Another puzzle thread. Is this one too hard to solve?

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My group loves puzzles. The more difficult, the better. As long as it makes sense, that is. I need help with two things. First, I wanted to know how hard this nut is to crack. Secondly, I don't know how to make it DnD-compatible.

Here goes:



  • A hundred men and women sit in a circle in a locked room.

  • They are all highly intelligent and have a perfect sense of logic, and they also know everone else is equally intelligent and logical.

  • They are all part of an experiment. Before they got here, they were told that at least one of them had a red mark on his/her forehead.

  • They can't see whether they bear the red mark themselves, but they can see whether or not the others do.

  • They are not allowed to communicate in any way. Speech, body language, it's all strictly prohibited.

  • The lights in the room switch on and off in intervals.

  • When the lights are off, they are allowed to leave, but only if they KNOW they bear the red mark.

  • Everyone bears the red mark.

  • This puzzle has a perfectly logical solution.


How does this pan out and why?

EDIT: Please tell me if anything needs to be clarified.

EDIT AGAIN: I just realized this puzzle is almost impossible to implement in a DnD setting. Shouuld I remove the thread? 
It could always be a verbal question by an NPC gatekeeper or whatever.

Anyway, I think they would all leave. They're not allowed to communicate, but they're obviously allowed to look at each other. Every person can see every other person has a red mark, so they know that, at most, they're the only person who doesn't. They're intelligent enough to realise that, being the odd one out, the other people would naturally glance in their direction more often if they stood out. Since nobody will be paying any more attention to them than the others, they'll reason they are just as interesting, and thus they must also have the mark.
It could always be a verbal question by an NPC gatekeeper or whatever.

Anyway, I think they would all leave. They're not allowed to communicate, but they're obviously allowed to look at each other. Every person can see every other person has a red mark, so they know that, at most, they're the only person who doesn't. They're intelligent enough to realise that, being the odd one out, the other people would naturally glance in their direction more often if they stood out. Since nobody will be paying any more attention to them than the others, they'll reason they are just as interesting, and thus they must also have the mark.



I like the answer, but it's not the right one. They have to KNOW that they bear the red mark and they really don't. Also, assume the only information they can process(since no communication is allowed, eye movement included) is the red marks or the absence of them and how many (if any) people leaving the room each time the light goes back on again.

I would like to make clear that the lights are turned  off, then on, then off, then on, off, and so on forever. 
If no communication is allowed, then they can't know they wear the red mark. So everyone stays put forever.

Having said that, the puzzle says they can't see their own mark. It's possible they knew ahead of time if they had it or not. If so, everyone leaves when the lights are first turned off.
I don't agree looking at things is communication(they have to gather info someway, after all, and the glancing at 1 guy more often is an involuntary reaction, not an attempt at communication ^^), but so we're assuming they're all wearing sunglasses, fair enough.

Anyway, if a logical deduction isn't counted as "knowing", then they can never leave, because they will never have anything more than that to go on. Seeing 99 red dots doesn't let you know anything, and since all that the 100 contestants can do is see 99 red dots, none of them will ever try to leave, which doesn't tell the other 99 people anything at all.

If this is a play on the classic "3 wise pupils with red or blue dots" riddle, then I'm afraid it may be missing something :p
- Have the participants agreed or been otherwise compelled to play this game by the rules?

- Have the officially accepted methods of acquiring knowledge been explained to and understood by the participants?  If so, what are they?

- Were the participants aware of the application of the red marks to their heads?      

- Are the doors unlocked when the lights are out, or are all of the other details supplied to misdirect attention from the fact that the doors are locked?    
"When Friday comes, we'll all call rats fish." D&D Outsider
- Have the participants agreed or been otherwise compelled to play this game by the rules?

- Have the officially accepted methods of acquiring knowledge been explained to and understood by the participants?  If so, what are they?

- Were the participants aware of the application of the red marks to their heads?      

- Are the doors unlocked when the lights are out, or are all of the other details supplied to misdirect attention from the fact that the doors are locked?    



1. and 2. The participants are like robots, they are perfectly logical and play by the rules no matter what.

3. No, they were  not aware. The only thing they do know is that there is at least one red mark in the room. They also know what they see, that all the others have the red mark.

4. No, the solution to this logic puzzle is perfectly logical. When I tell you the answer, you will probably get an aha-experience. Seriously though.

 Here's a hint, or... I have said this before:

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There's a reason I told you they know there is at least one red mark in the room.


Another one:

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They are all in the same situation. WHatever happens, they get exactly the same information every time the lights go off and on again.
 
The only thing I can figure is that they know they have the mark, because they were told there was one mark present before they arrived, and seeing as the people who told them didn't have a mark, that means they have one.
I don't agree looking at things is communication(they have to gather info someway, after all, and the glancing at 1 guy more often is an involuntary reaction, not an attempt at communication ^^), but so we're assuming they're all wearing sunglasses, fair enough.

Anyway, if a logical deduction isn't counted as "knowing", then they can never leave, because they will never have anything more than that to go on. Seeing 99 red dots doesn't let you know anything, and since all that the 100 contestants can do is see 99 red dots, none of them will ever try to leave, which doesn't tell the other 99 people anything at all.

If this is a play on the classic "3 wise pupils with red or blue dots" riddle, then I'm afraid it may be missing something :p



Logical deduction is counted as knowing. They are equally intelligent. I should probably had made that clear. I'll edit now.

The "3 wise pupils with red or blue dots"- riddle is similar to this one, but I think this one is a lot more difficult though.
I saw this on Khan Academy and really enjoyed it. If you head over to that website, Khan does a pretty good job explaining the solution, it's very interesting. That said, I think it's a very difficult puzzle, specially to be solved during an RPG session! That really depends on your group, you say they love tough puzzles, but I personally can't see this working with any of the players I know!

The best hint you can give (and the one that made me solve the puzzle) is:

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Try to solve for smaller numbers of people. What would happen if (mantaining all the rules) there was only 1 person in the room? What if 2? What if 3? If you solve these then 100 will be easy.


 
Sorry for double posting, but as for how to make the puzzle D&D compatible:

Have the PCs be inside the puzzle, among the logical people. Maybe it's an intelligence test for a circle of wizards. Perhaps the PCs are infiltrating a cult or organization and have to be perfectly logical and solve the puzzle to mimic everybody else in order to remain undiscovered. So, if they were supposed to leave and don't leave, they're busted. 

Perhaps they can communicate with each other but can't tell each other the colors of their foreheads (this would at least help them find the solution cooperatively). It will be interesting if the players know their PCs can see each others red marked foreheads but cannot communicate that in character, and have to deduce how to act anyway. Then when the lights go out, they have to decide if they'll leave or not without seeing what the other people will do. Maybe some players will get it right while others won't.

Like I said in the previous post, to make the puzzle more manageable, start with the 1 person case (1 PC alone in a room. does he leave?), then a PCs and a logical person (do they leave?). Then the PCs + many intelligent people totalling 100.

 
Cool. My father gave the puzzle to me. I think I used one and a half hour before I solved it. Thanks for your ideas as to how to implement this into my campaign.

Another useful hint:

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You get information each time the lights are turned off and on.
 
I know the answer to the puzzle because I have seen it with three or five individuals, and I can see how it would scale up to 100.  

It can be kind of tricky if you haven't seen something like it before and most people are not logical enough to work it through carefully.  If your group really likes tough puzzles, it's a good one, but if they are easily frustrated by this sort of thing be willing to give them some help or substitute some kind of skill challenge if you don't want things to drag out too long.
I heard that they are making a new video game, where you control the Netherese flying citadel of Sakkors, raining death on your helpless enemies below. Working title: Mythal Command.
The puzzle is interesting (I don't like these logic puzzles, but I can imagine it's interesting for puzzle fanatics), but your hints aren't going to help your players if they don't figure it out. What helped me was the insight that you should ask yourself what each person is thinking when they are looking at others. That helped me realize that they will imagine 2 scenario's: either they have a red mark, or they don't. 

Oh, and the hint that they should consider the same puzzle with 1, 2, 3 and 4 people.
The puzzle is interesting (I don't like these logic puzzles, but I can imagine it's interesting for puzzle fanatics), but your hints aren't going to help your players if they don't figure it out. What helped me was the insight that you should ask yourself what each person is thinking when they are looking at others. That helped me realize that they will imagine 2 scenario's: either they have a red mark, or they don't. 

Oh, and the hint that they should consider the same puzzle with 1, 2, 3 and 4 people.



That last hint is maybe too good though. My players are really good at solving puzzles.

Anyways, I don't think this puzzle will be a part of my campaign after all. Maybe I just posted it here because it is my favorite puzzle of all time and the one I have had the most trouble solving myself

I really wanted to make it work in my game, but I think it might be a little too hard and time-consuming. And the set-up is weird. But thanks anyway for your input. I'll throw some easier ones at them to begin with, and take it from there. 
Yeah, after that last hint I had the answer right away. Before that, I only spend like about five minutes thinking about it, as that's about the limit at which I start to feel the game is getting stalled.
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