Timeline for Are there eighteen or twenty bars in my castle?
Current License: CC BY-SA 3.0
25 events
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| Mar 13, 2020 at 2:09 | comment | added | Christopher Theodore | @Rubio I just posted a 2 Day Solution I would like you to take a look at. | |
| Apr 13, 2017 at 12:50 | history | edited | CommunityBot |
replaced http://puzzling.stackexchange.com/ with https://puzzling.stackexchange.com/
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| Nov 17, 2016 at 19:46 | comment | added | Brian |
To clarify, this shortcut works when they don't have even numbers, too. They each know that y = (a-x) ± n(a-b) where a and b are the possible total numbers of bars, x is the number of bars they have, y is the number of bars the other one has, 0 < x < (a + b), and 0 < y < (a + b). n represents the number of deviations of (a-b) that y is from (a-x). While it's unimportant what n is, especially since a and b are interchangeable and x and y are swapped for either person, what's important is that both people know that n is an integer, which enables this shortcut.
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| Nov 16, 2016 at 0:24 | comment | added | Rubio♦ | @Joe Props to you for figuring out there was a faster path. I had looked at even numbered steppings well earlier but obviously messed up my limiting rules because I found it no better than my eventual solution. Without your solution, which I couldn't refute, I wouldn't have found why it works. Nice job :) +1 from me. | |
| Nov 16, 2016 at 0:22 | comment | added | Rubio♦ | @Joe Your method works by crossing off possibilities after the series of non-answers precludes them; thus it can't operate any faster than the non-answers narrow the limits. (Since the two choices, 18 or 20, are separated by 2, you can never reduce the range of options remaining by more than two per step.) Since correctly determining they both know each has to have an even number of bars reduces the problem to steppings of two, the two methods converge identically. My way takes a lot less book-keeping. Your way intuitively makes better use of available info. Both work, equivalently. | |
| Nov 15, 2016 at 23:23 | comment | added | Joe | @MarcoBonelli you should have kept at your initial approach of writing every consequence! Rubio's updated approach clearly works, but the "trick" in his solution - the importance of evenness - comes out directly if you follow my method. | |
| Nov 15, 2016 at 23:17 | comment | added | Joe | @Rubio good call on evenness being the key factor slowing your solution down. I'm still a fan of my explanation - explicitly enumerating the pairs of options at each level makes more intuitive sense to me than the ranges of values - but to each their own. Though Jonathan's table does look nice, admittedly. | |
| Nov 15, 2016 at 23:07 | comment | added | Sejanus | @Rubio and I and some others wrote about how their reasonings are illogical and only happens to provide the correct answer in the end because you knew the answer in advance and tailored their illogical way of thinking so that it would give the correct answer. Fundamentally no different from "the sky is clear therefore 20", answer is correct but there's no logic in it. | |
| Nov 15, 2016 at 22:58 | history | edited | Rubio♦ | CC BY-SA 3.0 |
Joe is right!!
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| S Nov 15, 2016 at 22:24 | history | suggested | Marco Bonelli | CC BY-SA 3.0 |
better formatting
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| Nov 15, 2016 at 20:58 | review | Suggested edits | |||
| S Nov 15, 2016 at 22:24 | |||||
| Nov 15, 2016 at 19:51 | comment | added | Rubio♦ | @Brian That is addressed explicitly by the OP in the comments under the question. It doesn't matter that Mark or Rose may choose to misinterpret the plain intent of the question; they're free to do so and answer accordingly, and the Evil Logician is free to interpret their answer as a manifestly incorrect response to what his intended question is, and throw away their keys. | |
| Nov 15, 2016 at 19:49 | comment | added | Rubio♦ | @jkhan and Sejanus - I wrote out long-hand exactly what each person's reasoning and conclusions are on which day, at the expense of an easier format, precisely to answer the question of how each person knows what they know and when they know it. Read through it, and you'll see how each time Mark fails to answer provides Rose additional information about how many bars Mark has, and vice versa. | |
| Nov 15, 2016 at 18:08 | comment | added | Brian | Mark realizes that the evil logician meant for this to be a question of '18 or 20', but it could be interpreted as '(18or20) or (not(18or20))'. He answers "yes" on the first day and they both go free. | |
| Nov 15, 2016 at 17:25 | comment | added | jkhan | I have trouble with these sorts of problems. Here's where I get hung up: Mark not answering on day one tells Rose nothing she doesn't already know: Mark must have either 10, 12 or 14 bars. She can not possibly think that Mark has 1.. 17. Likewise, Rose not answering on day two does not tell Mark anything he doesn't already know. He knows that Rose has either 8 or 6 blocks, and further, knows that Rose obtained no new information by him not answering on day 1. Mark has no new information on day 3. The cycle repeats. I understand this is probably wrong - but what am I missing? | |
| Nov 15, 2016 at 10:08 | vote | accept | Marco Bonelli | ||
| Nov 15, 2016 at 23:45 | |||||
| Nov 15, 2016 at 9:32 | comment | added | Marco Bonelli | This is actually true, I tried solving this riddle by myself working on the 10/12 and 6/8 writing down every consequence (he knows that she knows that he knows that 6/8/10/12/14/...) and it just is useless information, but still it looks somehow better to the human eye to look at the two numbers instead of the range of numbers. | |
| Nov 15, 2016 at 9:06 | comment | added | Rubio♦ | (It's actually even more complicated than that—Mark has 12 bars so he knows Rose has to have 6 or 8; he also knows if Rose has 6, Rose knows he has 12 or 14, and if Rose has 8, she knows he has 10 or 12. So they each know what they know, and what the other knows, and what the other knows THEY know. But in this case the numbers just happen to be such that this extra knowledge doesn't actually help them at all. So it's not included in my analysis.) | |
| Nov 15, 2016 at 9:02 | comment | added | Rubio♦ | There are two things limiting how many bars each knows the other can have: one is their knowledge of how many their own window has—which is static—and the other is their knowledge of what the other's (lack of) answers tells them. Rose knows both that Mark has 10 or 12, and also that because Mark didn't give an answer that he cannot have more than 17 or fewer than 2. This second bit of knowledge continues to be refined as time passes with no answer given, until it finally decides between the two possibilities each knows the other can have from the first bit. | |
| Nov 15, 2016 at 8:57 | comment | added | Walfrat |
Rose gets asked, and knows Mark has 1..17 bars. i don't get it, wouldn't it be 10 or 12 since Rose has eight and she knows it ?
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| Nov 15, 2016 at 8:55 | comment | added | Rubio♦ | Nice. Thanks for the downvote, whoever. | |
| Nov 15, 2016 at 8:08 | comment | added | Marco Bonelli | You got it fast, nice job, good explanation for every day and number range, it helps understanding the problem a lot. I would have formatted it a bit better though. | |
| Nov 15, 2016 at 7:51 | history | edited | Rubio♦ | CC BY-SA 3.0 |
update solution with better constraints
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| Nov 15, 2016 at 6:01 | history | edited | Rubio♦ | CC BY-SA 3.0 |
add assumptions, and minor edits
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| Nov 15, 2016 at 5:50 | history | answered | Rubio♦ | CC BY-SA 3.0 |