pretty tough/hard riddle

[looseswing]

Friend showed me this, see if you guys can reason it out. I have not figured it out yet, he's going to tell me the answer tomorrow if I have not gotten it by then:

200 men and a queen are living on an island. Queen has brown eyes, 100 men have blue eyes and the other 100 have green eyes. Nobody knows the color of his own eyes but he can see the other people living on the island, so a green eyed man will see 99 other green eyes and 100 blue eyes. No communication is allowed between the men so no one can simply tell the others the color of their eyes using any kind of communication. Also, No one knows that there's 100 men with green eyes and 100 with blue eyes except the queen, so every man might think his eyes are brown, black or whatever. There's only one rule in the island:

-If someone is sure of the color of his eye, he has to leave the island in the same day!

The queen wakes up everyday and makes one announcement:

"There's at least one man with green eyes", if there's at least one man with green eyes on the island.
"There are no men with green eyes", if there are no green eyed men on the island.

The queen never lies.

The question here is: Who will leave the island and when ?

---------------------------------------------------------

Hint: The Answer is not "No one will ever leave". I promise!

Clarifications:

1- No one can use any kind of material to know the color of his eyes(mirros, water, etc)

2- Queen makes sure that everyone hears the announcment everyday.

3- No one can ask the queen anything.

[SuperFly]

I got it.






















The men execute a coup against the queen because she's making their lives harder by giving them a stupid riddle while they are stuck on a deserted island. The men then proceed to build shelters, gather food and make a rescue fire.

[cucio]

The queen. As soon as possible. No woman could endure sharing an island with 200 horny baastards.

[TheJRK]

Is this the finale from "Lost"? Don't spoil it for me, I'm still on Season 3.

[Kenny022593]

Originally Posted by TheJRK

Is this the finale from "Lost"? Don't spoil it for me, I'm still on Season 3.

Magnets

10char

[sureshs]

Can any guy remember everyone and count to see how many have what eye color? If he counts only 99 of a color, that means he has that color?

[ProgressoR]

think i figured it out.....do you want me to post my guess on here? or let others have time to ponder on it?

[TheJRK]

I had two other guys at work helping me out with this and we were drawing it out on a dry-erase board.

I think we figured it out.

[looseswing]

Well I put this up so people coul guess and collaborate on it here, thought it would be a fun little activity for the board. And he can't be sure that he has a certain color if he counts 99 of it because remember he could have black/brown etc eyes and does not know that there 100 blue and 100 green.

[ProgressoR]

ok here are my thoughts. Nobody will leave on the first day because some will see 100 greens and some will see 99 greens.

Actually i might change my thoughts as i write this....

Imagine there are 2 greens (g1 and g2) and 100 blues. Bear with me.
The blues see 99 blues and 2 greens, and wouldnt leave as they have no idea of their own colour.

The greens will see 1 green and 100 blues. So will not leave as that doesnt tell them their own colour.

on the second day, again queen says there is at least one green. G1 can still only see 1 green, so can G2.

But G1 knows g2 didnt leave yesterday, but if g2 did not see any greens yesterday, he would have left as g2 would have known he was the green, so g1 knows g2 saw at least one other green. But g1 sees no other greens, so today g1 knows he must be the other green. He will leave on the second day. Similarly, G2 goes through the same process and he would also leave the second day. The 100 blues stay where they are. The next day queen says no greens and no one leaves because they know they are not green and see only 99 other blues, so cannot know their own colour.

To extrapolate, imagine there are N greens. if n=2 they both leave on second day. the same process tells us if n=3 then they all leave on the 3rd day. So if there n=100, then all 100 greens should leave on the 100th day.

Nobody will leave after that day.

that is what my initial thoughts are....

comments?

[fed_the_savior]

Theoretically, if all the men wanted to know how many had green eyes, and they were logical geniuses, they would know there was only one sure-fire way to find out without communicating, and that is to use a system where they wait as many days to leave as they see green eyed men. That way the men that actually have green eyes and would see the lowest number of green eyed men, would all leave together on the soonest possible day, which would be the 100th day in this case. The leftover men would never leave, because even though they all know the others are blue eyed, they would never know for sure what color they had themselves, they would just know "There are no men with green eyes." But this system requires that the men have a desire to find out how many green eyed there are. If they don't care, they will won't follow the plan, and they will never know.

[Jennifer]

Queen is the only one that leaves the island. She is the only one who knows her eye color.

-Jennifer

[looseswing]

Originally Posted by ProgressoR

ok here are my thoughts. Nobody will leave on the first day because some will see 100 greens and some will see 99 greens.

Actually i might change my thoughts as i write this....

Imagine there are 2 greens (g1 and g2) and 100 blues. Bear with me.
The blues see 99 blues and 2 greens, and wouldnt leave as they have no idea of their own colour.

The greens will see 1 green and 100 blues. So will not leave as that doesnt tell them their own colour.

on the second day, again queen says there is at least one green. G1 can still only see 1 green, so can G2.

But G1 knows g2 didnt leave yesterday, but if g2 did not see any greens yesterday, he would have left as g2 would have known he was the green, so g1 knows g2 saw at least one other green. But g1 sees no other greens, so today g1 knows he must be the other green. He will leave on the second day. Similarly, G2 goes through the same process and he would also leave the second day. The 100 blues stay where they are. The next day queen says no greens and no one leaves because they know they are not green and see only 99 other blues, so cannot know their own colour.

To extrapolate, imagine there are N greens. if n=2 they both leave on second day. the same process tells us if n=3 then they all leave on the 3rd day. So if there n=100, then all 100 greens should leave on the 100th day.

Nobody will leave after that day.

that is what my initial thoughts are....

comments?

I thought the same at first. However, think about it this way in the same scenario (g1 and g2 with 100 blue eyes).

Day 1: queen makes the announcement
g1: looks around and sees g2, and the blues.
g2: knows that g1 must have seen someone with green eyes because otherwise he would have left himself. He knows that he must be that someone because everyone besides him and g1 have blue eyes. He leaves.

Day 2: queen makes the announcement
g1 leaves as everyone else has blue eyes.

At this point I'm not really sure how to extrapolate out though.

[aceX]

I also came to the independent conclusion that all the greens will leave on the 100th day.

[aceX]

Originally Posted by looseswing

I thought the same at first. However, think about it this way in the same scenario (g1 and g2 with 100 blue eyes).

Day 1: queen makes the announcement
g1: looks around and sees g2, and the blues.
g2: knows that g1 must have seen someone with green eyes because otherwise he would have left himself. He knows that he must be that someone because everyone besides him and g1 have blue eyes. He leaves.

Day 2: queen makes the announcement
g1 leaves as everyone else has blue eyes.

At this point I'm not really sure how to extrapolate out though.

I don't think g2 will know that g1 doesn't know until the next day, but I'm not sure on this

[ProgressoR]

Originally Posted by looseswing

I thought the same at first. However, think about it this way in the same scenario (g1 and g2 with 100 blue eyes).

Day 1: queen makes the announcement
g1: looks around and sees g2, and the blues.
g2: knows that g1 must have seen someone with green eyes because otherwise he would have left himself. He knows that he must be that someone because everyone besides him and g1 have blue eyes. He leaves.

Day 2: queen makes the announcement
g1 leaves as everyone else has blue eyes.

At this point I'm not really sure how to extrapolate out though.

problem is the timing...if g2 leaves on day 1, then does g1 have time to process this and leave at the same time, because he will work out he must be green the second g2 leaves, he doesnt need to wait till next day. I am assuming that the leaving part happens or it doesnt, not that others can see them leave and then process something and leave immediately after them.

if that is the case, g1 has no time to process that g2 hasnt left, presumably he only finds out the next day - and i think that is a sensible approach, otherwise we get into a circular situation

[ProgressoR]

Originally Posted by aceX

I don't think g2 will know that g1 doesn't know until the next day, but I'm not sure on this

yep that is the conclusion i came to also

[ProgressoR]

Originally Posted by Jennifer

Queen is the only one that leaves the island. She is the only one who knows her eye color.

-Jennifer

lol smart answer, however being pedantic, and why not be pedantic, what makes you assume she knows her own eye colour?

and the question posited that if someone knows their eye colour, then HE must leave the island.

[aceX]

Originally Posted by looseswing

I thought the same at first. However, think about it this way in the same scenario (g1 and g2 with 100 blue eyes).

Day 1: queen makes the announcement
g1: looks around and sees g2, and the blues.
g2: knows that g1 must have seen someone with green eyes because otherwise he would have left himself. He knows that he must be that someone because everyone besides him and g1 have blue eyes. He leaves.

Day 2: queen makes the announcement
g1 leaves as everyone else has blue eyes.

At this point I'm not really sure how to extrapolate out though.

Day 1: queen makes the announcement (at least one green)
g1: looks around and sees g2, and the blues.
g2: looks around and sees g1, and the blues.
g1: knows that g2 must have seen someone with green eyes because otherwise he would have left himself.
g2: knows that g1 must have seen someone with green eyes because otherwise he would have left himself.

So they both leave as soon as the announcement is made.
But if they both leave as soon as the announcement is made they wouldn't know to leave because they wouldn't see the other person wait.

So they must only know if a person knows or not on the next day.

So for 2gs 100 bs the 2 gs leave on the 2nd day.
For the original, the 100gs leave on the 100th day

[aceX]

Originally Posted by ProgressoR

lol smart answer, however being pedantic, and why not be pedantic, what makes you assume she knows her own eye colour?

and the question posited that if someone knows their eye colour, then HE must leave the island.

The first two answers I wrote down were:
- Queen is a man and leaves the Island
- Queen tells them all their colour without them asking

But because this goes against the spirit of the riddle I decided there would be a more satisfying answer.