So if I understand this correctly, once the prisoners start opening boxes, there is no communication allowed between them, right?
Correct, and after each prisoner goes, the boxes are restored to their original state.
Puzzle HN: 100 prisoners, 100 boxes...
21–30 of 59 posts
Re: Puzzle HN: 100 prisoners, 100 boxes...
#22Found the solution here: http://www.sciencenews.org/view/generic/id/7649/title/Puzzli... http://ocfnash.wordpress.com/2009/12/12/pity-the-prisoners/ Warning: Don't spend hours of lateral thinking trying to solve this puzzle unless you have a degree in mathematics.
Assume the prisoners do not have access to the internet.
Re: Puzzle HN: 100 prisoners, 100 boxes...
#23The first prisoner opens 50 and sorts the 50 in alphabetical order (in an obvious manner). The second prisoner, upon seeing the sort, can quickly see if his name was in the original 50 (My name is Evan, I should be before Henry and after Bobby, etc). If he finds it quickly, he has plenty of "openings" to help sort the remaining boxes (maybe in a second row behind the first). The rest of the prisoners should be able t…
So how does this gel with "They cannot move the paper around between boxes"?
Re: Puzzle HN: 100 prisoners, 100 boxes...
#24Found the solution here: http://www.sciencenews.org/view/generic/id/7649/title/Puzzli... http://ocfnash.wordpress.com/2009/12/12/pity-the-prisoners/ Warning: Don't spend hours of lateral thinking trying to solve this puzzle unless you have a degree in mathematics.
Thanks for spoiling the fun for everyone. 8-(
Re: Puzzle HN: 100 prisoners, 100 boxes...
#25Found the solution here: http://www.sciencenews.org/view/generic/id/7649/title/Puzzli... http://ocfnash.wordpress.com/2009/12/12/pity-the-prisoners/ Warning: Don't spend hours of lateral thinking trying to solve this puzzle unless you have a degree in mathematics.
You don't need math skills to solve this, only problem solving skills. There are only so many ways to systematically choose 50 boxes from 100 when the only information is a name on the inside and a number on the outside.
Re: Puzzle HN: 100 prisoners, 100 boxes...
#26Found the solution here: http://www.sciencenews.org/view/generic/id/7649/title/Puzzli... http://ocfnash.wordpress.com/2009/12/12/pity-the-prisoners/ Warning: Don't spend hours of lateral thinking trying to solve this puzzle unless you have a degree in mathematics.
You don't need math skills to solve this, only problem solving skills. There are only so many ways to systematically choose 50 boxes from 100 when the only information is a name on the inside and a number on the outside.
I'm just trying to help people that might spend an hour looking for a simple kind of solution to this, when the answer is really quite complicated and the math involved in the linked solutions are way beyond the understanding of most non-mathematicians.
Re: Puzzle HN: 100 prisoners, 100 boxes...
#27Found the solution here: http://www.sciencenews.org/view/generic/id/7649/title/Puzzli... http://ocfnash.wordpress.com/2009/12/12/pity-the-prisoners/ Warning: Don't spend hours of lateral thinking trying to solve this puzzle unless you have a degree in mathematics.
Just because the explanations you've found use mathematical terminology, that doesn't mean you need a degree in math to understand the solution if it's explained properly.
Re: Puzzle HN: 100 prisoners, 100 boxes...
#28Earlier quoted context omitted.
You don't need math skills to solve this, only problem solving skills. There are only so many ways to systematically choose 50 boxes from 100 when the only information is a name on the inside and a number on the outside.
I'm just trying to help people that might spend an hour looking for a simple kind of solution to this, when the answer is really quite complicated and the math involved in the linked solutions are way beyond the understanding of most non-mathematicians.
I've explained it to many non-mathematicians, and they certainly seemed to have understood.
Re: Puzzle HN: 100 prisoners, 100 boxes...
#29So if I understand this correctly, once the prisoners start opening boxes, there is no communication allowed between them, right?
Correct, and after each prisoner goes, the boxes are restored to their original state.
I'm going to post my current thinking on this, in the hopes that maybe someone can give me a hint without revealing the whole solution:
It seems to me that the best that the prisoners can do is 1/2^50 (and the worst they can do is 0). For instance, if the prisoners decided that everyone would just open boxes 1-50, then they would have zero chance of finding all 100 names (since 50 of the boxes would never even be opened). It seems like the best they can do to maximize their chances is to make sure that each box is tried exactly 50 times. One way to do that is to divide the prisoners into two groups of 50, then assign the first group to boxes 1-50 and the second group to boxes 51-100. Then the chances that the first group all find their names is 1/2^50 (not 100% sure about this number, but it seems reasonable) - and if the first group all find their names, then the second group will too (since if all 50 in the first group were found in boxes 1-50, then all 50 in the second group must be in boxes 51-100). So the total probability of success is 1/2^50.
What's wrong with this?
Re: Puzzle HN: 100 prisoners, 100 boxes...
#30Earlier quoted context omitted.
I'm just trying to help people that might spend an hour looking for a simple kind of solution to this, when the answer is really quite complicated and the math involved in the linked solutions are way beyond the understanding of most non-mathematicians.
I've explained it to many non-mathematicians, and they certainly seemed to have understood.
Even the first solution linked to doesn't explain it. It only declares the result that the probabilities work out in a particular way.
The second link contains the math, and no way would a non-mathematician have been able to come up with that math.