A group of people with assorted eye colors live on an island. They are all perfect logicians -- if a conclusion can be logically deduced, they will do it instantly. No one knows the color of their eyes. Every night at midnight, a ferry stops at the island. Any islanders who have figured out the color of their own eyes then leave the island, and the rest stay. Everyone can see everyone else at all times and keeps a count of the number of people they see with each eye color (excluding themselves), but they cannot otherwise communicate. Everyone on the island knows all the rules in this paragraph.
On this island there are 100 blue-eyed people, 100 brown-eyed people, and the Guru (she happens to have green eyes). So any given blue-eyed person can see 100 people with brown eyes and 99 people with blue eyes (and one with green), but that does not tell him his own eye color; as far as he knows the totals could be 101 brown and 99 blue. Or 100 brown, 99 blue, and he could have red eyes.
The Guru is allowed to speak once (let's say at noon), on one day in all their endless years on the island. Standing before the islanders, she says the following:
"I can see someone who has blue eyes."
Who leaves the island, and on what night?
There are no mirrors or reflecting surfaces, nothing dumb. It is not a trick question, and the answer is logical. It doesn't depend on tricky wording or anyone lying or guessing, and it doesn't involve people doing something silly like creating a sign language or doing genetics. The Guru is not making eye contact with anyone in particular; she's simply saying "I count at least one blue-eyed person on this island who isn't me."
And lastly, the answer is not "no one leaves."
Answer
Spoiler:
The answer is that on the 100th day, all 100 blue-eyed people will leave. It's pretty convoluted logic and it took me a while to believe the solution, but here's a rough guide to how to get there. Note -- while the text of the puzzle is very carefully worded to be as clear and unambiguous as possible (thanks to countless discussions with confused readers), this solution is pretty thrown-together. It's correct, but the explanation/wording might not be the best. If you're really confused by something, let me know.
If you consider the case of just one blue-eyed person on the island, you can show that he obviously leaves the first night, because he knows he's the only one the Guru could be talking about. He looks around and sees no one else, and knows he should leave. So: [THEOREM 1] If there is one blue-eyed person, he leaves the first night.
If there are two blue-eyed people, they will each look at the other. They will each realize that "if I don't have blue eyes [HYPOTHESIS 1], then that guy is the only blue-eyed person. And if he's the only person, by THEOREM 1 he will leave tonight." They each wait and see, and when neither of them leave the first night, each realizes "My HYPOTHESIS 1 was incorrect. I must have blue eyes." And each leaves the second night.
So: [THEOREM 2]: If there are two blue-eyed people on the island, they will each leave the 2nd night.
If there are three blue-eyed people, each one will look at the other two and go through a process similar to the one above. Each considers the two possibilities -- "I have blue eyes" or "I don't have blue eyes." He will know that if he doesn't have blue eyes, there are only two blue-eyed people on the island -- the two he sees. So he can wait two nights, and if no one leaves, he knows he must have blue eyes -- THEOREM 2 says that if he didn't, the other guys would have left. When he sees that they didn't, he knows his eyes are blue. All three of them are doing this same process, so they all figure it out on day 3 and leave.
This induction can continue all the way up to THEOREM 99, which each person on the island in the problem will of course know immediately. Then they'll each wait 99 days, see that the rest of the group hasn't gone anywhere, and on the 100th night, they all leave.
Before you email me to argue or question: This solution is correct. My explanation may not be the clearest, and it's very difficult to wrap your head around (at least, it was for me), but the facts of it are accurate. I've talked the problem over with many logic/math professors, worked through it with students, and analyzed from a number of different angles. The answer is correct and proven, even if my explanations aren't as clear as they could be.
I think an easier way for a person to understand is by explaining how you eliminate possibilities. I'll give examples.
Scenario 1:
Two blue eyes, and one brown. I'll notate as b1 and b2 for blue and r1 for the brown eye'd guy.
b1 sees b2 and r1 and he can deduce if I have brown eyes the b2 will leave immediately because he knows there is at least one blue eye'd person and he sees two brown eyes so it must be him. If he doesn't leave right away, that means he cannot make this determination which means I have blue eyes too.
b2 has the exact same thought process.
r1 just waits for all the blue eyes to leave and the guru to change her message.
It doesn't matter how many brown eye'd people exist, the fact that b1 and b2 can't determine they are the sole blue eye'd people makes them stay one day.
Scenario 2:
Now expand it to three blue eye'd people, logic is the same it just takes longer. b1, b2, b3, r1 since the brown eye'd number of people don't really matter.
b1 sees b2 and b3 and thinks to himself if I have brown eyes then b2 and b3 are going to leave in two days, just as what happened in scenario 1. Since they don't, he can determine he has blue eyes.
Scenario 3:
b1, b2, b3, b4, and r1.
b1 is going to see b2 and b3 and b4 and now he's going to say hey look it's scenario 2! If I have brown eyes, those geniuses are going to figure out in less than three days they can leave, but since they didn't I can determine I have blue eyes.
And so on. I think if you were coding this it would be some kind of recursive loop.
Functionally would be something like this:
int BlueEyedWait(int numberOfPeopleISeeWithBlueEyes){
if(numberOfPeopleISeeWithBlueEyes)
return 0; // I'm free to leave!
return 1 + BlueEyedWaite(numberOfPeopleISeeWithBlueEyes-1)
}
I think an easier way for a person to understand is by explaining how you eliminate possibilities. I'll give examples.
Scenario 1:
Two blue eyes, and one brown. I'll notate as b1 and b2 for blue and r1 for the brown eye'd guy.
b1 sees b2 and r1 and he can deduce if I have brown eyes the b2 will leave immediately because he knows there is at least one blue eye'd person and he sees two brown eyes so it must be him. If he doesn't leave right away, that means he cannot make this determination which means I have brown eyes.
b2 has the exact same though process.
r1 just waits for all the blue eyes to leave and the guru to change her message.
It doesn't matter how many brown eye'd people exist, the fact that b1 and b2 can't determine they are the sole blue eye'd people makes them stay one day.
Scenario 2:
Now expand it to three blue eye'd people, logic is the same it just takes longer. b1, b2, b3, r1 since the brown eye'd number of people don't really matter.
b1 sees b2 and b3 and thinks to himself if I have brown eyes then b2 and b3 are going to leave in two days, just as what happened in scenario 1. Since they don't, he can determine he has blue eyes.
Scenario 3:
b1, b2, b3, b4, and r1.
b1 is going to see b2 and b3 and b4 and now he's going to say hey look it's scenario 2! If I have brown eyes, those geniuses are going to figure out in less than three days they can leave, but since they didn't I can determine I have blue eyes.
And so on. I think if you were coding this it would be some kind of recursive loop.
I spend considerable time, energy (and money!) making things I'll never make any money from ... I don't believe all joy in life is derived from weighing your likelihood of profit.
Fun .
Yes, it's work in some way, but it's enjoyable.
Same as for like every amateur artist, singer, musician, craftsman, whatever.
Nobody would do this if it wasn't.
It's a question of calling, a question of luxury. Sometimes things are one, sometimes they are both. Unfortunately, sometimes we have time for neither. And that's a rough go.
Many worthwhile things have been created throughout history and their creators never made any money off them.
I write fanfiction and filk music. I can't legally profit from it, but it's a worthwhile thing to create stories to entertain other people and further my own skills as a writer and storyteller. I'm also adding to the body of stories and songs written by other people for favorite TV series, movies, books, comics, games, etc.
And consider this: Many people start a hobby and then realize they can make money from it. I started a needlepoint hobby to deal with the downtime when I was working backstage in musical theatre, and less than a year later I got good enough that I thought I'd see if I could sell any of it (practice, practice, practice!).
I spent the next 13 years selling 3-D needlepoint and counted cross-stitch items in various craft stores and fairs around town, including a craft cooperative I helped to run. Some of my items have ended up on the other side of the country in Prince Edward Island and even as far as the UK (bought and sent as gifts by various people). And that was in the '80s and '90s, before Etsy, Artfire, and other craft websites were a thing.
I spend considerable time, energy (and money!) making things I'll never make any money from ... I don't believe all joy in life is derived from weighing your likelihood of profit.
My dad used to make banana bran muffins to sell at my table for the craft fairs. We had a 90-10 deal... I got 10% of what he sold to help pay for the table. I sold bread for another person for the same deal, and they were pleasantly surprised at the end of the day when I handed them the money they'd made.
Apart from some promotional accounts, all I can think of is Jon Shaefer. I think one of the Fall from Heaven guys got hired by Firaxis but I could be wrong.
It's a labour of love. I mod the game to do the things I want to do, how I want it to look, etc. And I share so that others can have the same experience. Nothing makes me feel as good as when I get a PM or see a comment on the site that someone enjoys my mods.
"Mike B." and "Dan Megaha" (sp.?) both have/had accounts here as well, and were active posters during the development/patching of the Civ3 expansion-packs back in the day.
I figure many people would probably enjoy the anonimity on this forum. Outing yourself as a Civ developer is just a setup for receiving hateful PMs complaining about "bad AI" maybe some of the regulars here have jobs at Firaxis...
They also did bring up copyright infringement. They've also said that if something is done for free or given away for free, it's clearly terrible as if it was any good, it would be sold to make money.
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maybe some of the regulars here have jobs at Firaxis...
