Talk:Blue Eyes - Revision history

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

165.225.213.98 at 14:03, 27 August 2025

2025-08-27T14:03:42Z

84.43.20.118: Moved to (and answered at) the bottom.

2025-08-22T01:02:55Z

Moved to (and answered at) the bottom.

Giraffequeries at 00:48, 22 August 2025

2025-08-22T00:48:19Z

172.70.162.57 at 16:08, 6 March 2025

2025-03-06T16:08:53Z

104.23.190.137: Simple Logic

2025-03-06T14:56:36Z

Simple Logic

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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}}

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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
 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?
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 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)

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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'
		+

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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)

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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.

← Older revision		Revision as of 14:03, 27 August 2025
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	If there are N islanders with blue eyes, every person sees at least N-1 blue eyed persons. Person A with blue eyes seeing N-1 blue eyed persons has to consider the possibility that there might be a person B who only sees N-2 blue eyed people and acts accordingly. However, everyone in that scenario will agree that it is absolutely impossible for anyone to see N-3 or less blue eyed people and that case cannot possibly be considered by anyone. Therefore the induction step is invalid and nobody will ever leave the island for N>3. [[User:Boopers\|Boopers]] ([[User talk:Boopers\|talk]]) 18:07, 15 October 2021 (UTC)		If there are N islanders with blue eyes, every person sees at least N-1 blue eyed persons. Person A with blue eyes seeing N-1 blue eyed persons has to consider the possibility that there might be a person B who only sees N-2 blue eyed people and acts accordingly. However, everyone in that scenario will agree that it is absolutely impossible for anyone to see N-3 or less blue eyed people and that case cannot possibly be considered by anyone. Therefore the induction step is invalid and nobody will ever leave the island for N>3. [[User:Boopers\|Boopers]] ([[User talk:Boopers\|talk]]) 18:07, 15 October 2021 (UTC)
		+
		+	:So, Boopers, you would buy Situations 0 through 2 above (under "Question 2" of "Randall's follow-up questions"), and you would even buy Situation 3, namely "If I see 3 blue-eyed people, they might each be in situation 2 watching to see whether anyone in situation 1 leaves the second night (I know nobody will leave that night, but they wouldn't know this), in which case they would leave together on night 3; or else they might be in situation 3 just like me, in which case we'll all leave together on night 4", but having bought that, you won't buy Situation 4? [[Special:Contributions/165.225.213.98\|165.225.213.98]] 14:03, 27 August 2025 (UTC)

	If a person B only sees N-2 blue eyed people, then surely they have to consider the possibility of a person C who only sees N-3 people. Sure, person B doesn't actually exist in this scenario, but you'd have to consider that person A would have to consider what a hypothetical person B would have to consider. It's turtles all the way down. [[Special:Contributions/172.70.110.171\|172.70.110.171]] 00:17, 19 October 2021 (UTC)		If a person B only sees N-2 blue eyed people, then surely they have to consider the possibility of a person C who only sees N-3 people. Sure, person B doesn't actually exist in this scenario, but you'd have to consider that person A would have to consider what a hypothetical person B would have to consider. It's turtles all the way down. [[Special:Contributions/172.70.110.171\|172.70.110.171]] 00:17, 19 October 2021 (UTC)

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 Is it really incomplete on the grounds that Joel hasn't be identified?  Explanations of comics 57-59 leave no more explanation of "Scott" than that he appears to be Randall's friend.  The fact that we don't have a last name for him doesn't make either [[Scott]] or those comic explanations incomplete.  Similarly, not have a full identifier for "Joel" in this one doesn't, in my opinion, warrant an incomplete tag.  I'm removing the tag.  If anyone object, revert it. [[User:Djbrasier|Djbrasier]] ([[User talk:Djbrasier|talk]]) 19:22, 22 May 2015 (UTC)
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 Why can't the guru just say "I see 100 blue eyed people and 100 brown eyed people" on day one?[[Special:Contributions/104.23.190.137|104.23.190.137]] 14:56, 6 March 2025 (UTC)
 :Then there wouldn't be a puzzle. (Or, if you prefer, "only the guru knows, probably hence why they're the guru".) You might as well ask why there's the rules on what people must and must not do (not openly speak/sign-language to others about their own status, and leave immediately upon having the required knowledge, plus ''never'' try to look into any decent reflective surface). Given the setting (presume some sort of island of myth), probably there's some sort of enchantment/geas/divine-command laid down upon the community, whether intended to be so restrictive (yet have the logical loophole that allows the guru their single utterance of no ''immediate'' value) or an unfortunate mistake by whatever power it was that blanketed them all within this scenario. [[Special:Contributions/172.70.162.57|172.70.162.57]] 16:08, 6 March 2025 (UTC)

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		+	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)
		+
	Is it really incomplete on the grounds that Joel hasn't be identified? Explanations of comics 57-59 leave no more explanation of "Scott" than that he appears to be Randall's friend. The fact that we don't have a last name for him doesn't make either [[Scott]] or those comic explanations incomplete. Similarly, not have a full identifier for "Joel" in this one doesn't, in my opinion, warrant an incomplete tag. I'm removing the tag. If anyone object, revert it. [[User:Djbrasier\|Djbrasier]] ([[User talk:Djbrasier\|talk]]) 19:22, 22 May 2015 (UTC)		Is it really incomplete on the grounds that Joel hasn't be identified? Explanations of comics 57-59 leave no more explanation of "Scott" than that he appears to be Randall's friend. The fact that we don't have a last name for him doesn't make either [[Scott]] or those comic explanations incomplete. Similarly, not have a full identifier for "Joel" in this one doesn't, in my opinion, warrant an incomplete tag. I'm removing the tag. If anyone object, revert it. [[User:Djbrasier\|Djbrasier]] ([[User talk:Djbrasier\|talk]]) 19:22, 22 May 2015 (UTC)

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	Why can't the guru just say "I see 100 blue eyed people and 100 brown eyed people" on day one?[[Special:Contributions/104.23.190.137\|104.23.190.137]] 14:56, 6 March 2025 (UTC)		Why can't the guru just say "I see 100 blue eyed people and 100 brown eyed people" on day one?[[Special:Contributions/104.23.190.137\|104.23.190.137]] 14:56, 6 March 2025 (UTC)
		+	:Then there wouldn't be a puzzle. (Or, if you prefer, "only the guru knows, probably hence why they're the guru".) You might as well ask why there's the rules on what people must and must not do (not openly speak/sign-language to others about their own status, and leave immediately upon having the required knowledge, plus ''never'' try to look into any decent reflective surface). Given the setting (presume some sort of island of myth), probably there's some sort of enchantment/geas/divine-command laid down upon the community, whether intended to be so restrictive (yet have the logical loophole that allows the guru their single utterance of no ''immediate'' value) or an unfortunate mistake by whatever power it was that blanketed them all within this scenario. [[Special:Contributions/172.70.162.57\|172.70.162.57]] 16:08, 6 March 2025 (UTC)

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	:::When the day count gets high enough that theoretically everybody that a person sees as blue ''should'' have left, this prompts the blueness-realisation in that person (and all fellow blues, who had themselves down as the unknown quantity instead) and creates a departure event upon the next day. (And thus forestalls all non-blues from erroneously thinking themselves "the last self-unknowing blue" and trying to depart the day after.)		:::When the day count gets high enough that theoretically everybody that a person sees as blue ''should'' have left, this prompts the blueness-realisation in that person (and all fellow blues, who had themselves down as the unknown quantity instead) and creates a departure event upon the next day. (And thus forestalls all non-blues from erroneously thinking themselves "the last self-unknowing blue" and trying to depart the day after.)
	:::Simple? [[Special:Contributions/172.70.160.230\|172.70.160.230]] 08:30, 2 October 2024 (UTC)		:::Simple? [[Special:Contributions/172.70.160.230\|172.70.160.230]] 08:30, 2 October 2024 (UTC)
		+
		+	Why can't the guru just say "I see 100 blue eyed people and 100 brown eyed people" on day one?[[Special:Contributions/104.23.190.137\|104.23.190.137]] 14:56, 6 March 2025 (UTC)