There's an island with an extremely intelligent native tribe, some people have brown eyes and some of them have green eyes. Since they don't have any mirrors and because it's not allowed to discuss eye colors, nobody knows their own color. And that's a good thing, because tribe members that figure out their eye color are forced to commit suicide at midnight. One day, an explorer enters that island and says: "Oh, some of you have brown eyes and some of you have green eyes." (Yes, everyone already knows that.) And three weeks later, the whole native tribe commits mass suicide. How many people died?

1

I think the key here is 3 weeks. That's because it takes 3 weeks for the tribe to self-annihilate, and there's a hint somewhere that "some of you have brown/green eyes" implies that whenever they kill themselves off they can surmise a percentage that has which. So reverse that percentage around, and you'll be able to figure out how many people there were originally.

Since it's "some" of each, that implies there must be at least 2 tribe members that have brown eyes, and at least 2 tribe members with green eyes. There cannot be just 1 member with green eyes and the rest with brown eyes.

Unfortunately, without knowing how many people the explorer first interacts with, I don't know how we can figure out the rest. If he interacts with 4 people on his first arrival, then any 1 person can look around at the other 3, see how many have brown eyes and how many have green eyes, then determine which they are (whichever is in the majority around them is NOT what they are). However, that would result in all 4 members killing each other off that night.


IF, however, the riddle is supposed to be "half of you have green eyes and the other half brown eyes", then we can figure things out! People could count how many people are left, and how many green or brown eyes they see, and determine which they are. In that case, half the population would die each night. Reversing that by 3 weeks and that leaves:

1,048,576 people that died (assuming the last one commits suicide on his own on the last night)

The problem is vague, and I think calculating the tribe numbers based on the three weeks time is a trap. The key here is "midnight," as in there is a specific time tribe members ca off themselves. Assuming you skim the math and deduce the tribe is halving itself based on eye color, on the final day there will only be one tribe member left, and they will deduce their eye color based on this alone, and commit suicide. At that point, they represent the whole tribe so, specifically three weeks later, when the tribe is already decimated, that last person will represent the entirety of the native tribe. This is assuming there is an odd number of tribesmen.

Alternatively, there can be two tribe members left alive at that point if there are an even number of tribesmen, and assuming the fallacy that eye color is evenly distributed, they will simultaneously deduce their eye color and kill themselves together at midnight. So the answer could also be two as well.

One or two. Logical problems usually have more air tight language.

I think parts of the actual problem are being left out.

Sorry for being too vague, "some of them" = "more than one" and there's no suicide in the nights before the last one.

Okay, I just checked my opening post and I'm really positive there's nothing else that might need further explication.

It's because there's the vagueness between 1 and 2 that I didn't consider it the answer. And there can't just be 1 or 2 people in the tribe, because "some" implies more than 1, so some of each implies more than 2 people. If there were 3 or 4 people, everyone would have died on the 1st night:

If you have green eyes; then you will see 2 people with brown eyes and 1 with green eyes.
If you have brown eyes; then you will see 2 people with green eyes and 1 with brown eyes.

So that leaves "more than 4" people. If there were 5 people left, 3 in one group and 2 in the other, then that would take 2 nights to self-annihilate, as someone in the "2" group could identify their eye colour, but someone in the "3" group could not:

(assuming brown eyes is majority)
If you have green eyes; then you will see 3 people with brown eyes and 1 with green eyes. That means you must have green eyes.
If you have brown eyes; then you will see 2 people with green eyes and 2 with brown eyes. That means you might have brown or green eyes, and not know which is in the majority. But once the two green eyed people off themselves, you'll know you were in the brown eyed group, then all brown eyes also off themselves.

That means there must be more than 5 people in the tribe. Once you're at 6 people in the tribe, it's impossible to know for sure based on the "some" and "some".

(assuming you don't know the actual split, and there are at least 2 people with each colour of eyes)
If you have green eyes; and you see 3 people with brown eyes and 2 with green eyes. You might be a 4th person with brown eyes, or a 3rd person with green eyes.
If you have green eyes; and you see 2 people with brown eyes and 3 with green eyes. You might be a 3rd person with brown eyes, or a 4th person with green eyes.
If you have brown eyes; and you see 3 people with brown eyes and 2 with green eyes. You might be a 4th person with brown eyes, or a 3rd person with green eyes.
If you have brown eyes; and you see 2 people with brown eyes and 3 with green eyes. You might be a 3rd person with brown eyes, or a 4th person with green eyes.


Oddly, I think at 7 people you could solve your eye colour still.

If you are in the minority group (green eyes) and don't know the ratio, you would see 4 people with brown eyes and 2 people with green eyes. On the first night you wait to see if the green-eyed people kill themselves. If they do, then you have brown eyes, since only a pair of people would kill themselves on the first night. But if they didn't kill themselves, then you'd know that they saw a 3rd green-eyed person, so you would have to kill yourself, since you must be that person. On the third night the brown-eyed people would then kill themselves for the same reason.

At 8 people it's impossible, just like at 6.

At 9 people it's still possible to figure it out, but it takes longer (I think I'm onto the answer). If you're in the minority, you would see 3 others with green eyes and 5 others with brown eyes. You might have brown or green eyes (you're either a 4th person with green, or a 6th person with brown). You know that if anyone kills themselves in 2 nights there were only 3 people with green eyes (as per scenario: 7 people), which would mean you have brown eyes. If no one kills themselves in 2 nights, then you have green eyes.

I think I got this... for odd-numbered groups, you wait (N-1)/2 days for the group to kill itself. That would mean it'll take 5 days for an 11-tribe group to kill itself. Let's see if this holds...

At 11 people, if you're in the minority, you would see 4 others with green eyes, and 6 others with brown eyes. You might have brown or green eyes (you're either a 5th person with green, or a 7th person with brown). You know that if there were only 5 people with green eyes, they'll exterminate themselves in 3 nights. If they don't, then you have green eyes and off yourself on the 4th night. The rest take themselves out on night 5.


SUCCESS!!!

That means if it takes 21 days for the tribesmen to take themselves out, you can plug it into the equation:

(N-1)/2 = T
T*2 = N-1
T*2+1 = N
21*2+1 = N
42+1 = N
43 = N

There are 43 people in the tribe!

OUT OF REPLY EDIT: Wait wait wait... they didn't off themselves before hand but only because there was no explorer to make the number of people in the tribe an odd number. That means there were only 42 people in the tribe. That explorer just had to show up (and have green or brown eyes) to mess things up!

What I dont get is why they waited three weeks but slf says nobody died the night before o_o

This seems like a more obtuse version of the troll bridge riddle. I think it goes: there are two trolls guarding two separate bridges. One of the bridges leads to a troll cave where you'll be turned into a souffle. The other leads you safely to the other side of the canyon. One of the trolls can only tell lies, and one of the trolls can only tell the truth. What is the one question you ask to determine which bridge to use to cross the canyon?

I don't find them to be the same, as that one is based on the concept of a double-negative, and the OP's is based on a scaling equation.

If you're only looking at the answers, sure. But in both logic games you cycle through several scenarios before you arrive at the answer, it's just the OP's is more vague (hence: obtuse) and has a wider range of variables.

Yarium, I just posted that everyone dies in the last night and that nobody dies before that night while you were typing. Sorry, I thought that it's obvious that "the whole native tribe commits (not committed!) mass suicide" doesn't merely refer to 1-2 remaining tribe members. Oh, do you know that other math puzzle for little children where x people are unable to distribute a number of camels between them until another person shows up with another camel and then leaves with the same camel when they're done? I just attempted to calculate the right numbers, but it's pretty difficult because I don't remember how that puzzle works.

Now that Chaos showed up here, I should probably reveal that I'm Cats. I strongly refuse to remember the reasons why I created this other account, but it's definitely not because I wanted to deceive anyone. I wanted to post my logic puzzle in that Pablo thread (replacing that explorer with Pablo's ******-** and *****-*** ex-girlfriend who totally doesn't deserve him) until I saw that he didn't post within the last days. For some reason, it's not possible to send personal messages to him or any other member of this forum unless your post count raises above zero.

I think the key is that there are always at least 2 of each eye color.

If there are only two green they will realize this the first night after seeing the rest of the tribe has brown eyes. Because they are highly intelligent each person with brown eyes will infer the suiciders were the only green eyes, therefore they would all die the next night. But is this true?

Do the tribes know there are only two eye colors on the island? Are there only two eye colors?

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?

Does that fact change anything? Once it is know, it is enforced. Which means that, okay, everyone knows on the same night, so it'll take one additional night if everyone's doing it on the same night at the end of 3 weeks. That brings it to 44 people in the tribe. Is that number correct?

Unfortunately I don't know that other puzzle with the camels

Uhhh... doesn't there have to be a reason why someone has to leave the island? Otherwise there's absolutely no context. Also, there's no way to distinguish beyond eye colour and being the Guru or not, so at best the answer for "who" would be "a person with blue eyes" or "a person with brown eyes" or "the Guru" depending on the conditions of why someone has to leave. There's also no ordering system, so I can't say "the last person with blue eyes" or similar. Also, without a condition for leaving the island, there's no night that it can be determined. Is it the same as the OP? When you know your eye colour you must leave?

If that is the case, then I'd be able to figure out whether a blue or brown eyed person left the island, and on which night.

one sec here's the full:


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?

2. One guy has each eye color. The explorer tells them, then they look around, realize that they're the only one who could possibly have their eye color, and kill themselves.

whoever the guru made eye contact with