Editing Talk:Blue Eyes
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This was bugging me today - specifically the guru doesn't seem to actually give any information, because with at least 3 blue-eyed people, everyone on the island knows that the guru sees people with blue eyes, and also everyone knows that everyone knows the guru sees people with blue eyes. So for a while I thought the brown-eyed people must have as much information as the blue-eyed people, and either they both could leave or neither could leave. | This was bugging me today - specifically the guru doesn't seem to actually give any information, because with at least 3 blue-eyed people, everyone on the island knows that the guru sees people with blue eyes, and also everyone knows that everyone knows the guru sees people with blue eyes. So for a while I thought the brown-eyed people must have as much information as the blue-eyed people, and either they both could leave or neither could leave. | ||
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After a bunch of reading and testing possibilities I think I've actually figured it out now and why only blue-eyed people leave, but I haven't seen an actual good explanation for it yet, so here's my explanation: The information the guru gives is that, NO MATTER HOW MANY BLUE-EYED PEOPLE THERE ARE, they can figure out they have blue eyes. It is important that it is possible for blue-eyed people to be able to solve it for EVERY number, even if everyone knows there is more people than that number (basically because, everyone doesn't know that everyone knows there is more than that number and there's a gap in their logic without knowing that). If there is any number for which blue-eyed people cannot figure it out, then any solution (namely, what I thought before testing possibilities) would require that there is a number N of blue-eyed people that cannot leave, but a number N+1 of blue-eyed people that can leave. This is self-contradicting though. If N blue-eyed people can't figure it out, than N+1 people (regardless of eye color) can't get meaningful information from the action of those N blue-eyed people. And since they can't get meaningful information from N people's actions, N+1 people can't tell if there are N people and that individual is not blue eyed, or N+1 people and they are blue-eyed. It would be logically incorrect for them to assume an eye color at that point, which means they don't know if they can leave, and then N+2 people are similarly unable to get meaningful information from N+1 people's actions, and so on. Because a single blue-eyed person cannot figure it out, more blue-eyed people (regardless of number) cannot make any assumptions without additional information. Then the guru effectively states a single blue-eyed person could leave immediately (which means 2 could leave the next night confidently, and thus 3 the next, and so on in an UNBROKEN chain). Kejardon - [[Special:Contributions/162.158.214.82|162.158.214.82]] 11:15, 9 January 2020 (UTC) (I doublechecked and edited/corrected my post kind of at the same time, so your reply doesn't make sense anymore, sorry Lupo. Feel free to delete these two sentences if you change/delete your reply) | After a bunch of reading and testing possibilities I think I've actually figured it out now and why only blue-eyed people leave, but I haven't seen an actual good explanation for it yet, so here's my explanation: The information the guru gives is that, NO MATTER HOW MANY BLUE-EYED PEOPLE THERE ARE, they can figure out they have blue eyes. It is important that it is possible for blue-eyed people to be able to solve it for EVERY number, even if everyone knows there is more people than that number (basically because, everyone doesn't know that everyone knows there is more than that number and there's a gap in their logic without knowing that). If there is any number for which blue-eyed people cannot figure it out, then any solution (namely, what I thought before testing possibilities) would require that there is a number N of blue-eyed people that cannot leave, but a number N+1 of blue-eyed people that can leave. This is self-contradicting though. If N blue-eyed people can't figure it out, than N+1 people (regardless of eye color) can't get meaningful information from the action of those N blue-eyed people. And since they can't get meaningful information from N people's actions, N+1 people can't tell if there are N people and that individual is not blue eyed, or N+1 people and they are blue-eyed. It would be logically incorrect for them to assume an eye color at that point, which means they don't know if they can leave, and then N+2 people are similarly unable to get meaningful information from N+1 people's actions, and so on. Because a single blue-eyed person cannot figure it out, more blue-eyed people (regardless of number) cannot make any assumptions without additional information. Then the guru effectively states a single blue-eyed person could leave immediately (which means 2 could leave the next night confidently, and thus 3 the next, and so on in an UNBROKEN chain). Kejardon - [[Special:Contributions/162.158.214.82|162.158.214.82]] 11:15, 9 January 2020 (UTC) (I doublechecked and edited/corrected my post kind of at the same time, so your reply doesn't make sense anymore, sorry Lupo. Feel free to delete these two sentences if you change/delete your reply) |