I noticed this had been posted some time back, but knowing how it worked, I kept quiet. I'm a little surprised there hasn't been many to get it yet.

There is a straight forward solution.

Jerry

Nick , Where are you? I need a tutorial.

Somebody PLEASE give us a hint on this. I check here (at least daily) waiting for a clue....

Murf

Hey Nick, are you out there?

I agree with Tomas "At least one of you has a star" can't be a vital clue as everyone can observe that straight away.

Sourcerer, that info is only important in the general solution that goes something like "There are N people with a star on their forehead." to indicate that N is at least one. Somehow that info leaked into this more specific puzzle where it's not needed since N obviously is at least one.

So the hint to solve this is to actually go with the general puzzle where N is unknown, to solve that. When that is solved you set N = 81 to get the solution for this puzzle.

/Tomas

Tomas, gotcha :o)

Hmmm, I can again apply lawyer analysis to this. The question is 'when can someone escape', whereas the person knowing his symbol will be *released*, which is obviously not an escape!
...but again, I'm afraid that'll not lead me to the desired solution :op

Kaj

And I assume noone is told there is not 4 or more symbols? I am not sure how to break the deadlock of wondering whether they have a square (or whatever) on their forehead :o\

They were told so to make sure that eveyrone knows that everyone knows that everyone knows ... everyone knows at least one star exists, even if they could not see other's head.

They need to be infinetly logical beings in this puzzle. Why would they need to know this before even looking at others? I know why it's needed in the general problem, but don't understand why it's needed here. Surely their strategy can form the moment they each see at least one star.

/Tomas

Suppose there are only 3 people and two of them, say Alice and Bob, have a star on forehead.
They know at least one player has a star by seeing each others in current situation.
But what Alice need to know is, Bob knew that there is at least one star even if there was no star on her forehead.

"at least one star" should mean "at least one star in every possible situation", not "at least one star in current situation".

I still don't see how that is needed here. Every clever person on the Island will know that there is one good winning strategy as soon as they see all those stars:

They know that the hard to solve case of no one having a star is not existant so they can imagine what they'd do in the general case, correctly assuming that N > 0, and work from there. What hinders them?

Imagine if I present this problem to you and your puzzle solving buddies and you all see several stars each, and I do _not_ tell you that at least one of you has a star. Wouldn't you guys be able to work out a strategy to win?

I think you could.

If not, what would hinder you?

/Tomas

Sorry, what I wrote about "They know that the hard to solve case of no one having a star is not existant" is not correctly phrased. Should be:

"They know that they are not in the hard case to solve of _someone_ not seeing a star, and everyone knows that everyone knows that they can't be in that case."


In the problem you presented with Alice and Bob, Bob can't be sure Alice is seeing a star, so he can't be sure she knows that there is at least one star. In the problem presented in the original post in this case it's very different. There everyone knows that everyone knows that there is at least one star. So everyone knows that everyone knows that there is a winning strategy and can come up with the winning strategy.

So, imagine you and your puzzle solving buddies in that situation. Wouldn't you be able to leave even if I didn't tell you there is at least one star? I still think you would.

/Tomas

I agree with Tomas, with Alice and Bob it would be a vital clue, with 50 stars present at least it's an inrefutable fact to all.

I'm still clueless and refuse to Google.

200 people see 3 symbols, one sees 2.
Noone can savfly assume there's not 4 symbols - that part bugs me.

Savfly. I meant to say that. It's one of those words you can repeat any number of times and it will never make a valid sentence.

Okay, actually it's the keyboard on this netbook that makes it really intuitive to misplace your hands while typing.

Still clueless on the puzzle.