bonanova
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I picked 17 for two reasons: [1] to give a reasonable chance for all eight patterns to appear and be ordered. [2] because my computer will handle arrays of 8 x 217. Neither of these reasons bears on the idea of the puzzle, so let's examine the main idea more simply. Pick two triples, t1 and t2, then flip a coin until one of these patterns appears. What are the odds that it will be t1? Are they necessarily 50%?
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Hi Dupie, Great observation. What the OP should have done, to be more precise, is to prohibit the use of transmitted light, to observe the interior of the egg. Using reflected light, one can observe the exterior of the egg and see whether is spins or not. But if you like, you could touch the egg, lightly, with your fingertips to sense continued spinning. [Did someone here mention being smart-a**?] Welcome to the Den!
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Yes.
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For the purposes of this puzzle, a lie is not a statement that is incorrect, rather a statement that is contrary to what you believe is true. The OP says If you asked: "Is the sky blue?" both would answer: "Yes." The first, because he knew it to be true and answered truthfully according to his belief. The second, because he believed it to be false and lied according to his belief. So the second person is a liar because he spoke contrary to the information he believes to be true. The fact he affirms a blue sky does not make him truthful. In this case, what matters is his intention to provide information that he believes to be incorrect. Being ill-informed, or incompetent to make correct observations, does not heal the flaw in his integrity. If that makes sense, you'll see then that his "Yes" answer is a lie, in spite of its correctness.
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Nope, it's a brain fart - I'll edit the OP. Nice catch, thanks.
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Thanks for looking, SP, but it's been posted before.
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I'm not sure I follow your analysis. If they both give the right answer to "anything" that's asked, how does that make distinguishing them a "bit too easy"?
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I heard this posed [not original with me] and I have not worked out a solution. Yet. A truthful person who is aware of every fact will answer yes/no questions in a certain way. Curiously, a liar who is misinformed about every fact will answer yes/no questions in exactly the same way! If you asked: "Is the sky blue?" both would answer: "Yes." The first, because he knew it to be true and answered truthfully according to his belief. The second, because he believed it to be false and lied according to his belief. The puzzle is this: Can you distinguish between the two by asking a series of yes/no questions? If so [and why would we ask if you couldn't? ] what is the minimum number of questions needed?
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Yes. And if you are lead then to believe that can affect the likely order of occurrence, can you find a pair of triples for which one triple would be expected to occur before the other? Going further down that path: If different pairs of triples do not all have the same likelihood of an expected order, is there a pair of cases where the likelihood of an expected order is greater than for any other pair? With the exception of just interchanging H and T, of course; symmetry makes things happen in pairs. Or is equal likelihood the predominant force, and all outcomes are random?
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OK. I'll buy that....
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There are several kinds of symmetry - translation, reflection and rotation are three. And rotational has three axes and an infinite number of angles: 180, 120, 90, 72, 60, 45, 30, 15, 12 ... etc degrees. UR suggests that certain symmetries are attainable - e.g. stack them vertically and you can rotate about that axis any number of degrees while leaving the configuration unchanged. As UR points out, the OP seems to be talking about reflection or 180 degree rotational symmetry about an axis perpendicular to a 1-dimensional ordering of the six balls. Restricted to one dimension, reflection or 180-degree rotation symmetry can't be achieved.
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We usually reason that if something is improbable we will wait longer to see it happen. To be more specific, if p is the probability of something happening in one trial, we logically expect the event to happen after 1/p trials. So if two events have the same probability, we wouldn't expect [on average] to wait longer for one event than for the other. Flip a coin three times. One of these events will occur, each with likelihood of .53 = 1/8: HHH HHT HTH HTT TTT TTH THT THH Now suppose we flip a coin seventeen times [say]. Within that string of 17 Hs and Ts, would we expect these events to occur [a] with any predictable order, or in random order?
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Given that ... Twenty-five Robots, all named after BrainDenizens, are placed at random on a set of rails 1 mile long. The robot named Prime is the thirteenth robot from the North end of the rails. Each robot faces North or South with equal probability, and travels in the direction it faces. When two robots meet, they are unable to pass, so they simply turn around. When a robot reaches an end of the rail, it falls off and goes to sleep. All robots travel at a uniform speed of 1 mile/hour. How long does it take before we can be certain that Prime has begun his nap? Only half credit is available for those who resort to infinite series.
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Mac The Cat had it almost. Just he didn't normalize the odds. But I do like how mine turned out. Edit:
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Attack Risky! Null Easier Hits Palace, Stains Coin Anon Bravo! Nab Bond Try Gels, Or Clefs Irish Guzzle! Copy Urinal Email, A Tiny Sink Now, A Dead Moron Wren Ablaze! Try Panic Okay, Join An Area Ken? Recall A Rhyme
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Hats on a death row!! One of my favorites puzzles!
bonanova replied to roolstar's question in New Logic/Math Puzzles
Works for any sequence of hats. Try it; if it seems to fail, post the hat sequence you assumed, and which prisoner [after the 1st] does not survive. Then we'll discuss it on concrete terms. -
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Good one.
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