bonanova
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While your back is turned a friend places three coins, numbered 1, 2 and 3 on a table. They are placed so that 1, 2, or 3 Tails are showing. That is, they are not all Heads. Your task, without looking, is to have your friend make them all show Heads. You do this by a series of instructions in which you identify one of the coins by number and ask him to turn it over. After turning over the identified coin your friends tells you whether or not you have succeeded. Because this is a finite game, success is eventually guaranteed - within say N trials. What strategy minimizes N? What is the minimum value of N? What is the probability of success in (N-1) moves or fewer? (N-2) moves or fewer? ... down to 2 moves or fewer?
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A standard puzzle asks how many times between midnight and noon [not counting either] do the hour, minute and second hands of a clock point in the same direction? The result is not surprising that it never happens - 11 and 59 having no common factors. So let's ask instead: at what time(s) during the same interval are the three hands closest? . By closest we mean the smallest angle between the two hands farthest apart.We exclude the trivial answer that names a time very near noon or midnight.
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Bingo! Got a pic?
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This solution is from a colleague. I only wish I had seen it.
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Thanks for the info. Off to Others.
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By this note, we are alerting you to a heretofore unknown danger of altering the integral relating to the area of a triangle. Comments are welcome.
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Nice puzzle.
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You lay some white poker chips, all the same size, flat on the table so they touch only at their edges. Your friend wants to color them so that no two chips that touch [each other] will have the same color. What is the smallest number of chips you must place on the table to force the use of . 3 colors?4 colors?5 colors?. Note - all the chips are colored: none remain white.
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You live in Killville. Can you stay alive?
bonanova replied to bonanova's question in New Logic/Math Puzzles
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with different probabilities but same strategy. Locking this thread for now. If there are differences from previous puzzle, explain them to me in a PM, and I'll be happy to unlock. - bn
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Clarification? " For example a louge flat on the straight away ... " ?
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Hi Brandt, and welcome to the Den! Hope you enjoy your membership and take the time to post your favs as well. There is a helpful "read before posting" link at the top of the page. And a Search function to help determine if a puzzle has already been posted. No need to Search your own puzzles, of course.
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More? final: all caps.
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Yes, and the point [vertex] sampling was done as Bushindo describes. I actually did the calculation in response to a that asks the probability that four darts tossed at random on a circular dartboard form a convex set of points.
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For one million random triangles in the unit circle:
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Mathephobe and EventHorizon have solved it. Kudos. Edit: There's a square root missing in the above analysis - an easy fix. But I'm tired, and it doesn't invalidate the result.
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Current consensus says that triangles that cover the center of a circle comprise 25% of any large set of random interior triangles. Pieater argues persuasively that triangles that cover a point on the circumference comprise 0% of that set. Intuitively, large triangles tend to contain a mix of central points, while smaller ones can be more local; their points follow the general point distribution which is weighted toward larger radius values. So we have big triangles mainly accounting for the large 25% central coverage, and smaller ones having a higher likelihood of covering points near the perimeter. The question is still open: what is the average size of triangles within a unit circle? Dividing by pi will then answer Part 2.
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