[itachi-san]

There is an island upon which a tribe of blind people resides. They all answer devoutly to their chief. The tribe consists of 1000 people total, with 2 different eye colors. One day a miracle happened and every member (all 1000) was able to see for the first time. Without saying one word to each other they assembled in a congregation and their chief made the following rule: "Our religion forbids you to know your own eye color, or even to discuss the topic". Therefore, each resident can (and does) see the eye colors of all other residents, but has no way of discovering his or her own (there are no reflective surfaces in any way shape or form for this puzzle). If a member does discover his or her own eye color, then their religion compels them to commit ritual suicide at noon the following day in the village square for all to witness. All the tribespeople are highly logical and devout.

Of the 1000 islanders, it turns out that 100 of them have blue eyes and 900 of them have brown eyes. None of them know this at first of course, because any one member can only see the other 999 eye colors. What happens to the tribe, if anything, and why?

[itachi-san]

Do the people of the tribe know that 900 people have brown eyes and 100 people have blue?

They definitely don't begin with this knowledge. And maybe they never get it. That part's for you to figure out

[Guest]

I think, they will blind themselves to ensure survival of the

species

[Guest]

Ok, Neida posted the answer I was actually going to put down (I don't know if I would have worded it so eloquently), but that is the only logical progression. As long as they know 2 eye colors exist, then the iterative pathway in Neida's answer would be the answer.

[Guest]

In Josephine riddle, all the wives with cheating husbands shoot their husbands on the 40th day because there's the 'at least one' to kick it off. Obviously there's at least one of both eye colors- each person sees either 99 blue and 900 brown or 100 blue and 899 brown. But they don't know what there's SUPPOSED to be, so there's no ladder that leads up to mass suicide on days 101/102

I think you've inadvertantly proved that that the 101/102 answer is right here.

As you state, in the Josephine riddle they do not need to know what there's SUPPOSED to be, they only know that there is 'at least one'. But actually the 'at least one' statement is only relevant for the case where there IS only 1 - as you also point out "Obviously there's at least one of both eye colors- each person sees either 99 blue and 900 brown or 100 blue and 899 brown". As long as there is more than 1 person with blue eyes, they will all know there is at least 1 person with each colour eyes, as they can all see at least 1 person with each colour eyes.

In other words, the Josephine riddle would work equally as well without the 'at least one' hint. This puzzle is just a clever reword that drops the hint to see if the logic still stands, and it does. (I hadn't seen the Josephine puzzle before posting my first answer, but liked that one too!)

The only thing I can see that would fault the answer is if the islanders don't know that there are only two possible colours. Each may think that they are the only 'third' colour, if one were to exist. It is only if they know that there are only two colours that the 101/102 answer work, and the OP doesn't make this absolutely explicit.

An interesting point to take from this, is that if the puzzle said there were n people with blue eyes (blue eyes being the minority and all the islanders know there are only two colours to choose from), the answer is always n+1/n+2, except where n=0 or n=1, in which cases the islanders wouldn't be able to figure out anything without being given a clue.

New question

What if there were an equal number of blue eyed/brown eyed people? (If you get the above logic then this should be quite straightforward)

[Guest]

I Have changed my mind from my previous post, and I now think that there is a trigger and that trigger is that fact that the islanders know for sure is that there are 2 diferent eye colours on the island, by the OP's own confirmation, they do not start with a nowledge of the 100 /900 split.

The logic for a a mass suicide is: (If there can be logic for a suicide?)

1. If only one Islander has Blue eyes, on day one he looks around and see All Brown eyes and realising there are 2 eye colours he must be the only one with blue eyes. On the same day all with the Brown eyes sees on person with blue and is not sure whether they have blue or brown eyes and has to wait. However as soon as soon as ol' blues eyes tops himself the rest of the islanders realise they have brown eyes and kill themselves on day 3.

2. Following on from that if there are 2 islanders with blue eyes, they each see one pair of blue eyes, and don't know their colour so if the other pair of blues eyes kills himself on day 2 then he knows his eyes are Brown and acts as above. If the only other pair of blue eyes hasn't killed himself then their own eyes must be blue, and hence 2 die on day 3.

3. So if 3 have blue eyes all of the above is true. We know that Blue eyes one and two don't kill themselves on day three they each have seen 2 pairs of blue eyes meaning, their own must be blue, and on day 4 all 3 kill themselves, followed the next day be the general population.

4. Moving on to 4 people having blue eyes. they all see three pair of blues eyes and figure that each will be calculating scenario 3 above, realise this is not the case when day 4 passes without any suicides, they must conclude that they themselves have blue eyes.

So Each Island realises that however many people with the same eye colours they see is the next day is going to be key. In this instance all blue eyed people see 99 pairs of blue eyes so they figure either all of these 99 pairs of eyes see 98 other pairs of blue eyes and kill themselves on day 100, or all 99 blue eyes see 99 pairs of blue eyes and they themselves have blue eyes, so Day 101 there is 100 deaths. The brown eyes in the meantime are thinking I see 100 Blue eyes so if they haven't killed themselves by day 101 then I have blue eyes.

I started this reply thinking that there was no deaths and in trying to prove my theory I found that I disproved it, so I went back and re-wrote some of it so I'm sorry if it doesn't make perfect sense

Good Puzzle Itachi-san

[Guest]

New question

What if there were an equal number of blue eyed/brown eyed people? (If you get the above logic then this should be quite straightforward)

Well, if there are 500 blue eyed people and 500 brown eyed people, then everyone (both colours) would kill themselves on day 501.