Life In 19x19 :: Logical puzzles

congratulations both. Both very fast. Easy for go players???

I'm dumb enough not to get the first one, and have suppressed my shame enough to admit it. Even after reading the answers, I can't see why it would be that way. Explanation?

hyperpape wrote:

I'm dumb enough not to get the first one, and have suppressed my shame enough to admit it. Even after reading the answers, I can't see why it would be that way. Explanation?

I'm going to say that one's not the hardest.

Here's a harder one that originated with Raymond Smullyan:

Three gods A, B, and C are called, in some order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for yes and no are 'da' and 'ja', in some order. You do not know which word means which.

Both answers correct for the fuses problem. Next problem.

on a strange island there lives a strange tribe of 300 perfectly logical and perfectly intelligent persons. And they know it of each other. Each member has a spot, red or black, on the back of the head. Nobody knows the color of his own spot but they do know the color of everybody else's. If a tribesman ever realizes the color of his own spot it is strict custom that he publicly announces this fact the next morning and leaves the island forever. So they never mention spot colors and have no mirrors. But one day a tourist, American OC, visits the island and announces to the entire tribe: "I can see at least one of you has a red spot!". The tourist leaves to return a year later.
He is surprised. Why?

Weighing:

Author:	cyclops [ Wed Nov 24, 2010 8:10 am ]
Post subject:	Logical puzzles
Attachment: puzzle.jpg [ 25.59 KiB \| Viewed 18891 times ] Describe the next figure in this array. How long did it take you?

Author:	robinz [ Wed Nov 24, 2010 8:14 am ]
Post subject:	Re: Logical puzzles
Can't be bothered to try to draw one and upload it, but it'll be the number 6, glued to its reflection about a vertical axis. I saw this instantly - but that doesn't necessarily mean that I would always have done so. In any case, it's more of a visual puzzle than a logical one, surely?

Author:	Gresil [ Wed Nov 24, 2010 9:01 am ]
Post subject:	Re: Logical puzzles
Something like 6d. About twenty seconds.

Author:	cyclops [ Wed Nov 24, 2010 9:59 am ]
Post subject:	Re: Logical puzzles
congratulations both. Both very fast. Easy for go players???

Author:	cyclops [ Wed Nov 24, 2010 10:25 am ]
Post subject:	Re: Logical puzzles
Next puzzle: You have 2 lenghts of fuse and 2 matches. One fuse will burn from start to end in 10 minutes. The other in 15 minutes. However the burn rate is not steady along their lenghts. Measure 20 minutes of time. ( for the not native english: a fuse is the sort of rope they used to ignite bombs in the good old days, also used in fireworks. It has nothing to do with electricity OC )

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Author:	Redundant [ Wed Nov 24, 2010 11:10 am ]
Post subject:	Re: Logical puzzles
Fuses If I know which fuse is which, light the 10 minute fuse on both sides, and when it finishes burning in five minutes, light the 15 minute fuse. If I don't know which is which ... not sure if it's solvable. Will have to think some more.

Author:	Bill Spight [ Wed Nov 24, 2010 11:14 am ]
Post subject:	Re: Logical puzzles
cyclops wrote: congratulations both. Both very fast. Easy for go players??? Who knows? It might be hard for go players. After all, solving it demands breaking down the gestalts. That might be difficult for a whole board thinker.

Author:	Koroviev [ Wed Nov 24, 2010 11:33 am ]
Post subject:	Re: Logical puzzles
Fuses: Light the 10 minute fuse from both ends with one match - it will burn for five minutes. When it burns out, light the 15 minute fuse with the other match. When it burns out 20 minutes have passed. How's that?

Author:	hyperpape [ Wed Nov 24, 2010 11:44 am ]
Post subject:	Re: Logical puzzles
I'm dumb enough not to get the first one, and have suppressed my shame enough to admit it. Even after reading the answers, I can't see why it would be that way. Explanation?

Author:	amnal [ Wed Nov 24, 2010 11:55 am ]
Post subject:	Re: Logical puzzles
hyperpape wrote: I'm dumb enough not to get the first one, and have suppressed my shame enough to admit it. Even after reading the answers, I can't see why it would be that way. Explanation? Cover up the left half of each symbol

Author:	SoDesuNe [ Wed Nov 24, 2010 1:05 pm ]
Post subject:	Re: Logical puzzles
amnal wrote: hyperpape wrote: I'm dumb enough not to get the first one, and have suppressed my shame enough to admit it. Even after reading the answers, I can't see why it would be that way. Explanation? Cover up the left half of each symbol hyperpape, I'm with you.

Author:	hyperpape [ Wed Nov 24, 2010 1:21 pm ]
Post subject:	Re: Logical puzzles
@amnal Thanks. I kept looking at how 3 looked a bit like you'd fused copies of 2, then started imagining that there could be some sort of complicated pattern.

Author:	cyclops [ Wed Nov 24, 2010 6:13 pm ]
Post subject:	Re: Logical puzzles
Both answers correct for the fuses problem. Next problem. on a strange island there lives a strange tribe of 300 perfectly logical and perfectly intelligent persons. And they know it of each other. Each member has a spot, red or black, on the back of the head. Nobody knows the color of his own spot but they do know the color of everybody else's. If a tribesman ever realizes the color of his own spot it is strict custom that he publicly announces this fact the next morning and leaves the island forever. So they never mention spot colors and have no mirrors. But one day a tourist, American OC, visits the island and announces to the entire tribe: "I can see at least one of you has a red spot!". The tourist leaves to return a year later. He is surprised. Why?

Author:	Dusk Eagle [ Wed Nov 24, 2010 8:41 pm ]
Post subject:	Re: Logical puzzles
All the people with red spots have left the island. If everyone on the island knows that their spot is either red or black, then everyone will have left by a year later. Why? See: http://xkcd.com/blue_eyes.html and http://xkcd.com/solution.html. This is basically my favorite logic puzzle of them all. Unfortunately, no one I've ever told this puzzle to is able to understand the solution.

Author:	Monadology [ Wed Nov 24, 2010 9:02 pm ]
Post subject:	Re: Logical puzzles
Quote: Unfortunately, no one I've ever told this puzzle to is able to understand the solution. Really? It was used in an informal logic class I had full of a decent range of folks, and they all got it eventually. For anyone interested, I recently read an essay by Jacques Lacan on it. It can be found here: http://www.soundandsignifier.com/files/ ... l_Time.pdf though I don't know if it's the same translation I read. Lacan is kind of pretentious, but fortunately it's not one of his obscurantist pieces. I think Lacan arguably misses the point (though I think he may also be somewhat aware of that) inasmuch as he analyses the solution as if the 'prisoners' or 'islanders' are not absolutely and equally perfect reasoners who would be acting synchronously. In any case, I think he misses the point in an interesting way.

Author:	entropi [ Fri Nov 26, 2010 5:04 pm ]
Post subject:	Re: Logical puzzles
Gresil wrote: Weighing: Take 1 coin from the first box, 2 from the second etc. and measure the combined weight of these. If the first box has the heavier coins, the weight will be 1010 grams; if the second one has them, 1020 grams, etc. the idea is correct But a minor correction: the total weight will be 5500+10N grams (N being the number of the box). 100+200+...+Nx110+...+1000

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Author:	hyperpape [ Wed Nov 24, 2010 9:53 pm ]
Post subject:	Re: Logical puzzles
I'm going to say that one's not the hardest. Well, I guess it depends. Convincing yourself how it works isn't hard. Carefully stating the induction on number of red-spotted villagers or characterizing the change in their information each night seems like a royal pain in the butt. Here's a harder one that originated with Raymond Smullyan: Three gods A, B, and C are called, in some order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for yes and no are 'da' and 'ja', in some order. You do not know which word means which.

Author:	ethanb [ Thu Nov 25, 2010 6:42 pm ]
Post subject:	Re: Logical puzzles
hyperpape wrote: I'm going to say that one's not the hardest. Well, I guess it depends. Convincing yourself how it works isn't hard. Carefully stating the induction on number of red-spotted villagers or characterizing the change in their information each night seems like a royal pain in the butt. Here's a harder one that originated with Raymond Smullyan: Three gods A, B, and C are called, in some order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for yes and no are 'da' and 'ja', in some order. You do not know which word means which. Haven't worked out a total solution yet, but I have figured out how to make Truth's head blow up: Ask all three of them the same question, while pointing at one of the others: "Would he say 'ja' if I asked him if the other god would say you were Random?" False will answer "yes" unconditionally. Random is inscrutable in this regard. Truth will strike you with lightning. EDIT: that's not necessarily a full solution for Truth either - if False is a literal-minded negative answerer, he may also have issues answering. My guess as to his answer depends on him being somewhat of a trickster and also somewhat antipathic toward Truth (and therefore might answer firmly but misleadingly rather than striking you with lightning ambiguously.)

Author:	entropi [ Fri Nov 26, 2010 7:48 am ]
Post subject:	Re: Logical puzzles
cyclops wrote: Both answers correct for the fuses problem. Next problem. on a strange island there lives a strange tribe of 300 perfectly logical and perfectly intelligent persons. And they know it of each other. Each member has a spot, red or black, on the back of the head. Nobody knows the color of his own spot but they do know the color of everybody else's. If a tribesman ever realizes the color of his own spot it is strict custom that he publicly announces this fact the next morning and leaves the island forever. So they never mention spot colors and have no mirrors. But one day a tourist, American OC, visits the island and announces to the entire tribe: "I can see at least one of you has a red spot!". The tourist leaves to return a year later. He is surprised. Why? Wonderful puzzle. I could not solve it but at least understand the solution Here is my favourite one: There are 10 boxes full of golden coins. 9 of the boxes contain 100 gram coins, and one of them 110 gram coins. You are allowed to weigh only once for finding out which one of the boxes contains the 110 gram coins. (Note: By weighing I mean not comparing two (sets of) coins with each other but really measuring how many grams a (set of) coin(s) weighs.). If you hear it for the first time it may not be so simple to solve. But once you know the solution it seems very very obvious, which is for me a good indication of a quality puzzle.

Author:	Gresil [ Fri Nov 26, 2010 12:43 pm ]
Post subject:	Re: Logical puzzles
Weighing: Take 1 coin from the first box, 2 from the second etc. and measure the combined weight of these. If the first box has the heavier coins, the weight will be 1010 grams; if the second one has them, 1020 grams, etc.