euklyd Posted April 17, 2014 Share Posted April 17, 2014 Got it. Thanks to Makaze to confirming that I wasn't making shitty logical leaps. [4/17/14 3:21:06 PM] Makaze: What is the answer to the original riddle, then? [4/17/14 3:21:46 PM] Euklyd: [4/17/14 3:16:41 PM] Euklyd: they leave on D[number of blue people] [4/17/14 3:16:55 PM] Euklyd: And all at the same time. [4/17/14 3:21:49 PM] Euklyd: therefore D100 [4/17/14 3:21:52 PM] Euklyd: all the blue [4/17/14 3:22:32 PM] Euklyd: Is there something else that I need to answer? [4/17/14 3:23:24 PM] Makaze: Nope. Not sure if I would have figured it out entirely on my own, but I wasn't being led to the solution at all, so I'm happy. I'd say the thing that gave it away was Hextator's post about "it involves induction." was pointed out that brown eyes too, actually. I considered that and then lost that train of thought before examining it. Guru never leaves, though. Now to read other people's spoiler tags. Quote Link to comment Share on other sites More sharing options...
Makaze Posted April 17, 2014 Share Posted April 17, 2014 was pointed out that brown eyes too, actually. I considered that and then lost that train of thought before examining it. Guru never leaves, though. Now to read other people's spoiler tags. Steal my thunder, why don't you. Quote Link to comment Share on other sites More sharing options...
Kriemhild Posted April 17, 2014 Share Posted April 17, 2014 Got it. Thanks to Makaze to confirming that I wasn't making shitty logical leaps. [4/17/14 3:21:06 PM] Makaze: What is the answer to the original riddle, then? [4/17/14 3:21:46 PM] Euklyd: [4/17/14 3:16:41 PM] Euklyd: they leave on D[number of blue people] [4/17/14 3:16:55 PM] Euklyd: And all at the same time. [4/17/14 3:21:49 PM] Euklyd: therefore D100 [4/17/14 3:21:52 PM] Euklyd: all the blue [4/17/14 3:22:32 PM] Euklyd: Is there something else that I need to answer? [4/17/14 3:23:24 PM] Makaze: Nope. Not sure if I would have figured it out entirely on my own, but I wasn't being led to the solution at all, so I'm happy. I'd say the thing that gave it away was Hextator's post about "it involves induction." I'm not sure how it involves induction, actually. What bugged me the most was that the Guru basically confirmed a fact that everybody already knows, since everybody sees 99-100 blue-eyed people. So I figured that the only way it could have any effect is if it affected their perception of what other people think. Each blue-eyed person deduces that b is either 100 or 99, but for the Guru to affect anything, there must be a possibility of b = 0 that is eliminated. Then I thought of the chain of hypothetical scenarios that reduces the 99 all the way down to 0, which is then eliminated by the Guru. The rest was built from my imagination of what would happen. Honestly, if the question didn't explicitly say that the answer is not "no one leaves the island", I would probably have just accepted that as the solution without trying to think. But nope, the Guru is really clever, and wanted to free all of the blue-eyed people if they had faith in each others' perfect logical reasoning abilities. The sad part is that the Guru herself will never be able to leave the island even if she frees everyone else... Quote Link to comment Share on other sites More sharing options...
Makaze Posted April 17, 2014 Share Posted April 17, 2014 (edited) I'm not sure how it involves induction, actually. What bugged me the most was that the Guru basically confirmed a fact that everybody already knows, since everybody sees 99-100 blue-eyed people. So I figured that the only way it could have any effect is if it affected their perception of what other people think. Each blue-eyed person deduces that b is either 100 or 99, but for the Guru to affect anything, there must be a possibility of b = 0 that is eliminated. Then I thought of the chain of hypothetical scenarios that reduces the 99 all the way down to 0, which is then eliminated by the Guru. The rest was built from my imagination of what would happen. Honestly, if the question didn't explicitly say that the answer is not "no one leaves the island", I would probably have just accepted that as the solution without trying to think. But nope, the Guru is really clever, and wanted to free all of the blue-eyed people if they had faith in each others' perfect logical reasoning abilities. The sad part is that the Guru herself will never be able to leave the island even if she frees everyone else... Covered these points with Euklyd. There is a mix of induction and deduction. We are given a very small amount of information and must extrapolate up from the bottom to reach a general rule instead of reaching a particular conclusion. The induction part is where you make your hypothesis about there being only 99 blue eyed people and test it by waiting. The deduction part is where you work with the data you get back from your test. That is, assuming I have a proper understanding of inductive and deductive reasoning. Feel free to correct me. The Guru's purpose is compatibility and thought leading. The Guru would be necessary if there were only one blue eyed person. Thinking of a scenario where there is only one blue eyed person is important to solving the puzzle. Edited April 17, 2014 by Makaze Quote Link to comment Share on other sites More sharing options...
Kriemhild Posted April 17, 2014 Share Posted April 17, 2014 (edited) I can already imagine the despair of those hundred brown-eyed people that waited 99 nights hoping that they were among the blue-eyed people, only to be emotionally crushed when they see the 100 blue-eyed people all leaving on the 100th night... Edited April 17, 2014 by Railgun Quote Link to comment Share on other sites More sharing options...
euklyd Posted April 17, 2014 Share Posted April 17, 2014 Guru would also be necessary if there were only two blue-eyed people, actually. Neither one would know that the other knows that there exist blue-eyed people. Quote Link to comment Share on other sites More sharing options...
Aleph Posted April 17, 2014 Share Posted April 17, 2014 (edited) Broto...that IS induction. You prove the base case for the case of n = 1 (how you determined the guru was even be important, which also fortifies Makaze's point about studying the n = 1 case despite that n = 100), then prove that n + 1 holds for any n >= 1 (the chain you spoke of). @euklyd Well of course, the need for the guru isn't going to go away regardless of what n is, which is why need to test every n. Edited April 17, 2014 by Kaname Quote Link to comment Share on other sites More sharing options...
Makaze Posted April 17, 2014 Share Posted April 17, 2014 I can already imagine the despair of those hundred brown-eyed people that waited 99 nights hoping that they were among the blue-eyed people, only to be emotionally crushed when they see the 100 blue-eyed people all leaving on the 100th night... The brown eyed people can leave using the same reasoning the blue eyed people use. All 200 leave on the 100th day. Quote Link to comment Share on other sites More sharing options...
Makaze Posted April 17, 2014 Share Posted April 17, 2014 (edited) Broto...that IS induction. You prove the base case for the case of n = 1 (how you determined the guru was even be important, which also fortifies Makaze's point about studying the n = 1 case despite that n = 100), then prove that n + 1 holds for any n >= 1 (the chain you spoke of). @euklyd Well of course, the need for the guru isn't going to go away regardless of what n is, which is why need to test every n. The guru is unnecessary for n > 2 because their statement adds no information if there are at least three of the color. Edited April 17, 2014 by Makaze Quote Link to comment Share on other sites More sharing options...
Kriemhild Posted April 18, 2014 Share Posted April 18, 2014 (edited) The brown eyed people can leave using the same reasoning the blue eyed people use. All 200 leave on the 100th day. The guru is unnecessary for n > 2 because their statement adds no information if there are at least three of the color. Uh, I think you're missing the point here. The brown-eyed people won't be able to deduce their own eye color. The only effect the guru's statement will have on the brown-eyed people is that they will know that they don't have blue eyes after all hundred blue-eyed people leave. Even if there was only one brown-eyed person, he won't know if he has brown eyes or red eyes or something else. The guru's statement doesn't directly add information. But it changes how you think the others would think. If there was 1 blue-eyed person, he'd leave on the first night because of what the guru said. If there were 2 blue-eyed people, the fact that nobody left on the first night will assure them that there are actually 2 blue-eyed people, so they both leave on the second night. Even though the guru didn't tell them anything that they didn't already know before, the guru's statement is what makes the lack of reaction in the first night to be relevant. Likewise, if there are 3 blue-eyed people, the fact that nobody left on the second night will assure all three of them that they have blue eyes and they leave on the third night. And if there are a hundred blue-eyed people, the fact that nobody left on the 99th night will assure them that they all have blue eyes and leave the island on the 100th night. But regardless of how many brown-eyed people there are, the guru's statement won't let them identify their own eye color. All they'll learn is that they don't have blue eyes, because 100 blue-eyed people already left on the 100th night. Edited April 18, 2014 by Railgun Quote Link to comment Share on other sites More sharing options...
Elieson Posted April 18, 2014 Share Posted April 18, 2014 This thread is no longer fun Quote Link to comment Share on other sites More sharing options...
Balcerzak Posted April 18, 2014 Share Posted April 18, 2014 (edited) A teacher asks their student: "Okay, say you have ten cakes, and somebody asks for two. How many cakes would you have left?" The student replies: "Ten." Teacher smiles a little, thinks to themselves 'I see what you did there', and tries again: "Fine, you have ten cakes but someone takes two cakes from you forcibly. Then what?" Student thinks deeply for a minute before confessing: "I guess I'd need to figure out how to dispose of a dead body." Edited April 18, 2014 by Balcerzak Quote Link to comment Share on other sites More sharing options...
Aleph Posted April 18, 2014 Share Posted April 18, 2014 Ballerzak bringing his violent lust and lustfully violent ways into the math jokes thread Didn't the thing with the stuff say that everyone knew that the only possible eye colours were the 3 and that there would be only one person with green eyes? Quote Link to comment Share on other sites More sharing options...
Integrity Posted April 18, 2014 Share Posted April 18, 2014 jesus christ did you fucking nerds just post a whole page of spoiler tags Quote Link to comment Share on other sites More sharing options...
Original Alear Posted April 18, 2014 Share Posted April 18, 2014 Richter and Poly broke it up a bit. Quote Link to comment Share on other sites More sharing options...
Ansem Posted April 18, 2014 Author Share Posted April 18, 2014 saw a good one on reddit the other day why do pirates like indefinite integral mores than definite integrals? because they love the c huehuehue Quote Link to comment Share on other sites More sharing options...
Tables Posted April 18, 2014 Share Posted April 18, 2014 jesus christ did you fucking nerds just post a whole page of spoiler tags Problem? Quote Link to comment Share on other sites More sharing options...
Original Alear Posted April 18, 2014 Share Posted April 18, 2014 You know when I look at all those spoiler tags opened up, it's like looking at a slowly narrowing staircase. Quote Link to comment Share on other sites More sharing options...
euklyd Posted April 18, 2014 Share Posted April 18, 2014 Problem? [spoiler][spoiler][spoiler][spoiler][spoiler][spoiler][spoiler][spoiler][spoiler][spoiler][spoiler][spoiler][spoiler][spoiler][spoiler][spoiler][spoiler][spoiler][spoiler][spoiler]Problem?[/spoiler][/spoiler][/spoiler][/spoiler][/spoiler][/spoiler][/spoiler][/spoiler][/spoiler][/spoiler][/spoiler][/spoiler][/spoiler][/spoiler][/spoiler][/spoiler][/spoiler][/spoiler][/spoiler][/spoiler] Much faster to read this way. Quote Link to comment Share on other sites More sharing options...
Groyer Posted April 18, 2014 Share Posted April 18, 2014 There are 10 types of people in this world. Those who understand binary, and those who don't. Quote Link to comment Share on other sites More sharing options...
Aleph Posted April 18, 2014 Share Posted April 18, 2014 I doubt it's because I'm a computer scientist, but either way I've heard that one way too many times. It wasn't even funny the first time. ;/ Quote Link to comment Share on other sites More sharing options...
Ansem Posted April 18, 2014 Author Share Posted April 18, 2014 xeld i keep mistaking you for one of those forum gamers Quote Link to comment Share on other sites More sharing options...
Esau of Isaac Posted April 19, 2014 Share Posted April 19, 2014 I doubt it's because I'm a computer scientist, but either way I've heard that one way too many times. It wasn't even funny the first time. ;/ Nah you just have high standards for bad jokes. D:< Quote Link to comment Share on other sites More sharing options...
Aleph Posted April 19, 2014 Share Posted April 19, 2014 you're a bad joke Quote Link to comment Share on other sites More sharing options...
Esau of Isaac Posted April 19, 2014 Share Posted April 19, 2014 your face is a bad joke Quote Link to comment Share on other sites More sharing options...
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