bonanova
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Everything posted by bonanova
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Quick back of the envelope sketch convinces me. Nice.
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That's it. There's no way other than luck or a computer to find this solution, and for that reason it's not really a Brain Teaser. I posted it, because it seems that an incremental search is possible using a checkerboard and 7 markers. But each move changes so many [6 distances] things, it's not practical. A while back, I used simulated annealing [i was a colleague of S. Kirkpatrick] to place 106-plus circuits on a chip. That approach would work well here. Kudos for pursuing to the answer.
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Ah! Thanks for pointing that out. There should of course be 4 X's in the bottom line. I've edited the OP to Make it So.
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* Moderator Hat On * The OP asks to evaluate the series. Infinite or undefined, the first reciprocal is problematical. The OP has asked us to ignore it. Does anyone have a clue about the next term of the sequence, or about the sum? * Moderator Hat Off * Infinity, in this forum, seems to be self-defining: Infinity: The number of posts that will be made on the subject before consensus is reached. The silver lining is that posts can be assigned integer values, so it's a countable infinity.
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Point taken. I'm not sure what normal practice dictates when knowledge outside the OP comes to bear on a solution. My approach [while others may differ] is to assume nothing of consequence outside the OP, and see if a solution can be obtained. Good example here is Hole in a Sphere. My intent was to imply a mathematical earth [as described] having oceans of sufficient depth to float the cube. I could have avoided the issue by making the cube edges 100 feet, and that might have been the better thing to do. But some might then answer: "by an insignificant amount" where what I was looking for was "not at all."
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This puzzle was originally published in 1954 in the American Mathematical Monthly, and was one of its most popular problems. The digits [not all the same] have been replaced by X's, except for the quotient where all but one have been removed! Although there are 81 x 109 possible solutions, this is really not as difficult as it looks, after some close inspection. For starters, the lone 8 is correctly placed, as the third digit of the 5-digit answer. Enjoy! . . . . . . . . . 8 . . . .---------------- X X X / X X X X X X X X . . . . . X X X . . . . . ----- . . . . . . X X X X . . . . . . . X X X . . . . . . . ----- . . . . . . . . X X X X . . . . . . . . X X X X . . . . . . . . -------
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Sounds good. Nice!
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Yes, that's the flaw. Assuming that P1's arrival throughout the one-hour interval has constant probability is wrong. If the two persons are John and Joe, the assumption is true for Joe: his arrival is equally likely at Noon, 1:00 or anywhere in between. If he arrives at Noon, the probability that he's the first to arrive is unity. But that probability decreases with time, being zero if Joe arrives at 1:00. So the arrival probability for P1, the first person to arrive, is weighted heavily away from the last 20 minutes, where the meeting probability is unity. This error can appear in discrete problems when the enumerated possibilities are not equally probable.
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That is indeed the question: Where is the flaw?
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Your picture does not apply to the flawed analysis. If it did, the analysis wouldn't be flawed. Now can you spot the flaw?
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Al Gore is stranded on a cubic iceberg that measures 100 miles on a side. To pass the time until his rescue, he recites from memory all his speeches on Global Warming. The hot air he produces melts the iceberg. What is the resulting rise in sea level world wide? You may assume: Water expands 10% when it freezes.The earth has a 4000 mile radius.Three quarters of the earth's surface is covered by connected oceans.
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Follow-on question: Can the sum of angles of a triangle be less than 180o? How small can that sum be?
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Brighter: Right on!
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Nice puzzle.
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Good point ... I hadn't noticed. And yes there is, but it's not trivial to find.
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Right again. Btw these animals are known as Steinmetz solids; Googling provides a look at their shapes.
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Yup.
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Not to worry; you made the effort, and finding the right search words is not simple. This is a nice puzzle, that has a glaringly correct but difficult to find solution.
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gurn has it. with groundwork by Dunpeal
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