 years prior, and he became such a good president that he has been re-elected ever since. #funfacts

@nileshmittal9971 6 жыл бұрын

I'm sad, no prisoners should be released like this... 😂

@timewalker2447 3 жыл бұрын

Underrated

@Raj-hm6qi 5 жыл бұрын

We can solve this pblm like below also: 1. Last prisoner know the color of his front prisoner. So he loudly says either Red or blue.. If it is loudly said then same color his front prisoner also wearing.. that's the hint here.. 2. Next prisoner know his hat color from previous prisoner based on whether previous prisoner said his hat color loudly or not.. Now he know the hat color of his front prisoner.. if his hat color and his front prisoner hat color are same then he will say his hat color loudly otherwise he will say his hat color no loudly.. by this way next prisoner will understood his hat color.. 3. The same logic follows Only the first prisoner don't know his own hat color so he will loudly say his front prisoner hat color always..

@Sab_Moh_Maya_Hal 5 жыл бұрын

great man

@shreyanray7624 4 жыл бұрын

Good one

@sunilsigar3145 4 жыл бұрын

Better one

@bosskiang4238 4 жыл бұрын

Nope, your method would require the passing of more than 1 bit of information (red/blue).It is mentioned in the video that hints such as melodies are not allowed, you are strictly allowed to solely answer either red/blue. I answered the same way as you did in Parallel Computation class this morning and got corrected.

@nassymcnute 4 жыл бұрын

I know one thing that's not right

@TheDeepakkandpal 4 жыл бұрын

Calculations can save you from being hanged 😂 ~ hence proved - be with mathematics

@merlinsheeba244 7 жыл бұрын

Mind blowing logic. Thanks for clear explaination.

@LOGICALLYYOURS 7 жыл бұрын

Thanks Sheeba for the appreciation. I hope you'd like other puzzles too :)

@alabamaal225 3 жыл бұрын

The puzzle initially stated that the red/blue hats were placed randomly on the ten prisoners. However, it did not state that there were five red hats and five blue hats. (Indeed, the first illustration showed the prisoners wearing six blue and four red hats.) Conceivably, there could be eight blue and only two red hats, or any other combination of red and blue hats, including all the hats being either red or blue. Not knowing the number of red and blue hats in the total of hats would make logically solving the puzzle impossible.

@bnitinb 2 жыл бұрын

You didn't read the puzzle, total prisoners are 10

@ktera Жыл бұрын

watch the video again, folk

@curosity276 Жыл бұрын

Yeah,I am also thinking the same , let's take 2 blue and 8 red hats consecutively. It fails in first attempt.

@kippe1221 Жыл бұрын

@@bnitinb you didnt understand what he wrote. Number of red and blue hats, not number of prisoners.

@1Pandaking Жыл бұрын

@@curosity276 It doesn't, the last prisoner calls out Even (Red), the second to last still sees even and calls out Blue thus correct, The third to last sees odd so calls out Red switching the Count from Even To Odd. Then each one in front of him sees the inverse of the count and Call out Red continuing down the line each one switching the count. Leading to all but the one in back has called out the right color and they are all free to go.

@maxkashyap3810 3 жыл бұрын

Awesome Problem. Upon this logic I sat down to program this approach. Really fascinated.

@swedishpsychopath8795 9 ай бұрын

Stupid puzzle: MY strategy would be: The last person tells the color the person in front of him has. The second to last will hear what color HE has and repeat his color. BUT: If he sees the next person has the same color then he will say the color name quickly. If the hext person has a different color then he will say his own color slowly. Every person will then know what color they have. Or they could have different intonation of the words. Starting high and going down for same color, and from low to high for different color.

@touchme2733 4 жыл бұрын

Great video by the way loving your content so far

@komalagarwal9830 6 жыл бұрын

Superb puzzle...n superb srategy...out of box situation.. awesome

@saj157 6 жыл бұрын

Awesome!! I finally got it!! yay!!:) you’re genius.

@LOGICALLYYOURS 6 жыл бұрын

Thank You :)

@mdmubashir743 7 жыл бұрын

amazing dude.....too good..

@jackpigeon2263 2 жыл бұрын

Wonderful logic Amar ji. Keep rocking with questions like this.

@CardCaptor32584 2 жыл бұрын

Your guard is a nice guy. When my friend told me this riddle, he let the last prisoner be the noble sacrifice.

@YEC999 3 жыл бұрын

cool logic nicely explained - came close but what i was missing the trick with the odd and even...

@PuzzleAdda 5 жыл бұрын

My goal as a puzzle designer is to create a meaningful experience for the player, not just 'I solved it.'

@tonir299 8 ай бұрын

1. Simple solution During discussing the strategy prisoner 10 can tell everybody the color of his hat. 2. If 1. is not allowed (and even talking is not allowed at all) Prisoner 10 can form 2 groups of prisoners with the same color. Every prisoner can see if he is in the same group as the prisoner standing in front of him. So he knows his color. Prisoner 1 says the color as his group members.

@charlesbromberick4247 2 жыл бұрын

Sounds like Schria Law to me. Thanks for the puzzles - i really like them.

@canale2303 3 жыл бұрын

I'd have answered differently. Prisoner 10 always says the hat's color of the prisoner 9. Prisoner 9 knows his hat's color. The agreed strategy is that each prisoner looks at the color of the prisoner in front of him and in case it is blu he SHOUTS his hat's color, otherwise it says it normally. So each prisoner knows his own hat's color just because of his partner's voice volume.

@bm-ub6zc 2 жыл бұрын

yeah i have the almost same solution (just with high pitched or low pitched voice, and with "next one has same/different color"), but in principle it's the same solution. the parity stuff is too difficult to figure out or memorize.

@mrgyani Жыл бұрын

You cannot give any kind of signal, be it with volume or whatever.

@matitiudeforever8155 6 жыл бұрын

that was the best riddle i've ever come across

@poornimanagaraju8534 7 жыл бұрын

Hey Amar..Awesome man!..Your passion towards puzzle has grown so much and it's spreading now!..Good to see you on youtube!..Nice explaination!

@LOGICALLYYOURS 7 жыл бұрын

Thanks Poornima... solved a lot.. now its time to teach to the world :) :) :P Must subscribe :)

@patrickjinks 5 жыл бұрын

I thought shout your own colour if the person in front is wearing a red hat and whisper it if they're wearing a blue one but only after listening to the answer, even though there's nothing against doing that, I feel I've let myself down

@GurpreetKaur-lp6cj 5 жыл бұрын

Patrick Jinks yeah I thought that too

@rgupta74211 3 жыл бұрын

Same

@index_s580 2 жыл бұрын

You gave a key tip to solving by precisely describing 10th person position.

@AmritEdits13 4 жыл бұрын

Your riddles are best than others It has a logic like your channels name

@dy4e02 5 жыл бұрын

The only way i up to that he should says the number of red he sees, And saying odd or even let the other hit the number while been asked, great job

@qc1okay 6 ай бұрын

Mr. Ammar, surprised you didn't first solve a case of just 4 or 5 prisoners, like you often do to show proof of concept, for viewers to catch on with. And I think if my life were on the line, I'd just be doing simple counting, not thinking about the concept of parity. "OK, so the first guy said "Red", so the other nine of us in front of him have an even number of red hats in total, and I see two reds in front of me, so I just have to listen to how many times the guys behind me say 'Red'." Then when it gets to be his turn, he thinks, "OK, so I've heard only one guy behind me say 'Red', so with one red behind me and two in front of me, that's three reds, so mine has to be red for there to be an even number of reds in front of the first guy. RED!"

@harnek.singh77 5 жыл бұрын

If they were tht smart thy won't be in prison 🤣🤣

@urbanarkoverland 5 жыл бұрын

Wouldn’t. Oh the irony.

@curious_one1156 5 жыл бұрын

What if they are political prisoners ?

@Aditya-yn5lk 4 жыл бұрын

Even wikileaks owner is in prison...lol

@joshmays7058 5 жыл бұрын

No way you get ten guys to do that correctly the first time!

@NK-fx1qs 3 жыл бұрын

nice thanks! these are fun to watch.

@mcger5624 7 ай бұрын

great - well done mate

@hyperfairy7779 7 жыл бұрын

do they get to keep the hats?

@lancerralseijoinedyourpart3633 6 жыл бұрын

i hope so xd

@rohitpawar4096 4 жыл бұрын

Noo

@timewalker2447 3 жыл бұрын

@priyanshuchaurasiya6184 4 жыл бұрын

Very typicall puzzle but also an exellent solution!

@tombratcher6938 3 жыл бұрын

I remember getting told this and thinking... " parity?... yep, works"

@kidsgameslearning 2 жыл бұрын

Nice. This logic will Work only if the total number of prisoners are even. If it is odd, difficult to solve. Because last prisoner can saw both Color ok odd number or even numbers. So difficult to give the clue to others.

@madhesh18 4 жыл бұрын

Terrific strategy

@anushams9828 6 жыл бұрын

Nice one🙂

@akhtar_Alee 5 жыл бұрын

I will see in reflexion of jailor's glasses

@nandhagopal8699 5 жыл бұрын

Amazing

@fomori2 3 жыл бұрын

Took about 3 minutes to figure out that the last guy in line will say "blue" if he sees an even number of blue hats, and "red" if he see an odd number of blue hats. This alerts the prisoners what the starting target count of hats is, even or odd. Each prisoner will count the number of blue hats and will know if his hat is blue, if the number of blue hats he sees is the opposite of the odd/even target count, or red, if the number of blue hats matches the odd/even target count. Whenever someone calls out blue the odd/even count target switches to the other. Zero is considered even.

@ottovaughnjr.9282 6 жыл бұрын

What type of jailor is that...?

@termin01 5 жыл бұрын

Amazing video bro

@uberfu 3 жыл бұрын

There's a flaw to the puzzle -- the puzzle assumes that the jailor will go in order of prisoners from back to front. Which is the only way this puzzle works. If the jailor calls out random prisoners or starts fromt eh front the entire puzzle fails.

@rajancherian4259 3 жыл бұрын

What if there are 0 red hats? Will it be seen as an even count? I think that calling out the color with an odd number of appearances is better. Cos even if red is 0, there will be 9 blue hats and vice versa.

@ammararfeen5644 5 жыл бұрын

My Naam is also ammar and your logic so clear and high I appreciate you for giving this knowledgful videos

@LOGICALLYYOURS 5 жыл бұрын

Good to know that ... Ammar :)

@basiliobastardo255 2 жыл бұрын

if the back prisoner can see in front and can pass message, why don't he just say the color of hat in front of him as a message?

@subhajitpal2407 2 жыл бұрын

Is this puzzle's logic actually comes in any real life implementation like in computer science concepts?

@ABCXYZ-zt3dr 3 жыл бұрын

I have easier approach to this : Last prisoner will tell second last prisoners hat color, if third last prisoner's hat color is equal to the second last prisoner's hat color then second last prisoner will tell his own hat color in louder voice otherwise in lower voice. From this third last prisoner will conclude his own hat color

@vichu8206 3 жыл бұрын

This dont need any calculations. Yes you are right

@mayukh_ 3 жыл бұрын

How does last prisoner would know his hat color?

@ABCXYZ-zt3dr 3 жыл бұрын

@@mayukh_ last prisoner can see second last prisoner's hat color

@jlugger 3 жыл бұрын

I got something similar and far easier than the original solution. Each prisoner says his hat color in either a loud voice or a soft voice. If his hat is the same as the prisoner in front of him he is soft and if it is different he is loud. EX: Prisoner sees P9 hat is blue. P10 guesses his own hat is blue so he says "blue" in a soft voice. P9 then knows his hat is blue. P9 sees P8 hat is red so he states "BLUE" in a loud voice. P8 knows his hat is different. This way 9-1 are correct and even if 10 was incorrect they all go free.

@mrgyani Жыл бұрын

Wow, this was brilliant.

@abhinavgupta7930 6 жыл бұрын

could not each prisoner just see their respective cap colours in jailors glasses.lol.XD

@mohammedzubair8618 7 жыл бұрын

very good logic. Good way of presenting. plz continue the same

@LOGICALLYYOURS 7 жыл бұрын

Thanks Zubair :)

@tigergaming7052 6 жыл бұрын

Who will arrange hat according to they calculation?

@bm-ub6zc 2 жыл бұрын

I have a much simpler solution: Prisoner 10: Says whatever color in front of him. Prisoner 9: Says the color said by prisoner 10, in a low pitched voice if the next one has the same color, and in a high pitched voice if the next one has a different color. And so on.

@saadmanahmed860 6 жыл бұрын

prisoners were really discerning... would i be in such a prison where gaoler makes redemption of prisoners such a logical way...!!!!

@pochyena555 6 жыл бұрын

I would not fancy the situation where there are only blue hats in front of him so the first prisoner would not know what to say (RED/BLUE) (Ofc. 0 is even but there are people who dont know that). Thanks for your content, great job ;-)

@LOGICALLYYOURS 6 жыл бұрын

Thanks Pochyena :)

@bosskiang4238 4 жыл бұрын

He/She can argue that since there are no red hats in front of him/her, his/her hat can't be red because red indicates even parity and if there is 0 red hat in front of me, his/hers can't be a red hat since that would make it odd.

@SAIMRIAZ 5 жыл бұрын

Nice

@hsingh-13 3 жыл бұрын

Wow! 👍

@ShanmukhaPulavarthy 9 ай бұрын

Here's how the logic works: If there are an even number of red hats in front of the counter, the guessers can deduce the color of their hat by counting the number of red hats they see. If the count of red hats among the first 9 prisoners (excluding the counter) is even, then the color of their own hat must be blue. If it's odd, their own hat must be red. If there are an odd number of red hats in front of the counter, the guessers can similarly deduce the color of their hat. This strategy ensures that the counter can make a correct guess based on the parity (odd or even) of the red hats in front of him, and the guessers can correctly infer their hat color based on the counter's response. This way, at least 9 prisoners will survive, and they will all be released.

@becalmandquiet881 3 жыл бұрын

Great video

@michaelbauers8800 4 жыл бұрын

I love hat puzzles

@aldenasuemia 2 жыл бұрын

Wow this is what I call genius.

@ajaykumargupta8504 4 жыл бұрын

Awesome 👌

@prashantkumargupta4996 6 жыл бұрын

elegant explanation.

@LOGICALLYYOURS 6 жыл бұрын

Thanks Prashant :)

@unbrokenriven1455 3 жыл бұрын

so how do you solve for the same problem but there are 3 different color hats?

@aashishkohli2387 4 жыл бұрын

Man fuck it this is hamming code 😬😬im so excited !! there not a better explanation of this thing thanks ammar

@sharukhshaik7476 4 жыл бұрын

As a digital design engineer, I have an idea to design a digital circuit using XOR gates, a Comparator, and Multiplexer for this problem 😉

@mythologygeek8888 3 жыл бұрын

Can u share??

@V7B817 2 жыл бұрын

Finally got the answer by odd/even logic 10th person would have said that I will told you the colour of the hat which is in odd number

@dreamstory979 2 жыл бұрын

Amar I have question if there are only 2 red cap then how it possible

@swapniljain2464 5 жыл бұрын

Awesome

@balajik8688 2 жыл бұрын

Y do they releasing the prisoners so freely..it's not even Gandhi jayanthi now 😂

@LaughterPlanet-mu1yp Жыл бұрын

There is another simplest way, prisonor 10 will say colour of 9th hat... Now 9th know the color of his hat, so if the color of his next is same as him he will answer his hat color within 1 second or if the color of his next hat is different he will answer his hat colour in 5 seconds.. So this 1 or 5 second time interwal will give hint to the next prisnor and so on... As we know that 10th prisonor will be release even if he is incorrect so in this way all of them will be released.

@arnabpersonal6729 5 жыл бұрын

Real genius

@shubham2927 2 жыл бұрын

wONDERFUL eXPLANATION sER

@SS-cr8hb 5 жыл бұрын

Very nice puzzle sir .According to me if the 10th prisoner speaks the colour of hat which is more in number among the 9(odd no.) hats infront of him, then also each prisoner would know his hat colour keeping in mind possible combinations of hats- 5,4 6,3 ....

@LOGICALLYYOURS 5 жыл бұрын

Dear SS.... nice to see that you tried to come up with a different approach(max), but it has limitation.... assume that only the first prisoner(front) and 9th prisoner are wearing Red Hat. Now, the prisoner 10 will call out "BLUE" (because they are more in number). But what would the 9th prisoner call out ?? For him still, majority is BLUE, but he can't decide what he is wearing. So, eventually an Even-Odd approach can get at least 9 correct answers.

@SS-cr8hb 5 жыл бұрын

You are right sir. Thank you so much for the explanation.

@CarlEmilKjellstrand 3 жыл бұрын

Checksums are the best :)

@shreyamaurya6410 5 жыл бұрын

Gr8

@vikashtiwari5505 6 жыл бұрын

Brilliant

@LOGICALLYYOURS 6 жыл бұрын

Thanks Vikash :)

@YatharthSharma 4 жыл бұрын

Kaaliya from SHOLE movie after watching this video "bhaiya ye trick hame bhi bta dete us bhosdiwale sardar gabbar singh se ham bhi bach jate" 😄😄😄

@rnegoro1 5 жыл бұрын

You can actually work it from the odd numbers too at the beginning instead of even.

@rajivpokharel88 3 жыл бұрын

didnt understand one bit...but enjoyed it anyways...xD

@murugankaruppaiah9537 4 жыл бұрын

I think they are studied in oxford university

@25_karansingh36 2 жыл бұрын

Is he Michael Scofield 😂

@haribattula5187 4 жыл бұрын

Do the front prisoner listens to answer told by back prisoner..and if he listens what if all hats are blue or red and only one blue or one black

@himanshusingh5056 3 жыл бұрын

Prisoners with calculus like idea's

@aryanrawat5961 2 жыл бұрын

Simplest tareeka: peeche wala apne aage wale ko bata de usne kaunsi pehni hai. Bas ho jaayega sab

@lovefor011 5 жыл бұрын

so here I am assuming that prisoners knows that the blue and red hats are in even or odd numbers..

@alencarfardin6650 4 жыл бұрын

Wait, the prisoners 1 to 4 are just kids...

@---4690 3 жыл бұрын

Lol 😂😂

@sabeenavahid8733 5 жыл бұрын

this was awesome

@abcdefgabcdefg3017 Жыл бұрын

Why should they even do that. Except the last one , everyone can know their colour from the previous person . Only the last person has to apply the given strategy to guess his own colour.

@bishnunepali3018 4 жыл бұрын

nice...

@sorsocksfake Жыл бұрын

Prisoner 10 will count whether the red hats are even or odd. If even, he says blue; if odd, he says red. Thus the other prisoners know whether the first 9 *including them* are an odd or even number. They can also see the prisoners in front of them, and have heard the ones behind them. So they know whether the first 9 *except themselves* is an odd or even number. If the two match, then their own hat must be blue. If they do not match, it's because their own hat is red. They speak accordingly.

@nenaramchoudhary998 3 жыл бұрын

If they can build such a strategy, then how they caught and put up in jail....

@abridgetool 3 жыл бұрын

They didn't commit the crime in the group. United they are intelligent, divided they are dumb.

@hxong4733 5 жыл бұрын

Genius

@mikael900 5 жыл бұрын

I got thrown off because you said only the last prisoner would be allowed to answer incorrectly but the first one would be hanged if he was wrong. Then at the end you said 9/10 were right so they were all let go.