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bonanova

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Everything posted by bonanova

  1. That agrees with simulations I ran, which gave, approximately, Nice solve.
  2. You're right. And it's not much of a puzzle after all. You have to allow Albert to lean forward as he runs to make this puzzle at all interesting. But even then, the obvious solution is to have Albert lie horizontally and crawl at infinite speed. Only the top of his head gets wet then. I ran into this puzzle a few years back and "solved" it, more interestingly but also more incorrectly, by multiplying his front and top areas respectively by sin theta and cos theta where theta was determined by his speed compared to the speed of the rain, and some other stuff. It was nonsense.
  3. @Thalia You are so right. Thanks. Locking this thread.
  4. You are wearing gloves while trying to retrieve the marbles contained in a bag. Because of the gloves, you're doing a pretty poor job of it. With each grab, you are only able to retrieve a random number of marbles, evenly distributed between 1 and n, the number of marbles currently in the bag. With 30 marbles initially in the bag, how many grabs do you expect it will take to retrieve them all?
  5. Twenty coins lie on a table, with ten coins showing heads and the other ten showing tails. You are seated at the table, blindfolded and wearing gloves. You are tasked with creating two groups of coins, with each group showing the same numbers of heads (and tails) as the other group. You are only permitted to move or flip coins, and you are unable to determine their initial state. What's your plan?
  6. For the purposes of this puzzle, consider our old friend Albert to have the shape of a rectangular paralellepiped (when he was born the doctor remarked to his mother, I don't explain them, ma'am I just deliver them) just meaning a solid having (six) rectangular sides. At a recent physical exam, Albert was found to be 2 meters tall, 1 meter wide and .20 meters thick (front to back.) He maintains his geometric rectitude by never leaning forward when he walks or runs. So anyway, Albert, alas, has found himself caught in a rainstorm that has 1000 raindrops / cubic meter that are falling at a constant speed of 10 meters / second, and he is 100 meters from his house. Just how fast should Albert run to his house so as to encounter as few raindrops as possible?
  7. If you chose to answer this question completely at random, what is the probability you will be correct? 25% 50% 0% 25%
  8. If 5+3+2 = 151022 9+2+4 = 183652 8+6+3 = 482466 5+4+5 = 202541 Then 7+5+2 = ______ ?
  9. It's an alternative representation to put the quotient to the right side. Here is the more familiar placement. The green (overlined) digits repeat forever. _________________ 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 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 ------------- 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 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 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
  10. Here are the placeholders for a long division, solvable, even with none of the digits filled in. The quotient has been placed to the side. It has a decimal point, not shown, and its last nine digits are repeating. Meaning, of course, the last row of X's replicates a previous row. Can you piece together the dividend? -------------- _________________ 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 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 ------------- 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 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 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
  11. Here are the placeholders for a long division, along with a single digit in the quotient. Can you piece together the dividend? x 7 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 x x ----------- x x x x x x x x ------- - - - - -------
  12. That was the first-cut answer in the ant-chessboard problem. The solution is easier to find if we (reasonably) assume that
  13. I'm humbled. btw I sharpened (with humor) the flavor text and posted this on another favorite site. It will be interesting to see how quickly it's solved there.
  14. @Molly Mae gets the coveted bonanova gold star for finding an algorithm and getting the answer in less than one day. So now that the cat (algorithm) is out of the bag, so to speak, it should be trivial to find whether an integer can triple, (or quadruple, or quintuple) under the same manipulation. It's also interesting that his solution forms a ring that shows the doubling process also occurs for four other ending digits (not 1, so his is the smallest.) But which ones? Incidentally, this also shows that all such integers have 18 digits.
  15. Things are not going well at the Acme Company. Executive talent is hard to come by, and it is not cheap. Folks at the water cooler have no ideas, and the coffee-breakers can't imagine how to improve things either. But those who party around the teapot, they came up with something. They suggested to the Board that Acme promote the newest hire in the mail room and make him the CEO! We need to shake things up, but good. Qualifications, job experience, brains, judgment, integrity, these are all things of the past. Some were not so sure. Doesn't make sense at all, the old timers said. Almost like appointing some guy with orange complexion to be President. That's exactly the idea, said the tea-people. Turn things on end, let the bull loose in the china shop, and see what happens. Hey -- how could it be worse than what we have now? Not surprisingly, the debate was long and heated. Such a risk merited proof of possible gain, so the old guard posed a challenge: produce a concrete example of where the idea had been tried with incontrovertible benefit. In fact, make it mathematical. You know, something that might make a good BrainDen puzzle. We'll promote the mail room guy, they said, if you can show us an integer that doubles in value when its least significant digit is promoted to its most-significant position. That is, give us a number { some digits } q that has half the value of q { same digits }. That all happened last week, and now we're looking for the mail room guy. Was he promoted? Did the tea people find such a number? Is there one? We need a number or a proof that one does not exist. T.L.D.R. What number doubles in value by by moving its last digit to the first position (if there is one)?
  16. Al, Bert and Charlie are on the ballot for secretary of the local yacht club, and they finish in a three-way tie. To break it, they solicit the members' second choices, and again it's a three-way tie. Al notes that since the number of members is odd, a series of two-way votes would be decisive. As a reward for finding a way past the impasse, Al receives the bye and will take on the winner of a Bert vs Charlie vote to decide who gets the position as secretary. Assuming voter preferences do not change, what are the winning probabilities for the three gentlemen?
  17. Alternate approach to the ant-checkerboard problem asks: What is the probability of flipping 8 heads before 5 tails?
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