100 Doors Puzzle Hard Puzzle for Genius minds
video description
But then each factor p2-n2 is a perfect square, and as any product of perfect squares is also a perfect square, the condition for an open door is that N should be a perfect square.
The approach in the video using matching of divisors is simpler than mine, and also very intuitive: -.
Date: 2023-11-15
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Comments and reviews: 21
Sankhya_0
haven't looked at the video but the answer has something to do with a number of factor as 2-p. 3-q. 5-r. is the prime factorization of a number then it has (p+1(q+1(r+1) factors. But this will yield the factors as even and even number of factors means the door will be closed. The only way that they remain open is if they are squares as they are the only numbers with odd no of divisors. JEE aspirants should've done this during P&C and this question should be a piece of cake
Yes I was right.
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haven't looked at the video but the answer has something to do with a number of factor as 2-p. 3-q. 5-r. is the prime factorization of a number then it has (p+1(q+1(r+1) factors. But this will yield the factors as even and even number of factors means the door will be closed. The only way that they remain open is if they are squares as they are the only numbers with odd no of divisors. JEE aspirants should've done this during P&C and this question should be a piece of cake
Yes I was right.
reply
sorsocksfake
Only the perfect square doors will remain open: 1, 4, 9, 16, 25, 36, 49. 64, 81 and 100.
The reason is that whenever you can do the division, it gives you one of the other numbers. A prime will always have only two passages: itself and 1. This is a pair. Others, such as 6, have more pairs (2&3. But all of these pairs cancel out. The only way therefore to keep a door open, is with a divisor that doesn't create a pair: namely, if the divisor results in itself, i. e. is a squareroot.
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Only the perfect square doors will remain open: 1, 4, 9, 16, 25, 36, 49. 64, 81 and 100.
The reason is that whenever you can do the division, it gives you one of the other numbers. A prime will always have only two passages: itself and 1. This is a pair. Others, such as 6, have more pairs (2&3. But all of these pairs cancel out. The only way therefore to keep a door open, is with a divisor that doesn't create a pair: namely, if the divisor results in itself, i. e. is a squareroot.
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Christian
Made a table of door vs walk. Used 1s and 0s to signify open and closed. There was a diagonal pattern 100 10000 1000000. The difference between Every door number with the last zero went up by 2 every time. Door 99 was one of them so 100 must have been 1 (open. His way was better -
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Made a table of door vs walk. Used 1s and 0s to signify open and closed. There was a diagonal pattern 100 10000 1000000. The difference between Every door number with the last zero went up by 2 every time. Door 99 was one of them so 100 must have been 1 (open. His way was better -
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20JE0533
i just alnayzed this question with 10 door, then i analyze it for 20, i got 1, 4, 16 are opened, i immediately said all perfect square no. door will remain open, analyzing with small no. makes any question easy
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i just alnayzed this question with 10 door, then i analyze it for 20, i got 1, 4, 16 are opened, i immediately said all perfect square no. door will remain open, analyzing with small no. makes any question easy
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Bikky
in order to make such (easy to understand) animations, how much creativity and effort it would have taken i can understand, and i found whatever i was seeking for thanku for easy explanation
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in order to make such (easy to understand) animations, how much creativity and effort it would have taken i can understand, and i found whatever i was seeking for thanku for easy explanation
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Subodh
Good visual explaination.
I found the solution by programming and surprised to find that it's the square.
Which highlights the importance of correct thinking over computer program
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Good visual explaination.
I found the solution by programming and surprised to find that it's the square.
Which highlights the importance of correct thinking over computer program
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Dollcy
Amazing. Love the explanation, seemed so simple in the end, yet would have never analyzed it in that way. Thank you for making this video and giving the amazing explanation!
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Amazing. Love the explanation, seemed so simple in the end, yet would have never analyzed it in that way. Thank you for making this video and giving the amazing explanation!
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girlnado
Kinda proud of myself on this one. I usually suck at these problems but I was able to work through it on my own, find the patterns, and get the right result. Very fun!
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Kinda proud of myself on this one. I usually suck at these problems but I was able to work through it on my own, find the patterns, and get the right result. Very fun!
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hocaponttas
It took me like two hours and I still solved it partly wrong. - My answer was 1, 4, 9, 12, 25, 30, 60, 64, 80, 81, 84, 90 and 100. I'm not sure what happened
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It took me like two hours and I still solved it partly wrong. - My answer was 1, 4, 9, 12, 25, 30, 60, 64, 80, 81, 84, 90 and 100. I'm not sure what happened
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Khatune
What will happen to the prime numbers that were never closed after opening when multiplied by 1. if consider them then result will be 45 doors will stay open.
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What will happen to the prime numbers that were never closed after opening when multiplied by 1. if consider them then result will be 45 doors will stay open.
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Not
I seriously and totally respect you effort. and very MUCH thanks to you for giving these kinds of riddles and also for making its solution easy to understand --
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I seriously and totally respect you effort. and very MUCH thanks to you for giving these kinds of riddles and also for making its solution easy to understand --
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Ryan
I-m so sorry but I just said -none- because they all started closed and could only remain closed thinking of it in terms of remaining from start to finish
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I-m so sorry but I just said -none- because they all started closed and could only remain closed thinking of it in terms of remaining from start to finish
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Ashutosh
Here is a Simple CPP code:
#include -
using namespace std; -
int main)-
--
-vector doors (101, false); -
-for(int i=1; i
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Here is a Simple CPP code:
#include -
using namespace std; -
int main)-
--
-vector doors (101, false); -
-for(int i=1; i
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Rakshit
i saw it on gfg and i was unable to process whats behind the logic but your animation and moreover explanation method helped me to get it
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i saw it on gfg and i was unable to process whats behind the logic but your animation and moreover explanation method helped me to get it
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Dilip
What happens to, for example, door no 51? 1, 3 and 17 are the factors. So this door will remain open. As per your dolution, it is not so.
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What happens to, for example, door no 51? 1, 3 and 17 are the factors. So this door will remain open. As per your dolution, it is not so.
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Unformed
It seems hard at first glance, but when I wrote down factors for several numbers I quickly got the pattern. It was easy one actually.
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It seems hard at first glance, but when I wrote down factors for several numbers I quickly got the pattern. It was easy one actually.
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arc
This one is very difficult for those who did not learn permutations and combinations in 11th(or maybe its long time no see for some.
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This one is very difficult for those who did not learn permutations and combinations in 11th(or maybe its long time no see for some.
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Utpal
More than the puzzle I applaud you for the effort you put in making the graphics and explaining in the simplest terms.
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More than the puzzle I applaud you for the effort you put in making the graphics and explaining in the simplest terms.
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Mechalysis
gr8 explanation. really appreciate your effort. in this 6. 29 min video, I learn lot of concepts, Thanks
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gr8 explanation. really appreciate your effort. in this 6. 29 min video, I learn lot of concepts, Thanks
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education
I actually thought the same and it's based on factors theorem of class 11th permutation and combination
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I actually thought the same and it's based on factors theorem of class 11th permutation and combination
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Rohan
it square numbers, repeated factor so they have an odd number of unique factors, and will remain open
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it square numbers, repeated factor so they have an odd number of unique factors, and will remain open
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