Escape from Prison Puzzle

[dsvick]

Do the prisoners know in what order the other prisoners, and colors, were added?

[omk3]

Okay, just thinking aloud, so you're safe to click it:

Spoiler:

I'm thinking it must be a combination of probabilities and games theory. Which means that the fact that no one got away yet is a clue in itself.

What is the probability of each person being either blue or green? As it is random, I would have thought it's 50%. But in actual fact, it's 55% for blue, 45% for green. Is it because the numbers are relatively small, or is this the actual probability of each colour?

I tried to think by starting small. So you are inside the prison and the only other person is blue. What do you think about yourself? When one more comes along, how does the probability change? Not sure.

We have two groups of people with different views. Greens all see the same things as each other, so what one green does, every green does, as they are all so bright and clever. Same goes for blues. I'm not yet sure if the 100th person is in a different category or not. I feel he must be, but can't yet explain it.

Now there is a speech in both versions, that seems to reveal nothing new. But it must reveal something. Facts: there are greens and there are blues, you are 100, it's afternoon. Nothing new, right? Did the 100th person come before noon? So is the fact that no one left yet significant?

There is a question about when someone will get out. So I'm guessing there must be a test period, like wait one day, and when no one does something, you deduce something. All too general to help anyone, but well....

See? Not really a spoiler at all, just random thoughts that probably add nothing.

[poohbear_nc]

Originally Posted by omk3

Okay, just thinking aloud, so you're safe to click it:

Spoiler:

I'm thinking it must be a combination of probabilities and games theory. Which means that the fact that no one got away yet is a clue in itself.

What is the probability of each person being either blue or green? As it is random, I would have thought it's 50%. But in actual fact, it's 55% for blue, 45% for green. Is it because the numbers are relatively small, or is this the actual probability of each colour?

I tried to think by starting small. So you are inside the prison and the only other person is blue. What do you think about yourself? When one more comes along, how does the probability change? Not sure.

We have two groups of people with different views. Greens all see the same things as each other, so what one green does, every green does, as they are all so bright and clever. Same goes for blues. I'm not yet sure if the 100th person is in a different category or not. I feel he must be, but can't yet explain it.

Now there is a speech in both versions, that seems to reveal nothing new. But it must reveal something. Facts: there are greens and there are blues, you are 100, it's afternoon. Nothing new, right? Did the 100th person come before noon? So is the fact that no one left yet significant?

There is a question about when someone will get out. So I'm guessing there must be a test period, like wait one day, and when no one does something, you deduce something. All too general to help anyone, but well....

See? Not really a spoiler at all, just random thoughts that probably add nothing.

This puzzle is making your antennae point in different directions!!!

[dreams]

Oh wow, this one is a good one, pdurrant. Although, if it requires some kind of algebraic equation to set up and solve, I'm not sure I'll be able to figure out which one and actually do it.

I must give this some more thought.

[MJK2111]

I'm guessing that "get a razor blade, slice off a tiny bit of your forehead, and look at the color" is not a viable answer?

[omk3]

Originally Posted by poohbear_nc

This puzzle is making your antennae point in different directions!!!

I know!

So, people, any other thoughts? Even silly like mine? Come on! We have to all work together for a successful prison break

[dsvick]

Originally Posted by omk3

I know!

So, people, any other thoughts? Even silly like mine? Come on! We have to all work together for a successful prison break

Spoiler:

I was thinking along the lines of if they knew the order in which they arrived then knowing that were two colors represented at the time of the governors speech, then they could back track and the first person that only saw a single other color would know that he has the opposite color.

Or something like that, I'm not sure it holds water though...

[dreams]

OK, dsvick, before I click your spoiler (and by the way I can't quote it as it will show what is under it), it is a thinking about the problem clue or a partial solution?

[omk3]

The spoiler in post #13 is harmless, dreams. It's just to help you thinking. Hasn't helped me yet...

Oh, sorry. Dsvick's harmless too. Just a thought. Maybe an interesting one, but I'm not sure yet. I'm too easily confused today.

[dreams]

Thanks, omk3. I like to try these even though some are way over my head. I'll be off to work soon and will have to check back and keep trying when I get home tonight.

Good luck, these puzzles are fun to try and watch everyone's comments too.

[pdurrant]

Originally Posted by dsvick

Do the prisoners know in what order the other prisoners, and colors, were added?

Well, the first prisoner in knows of course. And the second prisoner. The third prisoner to enter the jail just knows that the first two were there before him, although they might have told him which of them was there first. Etc.

So at least two of the prisoners know the order. I don't think this knowledge helps them or you.

[pdurrant]

Originally Posted by omk3

Okay, just thinking aloud, so you're safe to click it:

I'll address some of your thoughts, just the clarify things that might not have been perfectly clear in the problem statement.

(i) the 45/55 split is just random chance. The problem still works with any similar numbers, e.g. 35/65, 50/50, 51/49, etc. The exact answer might be a little different though.

(ii) probability arguments won't help. The prisoner can't be 99% or 99.9% or even 99.99999% certain. The prisoner must be able to prove that they know their ink colour by a process of logical deduction.

[pdurrant]

Originally Posted by MJK2111

I'm guessing that "get a razor blade, slice off a tiny bit of your forehead, and look at the color" is not a viable answer?

Yes, that's not the kind of solution we (or the prisoners) are looking for.

[omk3]

Thanks! Probabilities out of the way is actually a relief...

[poohbear_nc]

Start digging the tunnel! No solution in sight!