Emoticorpse, your last posting expresses, more succinctly than I did, exactly what I was trying to say!
it’s not escaping the island that is in question here (that’s incidental). it’s KNOWING your own eye color. you can figure out your own eye color and choose to stay. KNOWING your own eye color is the goal. not (pretty much there and have a 50 50 chance because you know there’s only 2 color eyes) that’s not knowing it’d still be a guess when you have to answer to get on the boat.
Almost like if someone gave you a lotto ticket worth 5 million dollars and you had 5 or of 6 numbers.
it COULD be 3
it COULD be 6
which one is it
I am sorry, though, that no one tried out Indistinguishible’s game which he/she initiated in this thread.
Man I think if someone here would go through every post in the thread and Gather up the best of the best and vital and inspiring advice on how to figure this thing out it’d be one HELL Of a post.
yeah there is a right way and a wrong way to understand this puzzle. Doing the math really is too bloody complicated and I don’t think anyone in this thread really actually worked out 99 or 100 layers deep (I think Frylock did do some impressive diagrams though) on paper or even in there head (which isn’t really practical).
First do the logic if you need the formula look through the thread and get it because that’s the trick. once you work out the formula for 3 people or even 4 then you will prove that it works and is possible. once you understand the logic EVERYTHING else will fall into place and actually without the logic just about absolutely nothing from this exercise will fall into place.
it’s challenging and does take a bit of work and if you don’t intend to do that little bit of work then prepare to KEEP ON WONDERING…
What page is Indistinguishable’s game on?
Unless everyone knows that everyone leaves as soon as he knows his eye color, how does this puzzle work at all?
Doesn’t the puzzle specify that you don’t know there are only two colors? That your eyes could be any color?
Pitiful Yami Yugi - you cannot hope to defeat my Blues Logic Puzzle. And when I play three of them on the field, I can merge them into Blue-Eyes Ultimate Logic Puzzle!
What’s the difference between what you know to be true, and what you know to be possible? In general, you get the distinction, right? You’re just not clear how it applies here. The key point is that to the question, “Could the guru have called brown?” every islander can answer, “Yes”, but to the question, “Could the guru have called a different color?”, they can only answer, “Maybe”.
I feel like you’re nearly there, so I’ll try once more to push you over the hump. drew’s latest post, by the way, missed my premise that there are 120 brown-eyed islanders, so what he said was right, but not really relevant.
The 120 brown-eyed islanders on the 100th day realize they don’t have blue eyes, but really what they want is to leave the island. Here’s what each one would think:
- I see 119 people with brown eyes, but I don’t know what my own eye color is
- Whatever my own eye color, everyone on this island sees other people with brown eyes
- If I don’t have brown eyes, and the guru had called my eye color, but then I would have boarded the boat the first day and be sipping daiquiris in Mazatlan by now
- If I don’t have brown eyes, each other islander would know that if the guru had called my eye color, either I would have left alone on the first day, or with them on the second.
- If I do have brown eyes, each other islander knows he would have left alone on the first day if the guru had called another color. Basically, they would have reached my conclusion from step 3.
- Therefore none of us can pretend that the guru said another color because the results would conflict with our current situation.
- Whatever my eye color, the guru could have called brown, on behalf of all those other people I see.
- Based on my observation in step 2, everyone else also knows the guru could have called brown.
- Whatever my eye color, if the guru had called brown, everyone here right now would still be here, because there are 119 people with brown eyes and it’s only the 100th day.
- If my eyes aren’t brown, everyone else sees 118 people with brown eyes, so even in that case, they can pretend the guru called brown without there being any conflict with the current situation.
- If my eyes aren’t brown, then everyone else will be waiting to see if anyone leaves on day 118, but no one will, so they will all leave on the 119th day.
- If my eyes are brown, no one will leave on the 119th day either, so we can all leave on the 120th.
That’s about the best I can do for an explanation. Incidentally, the same thing would work if there were only 80 people with brown eyes. I think the general case is if there are n colors of eyes on the island, and there are at least of three people of each, and if the difference between counts of people with different eye colors is at least three (or possibly two, I’m still struggling with that one), then everyone gets off the island regardless of what color the guru chooses.
Is it also fair to say that the guru’s statement that he sees blue eyes it a BIT of a red herring because everyone sees a pair of blue eyes. But his pronouncement allows the islanders, who have no other way of communicating, to all get on the same page counting days?
No. It is vital that the guru state he sees a pair of blue eyes. If it didn’t matter what the guru said, the islanders could see a lightning strike and say, “Well, we could pretend a guru said he saw a pair of blue eyes.” Or, “Let’s just start counting nights now.” These are both as logical as counting brown eyes when the guru mentions blue; that is, not at all.
The important point is that everyone knows that everyone knows that … etc … someone has blue eyes. You can’t fake it by pretending it was said.
On day 101, if I’d told one of the remaining islanders he had brown eyes, would he have been any less surprised, in your view, than he would have been had I told him he had hazel eyes?
Check.
Check.
This is not grammatical. I think (but I’m not sure) you didn’t intend to have that word “but” in there. I can sign off on this statement if you take the “but” out.
Check.
check
This doesn’t follow as far as I can see. Can you explain what the results would be of the guru saying another color, and how exactly this result is made impossible by our current situation?
It appears you mean your lines 4 and 5 to explain what the results of calling another color would be. While line 5 does this under the hypothetical that I have brown eyes, line 4 fails to do so–since it explores a situation in which the guru calls my eye color, not some arbitrary non-brown eye color. And if we reword 4 as follows:
“If I don’t have brown eyes, each other islander would know that if the guru had called some non-brown color, either I would have left alone on the first day, or with them on the second.”
then it is no longer true. For this arbitrary non-brown color might have been my own color, in which case I’d leave the first day if they did not share it, or the second day if they did share it, or else the called non-brown color might have been a color that my eyes aren’t, and that a hypothetical other brown-eyed islander might have for all he knows, in which case that islander would have left on the first day and I never would have left.
It starts on page 2, post 68.
Go for it! I would myself, but this is probably one of the busiest weeks of my life…
Okay, but had the guru said, “I see a pair of brown eyes” it would follow the logic until all brown eyed people left on day 100, right?
ETA: In other words, its the guru mentioning an eye color that gets all of the islanders looking for that eye color and then knowing that…knowing that…knowing that others are looking and making logical deductions about that eye color?
That’s correct.
I’m pretty sure this is right. From which it follows that Greg Charles’ argument also is right. Stated a little differently, “everybody knows” is implied by the set-up of the puzzle, i.e., that everybody knows what s/he can observe and can assume everybody else does likewise (and draw the appropriate inferences). If this isn’t true, the inductive deduction never gets any traction.
Step 6 does not appear to be valid. The brown-eyed people *can *pretend that the guru said another colour (than brown), because he did!
The whole argument is based on what the Guru might have said, but didn’t. Therefore, steps 3, 4, and 5, while true, are of no use in working out what colour eyes one really has. You need sunsequent behaviour from the islanders to infer things from the Guru’s original statement, but the islanders only react to what the Guru did say, not what he might have said.
It is not right and neither is Greg Charles. An important point is that the islanders must know (not guess) their eye color before they get on the boat. Without going too far afield into the nature of knowledge, we can define an islander knowing something as:
If, in all possible worlds, something is seen to be true then an islander knows it to be true.
Once the guru speaks about blue eyes, the islanders each know that each know that each know (repeated how ever many times you like) that someone has blue eyes in all possible worlds. Once the second night passes, they know that everyone knows that everyone knows (repeated) that there are at least two people with blue eyes (Why this is necessary for the blue eyed people to leave the island is explained by people upthread who do a much better job about it than I could).
Until the guru speaks, they do not know this and are just guessing. If you are going to make the argument that we can pretend the guru said brown instead of blue, you’re choosing one possibility and ignoring the one where he said he saw a brown eyed person the next day. Or two days before. And more importantly, the real one in which he never said it before.
Because they’re just choosing a random event, they’re choosing one of many still possible worlds (And calling it a possible world is generous. It didn’t happen.) Therefore, the brown eyed people won’t know their eye color and are just guessing. The brown eyed people will not leave.
yeah they don’t know that there are only 2 colors but my point was that even in a best case scenario where you did have only 2 colors you still would be guessing if you weren’t sure.