A logic & probability problem. Need to solve today... Thank

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There was once a mythical village off in the woods somewhere. In this village lived a group of perfectly logical people, each of whom had either a red spot or a green spot in the middle of their forehead. No one in the village was allowed to know the color of the spot on their own forehead, and discussion of the color of other people's spots was strictly forbidden. Care had been taken to remove all mirrors and anything else reflective from the village so that accidental discovery of the color of one's own spot was unlikely. However, if in the unfortunate event that the color of one's own spot was accidentally discovered, village law required that the person throw him/herself down the well.

Each day every villager would gather in the village square for the morning meet-and-greet, during which every villager would shake hands with every other villager.

One day a stranger came into the village during the morning assembly. The stranger, unfamiliar with the customs of the village, spoke hastily and said "I see at least one red spot."

What happened then, and why?

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Don't drink the water.

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Suppose you're a villager. You can see everyone else's spots; if a stranger said he saw a red spot, but you don't see one, what are the implications?

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And suppose the only guy with a red spot that you can see jumps into the well.

What do you do then?

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I've got a couple of questions:

- How does the spot initially get on the villagers foreheads? Do they close their eyes and dip a finger in a pot and smear their foreheads? Does another villager do it for them? If so, how does this other villager make the decision of whether the spot should be green or red?

- Afterwards, how does the person maintain the spot without knowing what touch-up color to use? Or if another villager does the maintenance work for him, how does he know that they keep it the same color each time?

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more on the mythical village
I don't think the problem resides how the spot got in their foreheads, but what happens after the stranger blurts out: "I see at least one red spot".
If he says that, then it means that whoever has the red spot sees everyone else with a green spot and thus realizes he is the one with the red spot. Will he/she jump in the well? OR Will he/she ignore the comment and ask the stranger to leave. The other thing is that the villagers are perfectly logical people. If I was one of them. And saw all green spots, would I believe the stranger? would I then assume I am the only red spot and have to jump? Is the perfectly logical person means that I also have a high code of ethics and follow the rules?

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Ask the stranger if he is color-blind.

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Two scenarios:
1. As lab rat said, if there's only one person with a red spot, he knows on hearing the stranger's words what his color is. Therefore he jumps in the well. As Seal points out, all the others now know that they have green spots. So they jump in.
2. If there's more than one person with a red spot, everyone looks around, sees at least one red spot, says "whew," and life goes on.

Now for the rest of the story....

This actually happened! It was in a small town in Maine where an evil stranger initiated the mass suicide into the local water supply described in scenario 1. He was able to buy up the abandoned town for very little money. There he established a business that persists even to this day. He named both the town and the business....

Poland Springs

....and now you know the REST of the story.

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Reply to Poland Springs legend
I checked your "rest of the story" and couldn't find anything, except for a famous lady who might have been poisoned.
Poland Springs was founded by the Ricker family.
There's also a legend that one of the Ricker brothers is a ghost in one of the inss @ Poland Springs.
Thanks for your input... I sent it in. It really made sense.
Very Happy

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'course, we're missing the rest of the story...

S'pose I'm one of the unfortunate villagers, and I see one guy with a red spot. And he ain't jumpin'...

Perfectly logical, right... ?

So, if he's not jumping, then there's gotta be one other red spot, and I can't see it... so off I go to the well.

So if I see two spots, and neither of them are jumping...

Now, giggicat... a question for you: who did you send it in to. You know, the same question was asked on this forum yesterday...

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TO MY STATS PROFESSOR... WHO SAID WE COULDN'T FIGURE OUT THE ANSWER...
AND YES I POSTED IT IN RIDDLES, BUT THOUGHT THAT PEOPLE INVOLVED IN MATH OR SCIENCES WOULD BE INTERESTED IN A LOGIC AND PROBABILITY PROBLEM.
THANKS SO MUCH FOR YOUR PERSISTENCY IN FIGURING OUT.
ONCE MY PROF TELLS US THE ANSWER, I'LL POST IT...

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GEORGE, ARE YOU A SOCCER PLAYER AND/OR, ENTHUSIAST. MY LATE BROTHER WAS BOTH! AND I MISS HIM SOOOOO MUCH!

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Only play soccer in pickup games and with the kids I coach. Love it, tho.

Sorry to hear about your brother.

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Yeah, Daniel used to coach kids too! He went to college with a full soccer scholarship. One of my twins (they are almost 24 years old) played for his h.s. too. I love your icon! It just brought dear memories of a very fine man!
Thanks for sharing.

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Quote:

So if I see two spots, and neither of them are jumping...

There is a problem with extending this principle to the case of N red spots.
Let's say there are 5 red spots. EVERYONE knows already that there is at least one red spot, so there is nothing new learned when a stranger asserts this.
So there is no need to jump into the well for it - unless of course everybody SHOULD jump into the well for the same reason without even needing the stranger!

Or am I missing something?

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One more thought:

Say there are two red spots, person A and B. They look at each other for a monent, then A jumps.
Does B know his color now?

B thinks: "I must be green, because A saw all green and knew he is Red."

.. or does he?

"Or he saw one Red. He waited if I'd jump. When I didn't he knew he was red so he jumped. So I'm red."

No one can determine his/her color unless there is exactly one red spot.

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A logic & probability problem. Need to solve today... Thank

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