Raspofabs
Former 22Cans staff
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Post by Raspofabs on May 20, 2015 19:32:37 GMT
I've been a fan of unique logic puzzles, or counter-intuitive solutions to simple questions, such as the Blue-eyes problem, or the Monty Hall problem. If you can think of any other unique, and hard, problems that would go down well at the the local maths pub, then I'd love to read them. Blue eyes: xkcd.com/blue_eyes.htmlMonty Hall: en.wikipedia.org/wiki/Monty_Hall_problemAlso, another I like: I have three sock drawers, one labeled black, one labeled white, another labeled mixed. I know that all the labels are wrong (that is, none of them are actually on their right drawers). I pick one sock from a drawer of my choosing, and given the colour of that sock, I manager to relabel all the drawers correctly. How do I do that? |
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Deleted
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Post by Deleted on May 20, 2015 19:38:03 GMT
I've been a fan of unique logic puzzles, or counter-intuitive solutions to simple questions, such as the Blue-eyes problem, or the Monty Hall problem. If you can think of any other unique, and hard, problems that would go down well at the the local maths pub, then I'd love to read them. Blue eyes: xkcd.com/blue_eyes.htmlMonty Hall: en.wikipedia.org/wiki/Monty_Hall_problemAlso, another I like: I have three sock drawers, one labeled black, one labeled white, another labeled mixed. I know that all the labels are wrong (that is, none of them are actually on their right drawers). I pick one sock from a drawer of my choosing, and given the colour of that sock, I manager to relabel all the drawers correctly. How do I do that? Io9.com does a weekly puzzle, most of them are logic/math based. Some of them are more well known than others. Some are variations. Some are simply thought experiements. I enjoy the forum they are levied on, which is why I engage there. Edit: you may have to dig back a few weeks/months for the really good ones. Enjoy
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Post by morsealworth on May 20, 2015 20:15:42 GMT
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Lord Ba'al
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Post by Lord Ba'al on May 20, 2015 21:41:37 GMT
I've been a fan of unique logic puzzles, or counter-intuitive solutions to simple questions, such as the Blue-eyes problem, or the Monty Hall problem. If you can think of any other unique, and hard, problems that would go down well at the the local maths pub, then I'd love to read them. Blue eyes: xkcd.com/blue_eyes.htmlMonty Hall: en.wikipedia.org/wiki/Monty_Hall_problemAlso, another I like: I have three sock drawers, one labeled black, one labeled white, another labeled mixed. I know that all the labels are wrong (that is, none of them are actually on their right drawers). I pick one sock from a drawer of my choosing, and given the colour of that sock, I manager to relabel all the drawers correctly. How do I do that? Does "mixed" mean it is a sock that is neither white nor black or does it mean that the drawer has a mix of white and black socks in it? |
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Casinha
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Post by Casinha on May 20, 2015 21:55:18 GMT
Mad props to the Monty Hall problem, I've spent too much time trying to wrap my head around the concept and I love it. As for logic puzzles of my own, I've got a couple. Whether they're hard or not is up to the individual, I suppose. I may also just be repeating widely known puzzles, so apologies if I'm just repeating the equivalent of "Why did the chicken cross the road."
1) You are given two lengths of fuse. Both lengths burn for a total of one hour, but at inconsistent rates (one length might burn quickly for 5 minutes, slowly for another 20, quickly again for 30 seconds etc.) How would you use these two lengths of fuse to measure 15 minutes?
2) Three prisoners are given a chance at freedom. The king declares that he has 5 hearts, 3 of which are WHITE and 2 of which are BLACK.
Each prisoner shall have one of these hearts hung above his/her head.
Each prisoner shall see the other two prisoners' hearts, but not his/her own.
Each prisoner is tasked (in turn, one after the other) with deducing whether or not the heart dangling above his/her own head is BLACK or WHITE and announcing the logic behind the deduction.
3 WHITE hearts are then strung up above the prisoners and they answer thus:
Prisoner 1: I don't know.
Prisoner 2: I don't know.
Prisoner 3: White.
Explain the logic behind Prisoner 3's decision.
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Lord Ba'al
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Posts: 6,260
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I like: Cats; single malt Scotch; Stargate; Amiga; fried potatoes; retro gaming; cheese; snickers; sticky tape.
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Post by Lord Ba'al on May 20, 2015 23:45:53 GMT
The second one is actually not that hard.
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Post by Spiderweb on May 21, 2015 7:23:27 GMT
Mad props to the Monty Hall problem, I've spent too much time trying to wrap my head around the concept and I love it. As for logic puzzles of my own, I've got a couple. Whether they're hard or not is up to the individual, I suppose. I may also just be repeating widely known puzzles, so apologies if I'm just repeating the equivalent of "Why did the chicken cross the road." 1) You are given two lengths of fuse. Both lengths burn for a total of one hour, but at inconsistent rates (one length might burn quickly for 5 minutes, slowly for another 20, quickly again for 30 seconds etc.) How would you use these two lengths of fuse to measure 15 minutes? 2) Three prisoners are given a chance at freedom. The king declares that he has 5 hearts, 3 of which are WHITE and 2 of which are BLACK. Each prisoner shall have one of these hearts hung above his/her head. Each prisoner shall see the other two prisoners' hearts, but not his/her own. Each prisoner is tasked with deducing whether or not the heart dangling above his/her own head is BLACK or WHITE and announcing the logic behind the deduction. 3 WHITE hearts are then strung up above the prisoners and they answer thus: Prisoner 1: I don't know. Prisoner 2: I don't know. Prisoner 3: White. Explain the logic behind Prisoner 3's decision. I got stuck on the 2nd one so googled it....apparently one prisoner should be blind (They name the prisoners).
This riddle ONLY works if Carl is blind. If they all can see and are of equal intelligence 1) someone will dash out if they see 2 blacks, so no one has 2 blacks if any hesitation; 2) someone will dash out if they see 1 black and 1 white, since they know their hat must be white; 3) but with more hesitation they all rush out knowing they all have white.
Albert, Barry, and Carl with 1 = white and 0 = black:
A B C
1 1 1
0 1 1
1 0 1
1 1 0
0 0 1
1 0 0
0 1 0
If Carl is blind, then Albert and Barry could make no inferences based on Carl's actions. C knows he and B aren't both in black since A didn't run out, and he and A aren't both in black since B didn't run out. So the only possibilities now are:
A B C
1 1 1
0 1 1
1 0 1
1 1 0
0 0 1
Blind Carl knows Albert and Barry would be racing out if Carl had black, because they've made all the same intelligent inferences. So, Carl knows he has white before the others know, if everyone is standing around hesitating.
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Post by Spiderweb on May 21, 2015 7:37:57 GMT
Problem 1 My answer: The first one is to do with burning one fuse both ends first to give 30mins while burning the other at one end, then at 30mins (when the fuse burning both ends runs out) you start the 2nd fuse at its other end, it would really tell you 45mins, but the timing from the end of the first to the end of the 2nd would be 15mins |
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Post by Spiderweb on May 21, 2015 7:40:10 GMT
Did anyone play Dr Layton on the nintendo DS? I loved them.
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Casinha
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Post by Casinha on May 21, 2015 9:21:28 GMT
2) Three prisoners are given a chance at freedom. The king declares that he has 5 hearts, 3 of which are WHITE and 2 of which are BLACK. Each prisoner shall have one of these hearts hung above his/her head. Each prisoner shall see the other two prisoners' hearts, but not his/her own. Each prisoner is tasked with deducing whether or not the heart dangling above his/her own head is BLACK or WHITE and announcing the logic behind the deduction. 3 WHITE hearts are then strung up above the prisoners and they answer thus: Prisoner 1: I don't know. Prisoner 2: I don't know. Prisoner 3: White. Explain the logic behind Prisoner 3's decision. I got stuck on the 2nd one so googled it....apparently one prisoner should be blind (They name the prisoners). None of the prisoners are blind in the puzzle I gave  Something I failed to make clear (sorry) is that each prisoner is asked the colour of his/her heart in turn, they do not give an answer whenever they please (but the logical deduction works the same way regardless, you can just make the assumption that silence from both is enough for the third to make his decision). Will update my original post to include this. |
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Post by morsealworth on May 21, 2015 10:44:15 GMT
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Lord Ba'al
Supreme Deity
Posts: 6,260
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I like: Cats; single malt Scotch; Stargate; Amiga; fried potatoes; retro gaming; cheese; snickers; sticky tape.
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Post by Lord Ba'al on May 22, 2015 0:36:48 GMT
Regarding the sock problem, you might just want to remove all the labels and put all the socks in one drawer. That leaves two drawers to put other stuff in such as underwear and videogames. Problem solved. No more wasting time thinking about socks.
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Post by hardly on May 22, 2015 23:27:35 GMT
Here's my solution to the first second puzzle. I don't know how to do the spoiler thing so apologies if I ruin this for you. Its been a while so I figure posting my answer is ok. I'm generally not very good at this but lets see how it goes. Based on the first answer we know 2+3 are not both black since that would indicate that person 1 was white. Person 2 therefore knows they are either both white or one is black and one is white. Therefore if person 3 was black then person 2 would know they definitely are white. Since person 2 doesn't know then person 3 must be white. |
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Lord Ba'al
Supreme Deity
Posts: 6,260
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I like: Cats; single malt Scotch; Stargate; Amiga; fried potatoes; retro gaming; cheese; snickers; sticky tape.
I don't like: Dimples in the bottom of scotch bottles; Facebook games masquerading as godgames.
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Post by Lord Ba'al on May 22, 2015 23:48:20 GMT
I don't know how to do the spoiler thing so apologies if I ruin this for you. The spoiler thing is simple. You start with an opening tag. The tag has square brackets around it like these [ ]. Between the square brackets you put the word "spoiler". (without the ") Then you write whatever you want to be hidden in the spoiler tags. At the end you use a closing tag which is basically the same as the opening tag except it has a "/" in it. (so "/spoiler" again between square brackets and without the quotation marks) |
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Post by greay on May 24, 2015 22:05:16 GMT
This one is bullshit.
What if 5 has an even number on the opposite side?
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Lord Ba'al
Supreme Deity
Posts: 6,260
Pledge level: Half a Partner
I like: Cats; single malt Scotch; Stargate; Amiga; fried potatoes; retro gaming; cheese; snickers; sticky tape.
I don't like: Dimples in the bottom of scotch bottles; Facebook games masquerading as godgames.
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Post by Lord Ba'al on May 24, 2015 22:36:31 GMT
This one is bullshit.
What if 5 has an even number on the opposite side?
OMG that bitch managed to annoy me quite quickly. |
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Raspofabs
Former 22Cans staff
Posts: 227
I like: coding, high peat single malts, ... , yeah, that's about it.
I don't like: object oriented design, and liver.
Steam: raspofabs
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Post by Raspofabs on Jun 2, 2015 11:22:10 GMT
This one is bullshit.
What if 5 has an even number on the opposite side?
Awesome spot there. I like your thinking. |
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Post by morsealworth on Jun 2, 2015 13:11:12 GMT
This one is bullshit.
What if 5 has an even number on the opposite side?
Awesome spot there. I like your thinking. The starting conditions of the problem state that it has a number on one side and a color on another, so that would be impossible. |
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Post by 13thGeneral on Jun 2, 2015 13:59:04 GMT
Awesome spot there. I like your thinking. The starting conditions of the problem state that it has a number on one side and a color on another, so that would be impossible. I argued this puzzle with my wife, because to me the solution is actually faulty. But I just don't feel like starting that argument again. It all depends on how you interpret the phrasing of the question, and not everyone will read the conditions the same - many people don't understand the terms if/and/then and such as logic dictates, but that doesn't mean they are not logical thinking - also the example is not the best used method; putting it into a more personal situation actually yields better results (go check wiki). You also have to assume something about the cards, and that's inductive reasoning logic as opposed to deductive reasoning logic, so the problem never determine what type of logic the individual utilizes. Yes, I overthink logic puzzles, usually completely dissecting them to find faults; it's just how my brain works. |
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Post by greay on Jun 2, 2015 18:50:01 GMT
Awesome spot there. I like your thinking. The starting conditions of the problem state that it has a number on one side and a color on another, so that would be impossible. Not if it has a number and a color. |
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Something I failed to make clear (sorry) is that each prisoner is asked the colour of his/her heart in turn, they do not give an answer whenever they please (but the logical deduction works the same way regardless, you can just make the assumption that silence from both is enough for the third to make his decision). Will update my original post to include this.
