Logic Puzzles

[Kit-]

New thread because I have no idea where to find the old one, and I couldn't be bothered to search for it and bump it.

1. If you knew the answer beforehand, please don't spoil it for the rest of us.
2. Don't Google for answers, that defeats the whole purpose.
3. Don't bother with repost reposts like "Why did the man shoot himself after drinking repost soup?"

That being said, I'll kick it off with a really hard one. I don't think I've seen this anywhere else. It took me two hours to figure it out with a fairly big hint.

prty heug hint: Has something to do with a topic covered in group theory.

There are 100 people in prison with ID numbers from 1-100, and the warden makes them a proposal. There is a room with 100 boxes in a line, each with one of their ID numbers inside, and each person is allowed to open up to 50 boxes. If they can each find their own number within these 50 guesses, they're all set free. However, if even one person fails, they all die. They are only allowed to speak to each other beforehand; no information transfer takes place at any time after. So, for example, you can't tell the next person in line that his box is the 27th one by coming out after 27 minutes have passed, even though no actual speaking is involved. The room is reset to its original state after each person exits. What is the only strategy with at least a 30% success rate given an equal probability of any configuration?

[sammo123]

Re: Logic Puzzles

Everyone takes the numbers out of the box and puts them in there pocket then wehn they all get out of the room they switch to get the right id's then theyy win

or

they all decide not to go in there for never having the challenge of finding there number so technically never lose for never tryi9ng and they stay in jail and dont die

[Kit-]

Re: Logic Puzzles

Everyone takes the numbers out of the box and puts them in there pocket then wehn they all get out of the room they switch to get the right id's then theyy win

The room is reset to its original state after each person exits.

or

they all decide not to go in there for never having the challenge of finding there number so technically never lose for never tryi9ng and they stay in jail and dont die

What is the only strategy with at least a 30% success rate given an equal probability of any configuration?

PS: The solution is really elegant and cool.

[Risking]

Re: Logic Puzzles

100 people give 3 people 33(one with 34) ID numbers; That way, they have a 100% chance of not failing.

[Kit-]

Re: Logic Puzzles

100 people give 3 people 33(one with 34) ID numbers; That way, they have a 100% chance of not failing.

ID numbers are nontransferable.

[Doug31]

Re: Logic Puzzles

I don't really understand, is only one person in the room at a time, or are they all there?

[Kit-]

Re: Logic Puzzles

One at a time. One person allowed at a time. When they come out, they're sequestered and can't do anything else except hope other people don't mess up.

[TheRapingDragon]

Re: Logic Puzzles

I don't really understand, is only one person in the room at a time, or are they all there?

One at a time. Each person gets 50 attempts (with 100 boxes) to get their number. Each of the 100 prisoners has to do this in turn.

[Doug31]

Re: Logic Puzzles

Then unless they're something you're still not telling us, or there's something hidden extremely deep within the meaning of those words, then it can't be done.

[Kit-]

Re: Logic Puzzles

Oh no, it's very possible. There are no hidden meanings, twists, or tricks hidden in the problem. It means exactly what you think it means.

[thecheat372]

Re: Logic Puzzles

the first guy checks box 1-50
the second checks 2-51
the third 3-52
and so on...

[Doug31]

Re: Logic Puzzles

If you do it like that, then each person has a 1/2 chance and it all comes out to a (1/2)^100 chance just like any other possible way, the way I see it.

[Kit-]

Re: Logic Puzzles

the first guy checks box 1-50
the second checks 2-51
the third 3-52
and so on...

1 has a 50% chance of being in 1-50
If it is, then:
2% chance that 1 was in 1, in which case there is a 50/99 chance that 2 is in 2-51
98% chance that 1 was in 2-49, in which case there is a 49/99 chance that 2 is in 2-51.
.02*50/99+.98*49/99=49.52% chance that 2 is in 2-51.
50*49.52% = 24.76% < 30% for just the first two inmates.

If you do it like that, then each person has a 1/2 chance and it all comes out to a (1/2)^100 chance just like any other possible way, the way I see it.

As much sense as this seems to make, there is a method that can get over a 30% success rate. Read the hint.

[Doug31]

Re: Logic Puzzles

No, that's wrong from the way I understood it, since I thought it returned to its original state, which would have meant #2 still would have had to check a box even if someone else had already found theirs. Now I think I know how to do this...I'll type it up in a sec.

Edit: Ok, person 1 checks box 1, then person 2 checks box 2...all the way to person 100 checks box 100. Now, they should each have 49 left, and there should be 99 boxes left, on average. Now they repeat it again, and they should have 48 left except for one person with 49, and 98 boxes left, and just keep repeating that until they get to the end.

[Kit-]

Re: Logic Puzzles

No, that's wrong from the way I understood it, since I thought it returned to its original state, which would have meant #2 still would have had to check a box even if someone else had already found theirs. Now I think I know how to do this...I'll type it up in a sec.

Yes, but person 2 knows that he hasn't died yet, hopefully, meaning that he knows that 1 is somewhere in the range 1-50, which in turn means that it has a 2% chance of being in 1, and a 98% chance of being in 2-50.

Edit: Ok, person 1 checks box 1, then person 2 checks box 2...all the way to person 100 checks box 100. Now, they should each have 49 left, and there should be 99 boxes left, on average. Now they repeat it again, and they should have 48 left except for one person with 49, and 98 boxes left, and just keep repeating that until they get to the end.

They only get to go in once. Then they go off to the side and hope their fellow inmates don't screw them over. Also, it wouldn't help. The boxes aren't removed when they're gone, and they transfer information to each other once they start checking boxes.