bushindo
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Everything posted by bushindo
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Tuckleton is correct. I don't think it is possible to find a more optimal solution because of the way the information can be passed between turns. The requirement to either move the clock forward or backward 3 hours on a clock every turn gives a little bit more than 2 pieces or information, but not quite 4 neither. If the prisoner can turn the clock to any of the four positions, that would be a different matter. It's an interesting extension, so I'll post a new thread on it.
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Interesting questions. Perhaps the lady is question 1 is chinese? That's because there's a video of her on youtube.
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The response is encrypted. Decrypt the text and you'll find the answer. No hint is provided =)
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Interesting puzzle. Your puzzles are superb, howardl1963, and I hope you'll regularly post more.
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That's a very clever solution. Excellent puzzle.
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Please ignore the above posts. Unfortunately, there were grave errors in these approaches. It works generally, but there are 2-4 special pairs of (delta,pile number) that can not be uniquely identified. If there is a solution for this problem, I'd like to see it.
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Okay, third try. Please ignore the post above. I refined the approach a bit, and now I believe this one is correct. It will always give the correct X, delta, and pile number.
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Okay, second try. This approach basically refines the initial estimates of X so that we don't have to worry about identifiability issue.
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Some comments
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I was under the impression that delta is a random variable drawn from the range [ -5, 5], and hence it can not be a rational number as transcendental numbers are infinitely more dense. My algorithm was designed for work for that case. I see that delta is meant to be an arbitrarily chosen number from [ -5, 5]. Under this case, for certain rational values of delta, it is not possible to uniquely identify X, delta, and odd pile. Back to the drawing board.
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You're right. There are only 28 coins in the first weighing. Good catch. Thank you.
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Edit: Damn Bushido and his elegance! Haha, that's nice complement indeed. You just made my day.
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Interesting problem. Here's my attempt
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Reminds me of an old Norse story about Thor and a Giant king.
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I agree with everything here, but my version has a small change with respect to the integration.
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This is a good start. I should have clarified my question better in the OP. My main question is would box 1 take twice as long to completely drain all the water compared to box 2? Would box 1's drainage time be longer or shorter than twice the time of box 2?
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Suppose that we have two rectangular boxes that are exactly the same. Both are placed upright and filled to the brim with identical amount of water. Suppose that we drill a circular hole with radius r at the bottom of box 1, and we drill 2 separate holes, each also with radius r, in the bottom of box 2. Would box 1 take twice as long to completely drain all the water compared to box 2? Would box 1 take longer to drain? Shorter?
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How about this approach. This approach makes a less restrictive assumption that, given four groups of mice started at the same time eating 1 cake each, we can at some point tell which group is eating slower or faster than the rest.
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Interesting. The cut parts aren't easily to comprehend, but the properties of the whole stick are well understood.
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How about this statement, which everybody on the island should agree is true You are right in that the person chosen to save the logicians can not tell them any new information explicitly. However, the fact that such a statement, call it Q, is spoken in front of all logicians lead to a new piece of information: that is, all logicians now know that every other logician knows about Q. This new implicit piece of information allows for a solution to the puzzle.
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Your first answer seems to fit all the parameters of the puzzle. I'd consider that a perfectly satisfactory answer. Another answer that fits the hints the OP gave is
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I'm thinking the top one is better, but I'm not gunna try to calculate the probabilities... If the board has taught me anything, it's that random permutation study is immensely interesting
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Interesting problem
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This part seems counter intuitive to me.
