Talk:Blue Eyes - Revision history

81.179.199.253: /* Another question */ does it involve signing?

2026-05-15T23:23:54Z

‎Another question: does it involve signing?

69.125.189.79: /* Another question */ new section

2026-05-15T20:13:16Z

‎Another question: new section

81.179.199.253 at 17:34, 26 April 2026

2026-04-26T17:34:31Z

81.179.199.253: /* I have a different solution */

2026-04-26T17:28:25Z

‎I have a different solution

69.125.189.79: /* I have a different solution */ new section

2026-04-26T16:01:57Z

‎I have a different solution: new section

DollarStoreBa'al: fixed a typo

2026-02-12T19:09:51Z

fixed a typo

92.23.2.208: Signed, and sent tothe end, to be chronolofical.

2025-12-27T18:23:12Z

Signed, and sent tothe end, to be chronolofical.

2001:8003:DC65:7E01:4460:4138:3D1A:2B74 at 09:59, 27 December 2025

2025-12-27T09:59:43Z

165.225.213.98: Attempting to reduce the logical confusion

2025-09-09T13:59:48Z

Attempting to reduce the logical confusion

165.225.213.87: Responded to Flewk

2025-09-02T16:27:36Z

Responded to Flewk

← Older revision		Revision as of 23:23, 15 May 2026
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	There is exactly one thing the guru can say that gets everyone (including the guru herself) off of the island. What is it?		There is exactly one thing the guru can say that gets everyone (including the guru herself) off of the island. What is it?

−	There is an answer to this.	+	There is an answer to this. {{unsigned ip\|69.125.189.79\|20:13, 15 May 2026}}

← Older revision		Revision as of 20:13, 15 May 2026
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	:But is that assumption as perfectly logical as necessary? It may be playing the odds, to a (possible) immediate advantage, but you could just as easily be proven immediately wrong. Or as immediate as when the evacuating group gathers and starts to consider the choices made by everyone they can see having fallen for the same presumption. [[Special:Contributions/81.179.199.253\|81.179.199.253]] 17:28, 26 April 2026 (UTC)		:But is that assumption as perfectly logical as necessary? It may be playing the odds, to a (possible) immediate advantage, but you could just as easily be proven immediately wrong. Or as immediate as when the evacuating group gathers and starts to consider the choices made by everyone they can see having fallen for the same presumption. [[Special:Contributions/81.179.199.253\|81.179.199.253]] 17:28, 26 April 2026 (UTC)
	:(To expand on that... "I can see someone with blue eyes" doesn't even ''sound'' like it means "most, or nearly most, of the people I see have blue eyes". It sounds more like "I see one person with blue eyes", though it is technically "I see ''at least'' one person...". It only means anything definite for the immediate 'virtual' case of a single person (unknowingly of blue eyes themself) who can only see non-blue-eyes people, which of course cannot be taken advantage of in the given scenario where there is nobody who can absorb that message without further iterations of per-day logic.) [[Special:Contributions/81.179.199.253\|81.179.199.253]] 17:34, 26 April 2026 (UTC)		:(To expand on that... "I can see someone with blue eyes" doesn't even ''sound'' like it means "most, or nearly most, of the people I see have blue eyes". It sounds more like "I see one person with blue eyes", though it is technically "I see ''at least'' one person...". It only means anything definite for the immediate 'virtual' case of a single person (unknowingly of blue eyes themself) who can only see non-blue-eyes people, which of course cannot be taken advantage of in the given scenario where there is nobody who can absorb that message without further iterations of per-day logic.) [[Special:Contributions/81.179.199.253\|81.179.199.253]] 17:34, 26 April 2026 (UTC)
		+
		+	== Another question ==
		+
		+	If anyone wants another question, here it is:
		+
		+	Let us say that everyone knows that the only eye colors present are blue, brown and green. (The guru also knows this, but she could assume that there are zero green).
		+
		+	There is exactly one thing the guru can say that gets everyone (including the guru herself) off of the island. What is it?
		+
		+	There is an answer to this.

← Older revision		Revision as of 17:34, 26 April 2026
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	I would assume that the guru would give the information allowing escape to the largest group, or, if the groups are tied, to a random group. If I were brown eyed, this would give the same result. If I were blue-eyed, I would leave on day one, because if I weren’t blue eyed, then brown would have a majority and the guru would have given information to them. {{unsigned ip\|69.125.189.79\|16:01, 26 April 2026}}		I would assume that the guru would give the information allowing escape to the largest group, or, if the groups are tied, to a random group. If I were brown eyed, this would give the same result. If I were blue-eyed, I would leave on day one, because if I weren’t blue eyed, then brown would have a majority and the guru would have given information to them. {{unsigned ip\|69.125.189.79\|16:01, 26 April 2026}}
	:But is that assumption as perfectly logical as necessary? It may be playing the odds, to a (possible) immediate advantage, but you could just as easily be proven immediately wrong. Or as immediate as when the evacuating group gathers and starts to consider the choices made by everyone they can see having fallen for the same presumption. [[Special:Contributions/81.179.199.253\|81.179.199.253]] 17:28, 26 April 2026 (UTC)		:But is that assumption as perfectly logical as necessary? It may be playing the odds, to a (possible) immediate advantage, but you could just as easily be proven immediately wrong. Or as immediate as when the evacuating group gathers and starts to consider the choices made by everyone they can see having fallen for the same presumption. [[Special:Contributions/81.179.199.253\|81.179.199.253]] 17:28, 26 April 2026 (UTC)
		+	:(To expand on that... "I can see someone with blue eyes" doesn't even ''sound'' like it means "most, or nearly most, of the people I see have blue eyes". It sounds more like "I see one person with blue eyes", though it is technically "I see ''at least'' one person...". It only means anything definite for the immediate 'virtual' case of a single person (unknowingly of blue eyes themself) who can only see non-blue-eyes people, which of course cannot be taken advantage of in the given scenario where there is nobody who can absorb that message without further iterations of per-day logic.) [[Special:Contributions/81.179.199.253\|81.179.199.253]] 17:34, 26 April 2026 (UTC)

@@ Line 215: / Line 215: @@
 I think that the use of the word 'Guru' here confuses Zen and Indian mysticism. The puzzle depends on intentionality, a necessary condition which is not made clear by the word 'Guru' {{unsigned ip|2001:8003:dc65:7e01:4460:4138:3d1a:2b74|09:59, 27 December 2025}}
-== I have a different solution ==
+;I have a different solution
 Here is what I personally would do, although this relies on the fact that the guru is a good person:
-I would assume that the guru would give the information allowing escape to the largest group, or, if the groups are tied, to a random group. If I were brown eyed, this would give the same result. If I were blue-eyed, I would leave on day one, because if I weren’t blue eyed, then brown would have a majority and the guru would have given information to them.
+I would assume that the guru would give the information allowing escape to the largest group, or, if the groups are tied, to a random group. If I were brown eyed, this would give the same result. If I were blue-eyed, I would leave on day one, because if I weren’t blue eyed, then brown would have a majority and the guru would have given information to them. {{unsigned ip|69.125.189.79|16:01, 26 April 2026}}

← Older revision		Revision as of 16:01, 26 April 2026
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	I think that the use of the word 'Guru' here confuses Zen and Indian mysticism. The puzzle depends on intentionality, a necessary condition which is not made clear by the word 'Guru' {{unsigned ip\|2001:8003:dc65:7e01:4460:4138:3d1a:2b74\|09:59, 27 December 2025}}		I think that the use of the word 'Guru' here confuses Zen and Indian mysticism. The puzzle depends on intentionality, a necessary condition which is not made clear by the word 'Guru' {{unsigned ip\|2001:8003:dc65:7e01:4460:4138:3d1a:2b74\|09:59, 27 December 2025}}
		+
		+	== I have a different solution ==
		+
		+	Here is what I personally would do, although this relies on the fact that the guru is a good person:
		+
		+	I would assume that the guru would give the information allowing escape to the largest group, or, if the groups are tied, to a random group. If I were brown eyed, this would give the same result. If I were blue-eyed, I would leave on day one, because if I weren’t blue eyed, then brown would have a majority and the guru would have given information to them.

← Older revision		Revision as of 19:09, 12 February 2026
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	:The fact that the [[37: Hyphen]] "My hobby" comic is included in this page? [[Special:Contributions/84.43.20.118\|84.43.20.118]] 01:02, 22 August 2025 (UTC)		:The fact that the [[37: Hyphen]] "My hobby" comic is included in this page? [[Special:Contributions/84.43.20.118\|84.43.20.118]] 01:02, 22 August 2025 (UTC)

−	I think that the use of the word 'Guru' here confuses Zen and Indian mysticism. The puzzle depends on intentionality, a necessary condition which is not made clear by the word 'Guru' {{unsigned up\|2001:8003:dc65:7e01:4460:4138:3d1a:2b74\|09:59, 27 December 2025}}	+	I think that the use of the word 'Guru' here confuses Zen and Indian mysticism. The puzzle depends on intentionality, a necessary condition which is not made clear by the word 'Guru' {{unsigned ip\|2001:8003:dc65:7e01:4460:4138:3d1a:2b74\|09:59, 27 December 2025}}

@@ Line 2: / Line 2: @@
 The proof for this puzzle is incomplete, if not wrong. The theorem is too weak, it should be: "Theorem: N blue eyed people with Nth order knowledge of all N people being logicians, N people having blue eyes, and any blue eyed person will leave as soon as possible after deducing they have blue eyes, will be able to leave on the Nth day." This may seem pedantic, but it really gets to the heart of the problem, which is trying to illustrate the use of orders of knowledge. In the theorem as stated, just N blue eyed people will leave on the Nth day, the proof for the inductive steps does not hold. You need to further assume that the person is able to deduce the hypothesis (which should be proven). In other words, you say X-1 people would leave on the (X-1)th day by hypothesis, so the Xth person knows he can leave on the Xth day. But you did not prove that the Xth person can actually deduce this, namely that he has all the information necessary to do so. In the correctly stated hypothesis, you then need to show that N + 1 people with (N+1)th order knowledge of all those things can deduce that the N people would leave if it was just them, and further that N+1 people have (N+1)th order knowledge of all these things. This is very important, and holds true (Since N+1th order knowledge is equivalent to knowing the N people have the Nth order knowledge necessary to fulfill the hypothesis, and by symmetry if the N logicians can figure it out the (N+1)th can too. Also, they have (N+1)th order knowledge of people leaving as soon as they can and everyone being a logician since in the proper statement of the puzzle it should be noted this is common knowledge, and the guru makes the knowledge of someone having blue eyes common knowledge.). Then you have a full proof, since you have now included that they can actually deduce the inductive step. Again, this may seem pedantic, but is really necessary both to be correct and as it illustrates the key of the puzzle, namely the guru gives 100th order knowledge of someone having blue eyes (this is the main problem people have, realizing the concrete piece of information the guru gives). [[User:Jlangy|Jlangy]] ([[User talk:Jlangy|talk]]) 00:29, 9 July 2015
 What I don't follow here is that there's no clarification that the Guru is talking about someone different each time. Just because she says "I see someone with blue eyes" N times doesn't mean that there are N people with blue eyes; she could be talking about the same person every time, or each of two people half the time, etc. Can anyone clarify this?
@@ Line 217: / Line 212: @@
 Why is this in [[:Category:My_Hobby|My Hobby]]? Like, what's the hobby? [[User:Giraffequeries|Giraffequeries]] ([[User talk:Giraffequeries|talk]]) 00:48, 22 August 2025 (UTC)
 :The fact that the [[37: Hyphen]] "My hobby" comic is included in this page? [[Special:Contributions/84.43.20.118|84.43.20.118]] 01:02, 22 August 2025 (UTC)

← Older revision		Revision as of 09:59, 27 December 2025
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	The proof for this puzzle is incomplete, if not wrong. The theorem is too weak, it should be: "Theorem: N blue eyed people with Nth order knowledge of all N people being logicians, N people having blue eyes, and any blue eyed person will leave as soon as possible after deducing they have blue eyes, will be able to leave on the Nth day." This may seem pedantic, but it really gets to the heart of the problem, which is trying to illustrate the use of orders of knowledge. In the theorem as stated, just N blue eyed people will leave on the Nth day, the proof for the inductive steps does not hold. You need to further assume that the person is able to deduce the hypothesis (which should be proven). In other words, you say X-1 people would leave on the (X-1)th day by hypothesis, so the Xth person knows he can leave on the Xth day. But you did not prove that the Xth person can actually deduce this, namely that he has all the information necessary to do so. In the correctly stated hypothesis, you then need to show that N + 1 people with (N+1)th order knowledge of all those things can deduce that the N people would leave if it was just them, and further that N+1 people have (N+1)th order knowledge of all these things. This is very important, and holds true (Since N+1th order knowledge is equivalent to knowing the N people have the Nth order knowledge necessary to fulfill the hypothesis, and by symmetry if the N logicians can figure it out the (N+1)th can too. Also, they have (N+1)th order knowledge of people leaving as soon as they can and everyone being a logician since in the proper statement of the puzzle it should be noted this is common knowledge, and the guru makes the knowledge of someone having blue eyes common knowledge.). Then you have a full proof, since you have now included that they can actually deduce the inductive step. Again, this may seem pedantic, but is really necessary both to be correct and as it illustrates the key of the puzzle, namely the guru gives 100th order knowledge of someone having blue eyes (this is the main problem people have, realizing the concrete piece of information the guru gives). [[User:Jlangy\|Jlangy]] ([[User talk:Jlangy\|talk]]) 00:29, 9 July 2015		The proof for this puzzle is incomplete, if not wrong. The theorem is too weak, it should be: "Theorem: N blue eyed people with Nth order knowledge of all N people being logicians, N people having blue eyes, and any blue eyed person will leave as soon as possible after deducing they have blue eyes, will be able to leave on the Nth day." This may seem pedantic, but it really gets to the heart of the problem, which is trying to illustrate the use of orders of knowledge. In the theorem as stated, just N blue eyed people will leave on the Nth day, the proof for the inductive steps does not hold. You need to further assume that the person is able to deduce the hypothesis (which should be proven). In other words, you say X-1 people would leave on the (X-1)th day by hypothesis, so the Xth person knows he can leave on the Xth day. But you did not prove that the Xth person can actually deduce this, namely that he has all the information necessary to do so. In the correctly stated hypothesis, you then need to show that N + 1 people with (N+1)th order knowledge of all those things can deduce that the N people would leave if it was just them, and further that N+1 people have (N+1)th order knowledge of all these things. This is very important, and holds true (Since N+1th order knowledge is equivalent to knowing the N people have the Nth order knowledge necessary to fulfill the hypothesis, and by symmetry if the N logicians can figure it out the (N+1)th can too. Also, they have (N+1)th order knowledge of people leaving as soon as they can and everyone being a logician since in the proper statement of the puzzle it should be noted this is common knowledge, and the guru makes the knowledge of someone having blue eyes common knowledge.). Then you have a full proof, since you have now included that they can actually deduce the inductive step. Again, this may seem pedantic, but is really necessary both to be correct and as it illustrates the key of the puzzle, namely the guru gives 100th order knowledge of someone having blue eyes (this is the main problem people have, realizing the concrete piece of information the guru gives). [[User:Jlangy\|Jlangy]] ([[User talk:Jlangy\|talk]]) 00:29, 9 July 2015
		+
		+
		+	I think that the use of the word 'Guru' here confuses Zen and Indian mysticism. The puzzle depends on intentionality, a necessary condition which is not made clear by the word 'Guru'
		+

← Older revision		Revision as of 13:59, 9 September 2025
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	:You are 99% of the way there... to explaining why the solution does not work at all. You are absolutely correct that there is no reason for anyone to assume that anyone else would ever assume less than 97 blue-eyed people, and therefore the induction does not carry through. But this means they have absolutely no grounds whatsoever to start making any assumptions about who could possibly figure anything more out and therefore who & when could possibly be getting onto the boat. In the presented scenario, no one ever leaves. It could only be different if the guru spoke about seeing 98 blue-eyed persons. [[Special:Contributions/172.70.85.125\|172.70.85.125]] 11:11, 30 September 2023 (UTC)		:You are 99% of the way there... to explaining why the solution does not work at all. You are absolutely correct that there is no reason for anyone to assume that anyone else would ever assume less than 97 blue-eyed people, and therefore the induction does not carry through. But this means they have absolutely no grounds whatsoever to start making any assumptions about who could possibly figure anything more out and therefore who & when could possibly be getting onto the boat. In the presented scenario, no one ever leaves. It could only be different if the guru spoke about seeing 98 blue-eyed persons. [[Special:Contributions/172.70.85.125\|172.70.85.125]] 11:11, 30 September 2023 (UTC)
		+
		+	::No, neither of you are "99% of the way there". Dokushin's claim that the induction doesn't work is supported by nothing more than arbitrarily terminating the inductive chain after 3 steps, a move which is itself backed up by a whole lot of "I can terminate the chain after 3 steps, because, well, because I can terminate the chain after 3 steps". No, logic doesn't work that way. He says "every[one] knows, with certainty, there are 97 blue eyed people at a minimum". No, everyone knows, with certainty, that there are 99 other blue-eyed people. They can each see that. But none of them know their own eye colour, and seeing everyone else's eyes doesn't help them in the slightest. Not at first. They each have to work that out for themselves, symmetrically and in parallel, one step at a time, one day at a time, one empty boat departure at a time, starting from only what the Guru told them - i.e. 1. Not 97. That's a totally arbitrary number. [[Special:Contributions/165.225.213.98\|165.225.213.98]] 13:59, 9 September 2025 (UTC)

	;Unstated assumption (about motives)		;Unstated assumption (about motives)

← Older revision		Revision as of 16:27, 2 September 2025
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	[[User:Flewk\|Flewk]] ([[User talk:Flewk\|talk]]) 09:26, 26 December 2015 (UTC)		[[User:Flewk\|Flewk]] ([[User talk:Flewk\|talk]]) 09:26, 26 December 2015 (UTC)
		+
		+	:No, not quite. Although Blue #100 can see 99 other blues, he doesn't know that he's a blue-eye. So although he knows that each of those 99 can see 98 other blue-eyes, none of them know their own eye colour either. So in Blue #100's perspective, each of those 99 would have to assume that they may only be able to see 98, as you said - however, therefore, those 98 (from the perspective of any of the 99, itself being imagined from the perspective of #100) for the same reasons can themselves only assume that each of those 98 can see at most 97... etc. There is no lower limit until the Guru provides one. [[Special:Contributions/165.225.213.87\|165.225.213.87]] 16:27, 2 September 2025 (UTC)

	The solution here is different to Randall's solution, and I think is actually incorrect for two reasons that add confusion and prevented me from understanding the solution until I'd thought about Randall's solution and realised these are actually different.		The solution here is different to Randall's solution, and I think is actually incorrect for two reasons that add confusion and prevented me from understanding the solution until I'd thought about Randall's solution and realised these are actually different.