Uh, for those who are big musers on the 'Blue Eyes' logic puzzle... I have an extra little theory which I want to put forward here to be shot down before I try waving my banner at far more well educated people over at Xkcd. So could someone who already knows the answer tell me if I've got this fleshed out right?
100 blue eyes, 100 brown eyes, 1 'Oracle'.
200 people leave on the 100th day.
If the Guru/Oracle/Mystic saying 'I see a person with blue eyes' is only the statement which 'starts the clock', then why is it limited only to the blue-eyed people who make the assumption?
Consider from the mindset of a person with brown eyes.
I see 100 blues and 99 browns.
If on the 100th day, the 100 blues have not left, by this reasoning I am the 101st.
By this reasoning if on the 99th day the 99 browns have not left, I am the 100th.
This logic relies on everyone thinking the exact same -but it's the same pretense as the rest of the logic.
Therefore, a brown-eyed person who sees 100 blues and 99 browns will reason that if the 99 browns leave on the 99th day, therefore their color is either blue or X.
However if the 99 browns do not leave on the 99th day, the only other person who could have brown eyes is themselves and they can leave.
This is obviously just using the same logic for the other eye color, but there's a reason I'm walking back through it. Which is this:
A brown-eyed person sees 100 blue eyed people and 99 brown eyed people. Therefore, on the 100th day, by process of elimination, they Know they have brown eyes - irrelevant of the count by the blues at the time.
Therefore both browns and blues can show up at the harbor for the boat at the same time, whilst still being firm in the knowledge of their own eye color.
1. Everyone thinks the exact same.
2. There is a definite start point.
If there were 4 amber, 19 brown, 70 green and 100 blue, as long as you had those two assumptions you could logically conclude your own eye color by process of elimination.
1. Day 4, the ambers leave. Therefore I am not amber.
2. Day 19 the browns leave, therefore I am not brown.
3. Day 70, the greens have not left. logically I can be the only other green.
Etc, Etc.
Two However(s):
1.
It does rely on a single thing, which is all of the people coming to one unanimous conclusion.
"IF by day 100 the blue eyes have not left, then I have blue eyes.
ASSUME-
If the other eyes begin counting on this day, we have empirical evidence of passing time.
THEREFORE-
If the Ambers have not left after 4 days, I am amber.
ELSE: If the Browns haven't left after 19 days, I am brown.
ELSE: If the Greens haven't left after 70 days, I am green.
ELSE: If the Blues haven't left after 100 days, I am blue.
ELSE: IF all other eye colors have left the island on their scheduled days, I am none of these colors.
2.
It does have one big flaw, and that is that it won't go down to base 1.
If a single blue, green and brown are together, then the blue will hear 'one of you are blue', look around and leave. Green and brown will have no idea.
But if there are two of each, then each person will count 1/2/2. And therefore make the assumption "If X doesn't leave on day 1, I am X".
Because everyone is thinking alike, and perfectly.
To fit It to this scenario (there are is an infinite number of possible eye colors), there HAS to be at least 3 of each, to ensure that all islanders have the same knowledge.
Example: 2/2/2 (brown pov), They are informed that blue does exist and one of them is it, which starts the ball rolling. Through the reasoning brown can also assume that everyone is aware of the presence of green as there is two other greens (so they can look at eachother)- however, with there being only one definite brown, he cannot assume that the other brown knows there is any browns.
So- in order for everyone to know that Everyone Else knows what possible eye colors there are in order to start the clock, there must be at least 3 (or else just discount that color and continue calculating)
Any holes in that logic?
I'm not a mathmetician, so I dunno if I've divided by zero or something in there.
-PLEASE SPOILER YOUR REPLIES-
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