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bonanova

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Everything posted by bonanova

  1. Walk the pattern

    Looks like
  2. Walk the pattern

    With that interpretation,
  3. Walk the pattern

    Assuming the above, we note that
  4. Walk the pattern

    Just to be clear, n = 3 4 5 7 8 9 11 12 13 ..., and CW and CCW alternate untethered (my new favorite word) to parity?
  5. Strange math problem

    The professor writes a problem on the whiteboard, thus: 25 - 55 + (85 + 65) = ? He then inexplicably states that, even though you might disagree, the correct answer is actually 5! Explanation?
  6. Twins birthday puzzle

    Nice solve. And the "few years back" is actually two years ago, when Feb 28 was Sunday and March 2 was Wednesday.
  7. Twins birthday puzzle

    A few years back while visiting friends, we celebrated the birthdays of their identical twin daughters Joan and Jane, born just 5 minutes apart. Joan had her party on Sunday, and Jane had hers on Wednesday. Explanation?
  8. Random passengers

    Al and Bert are among 100 passengers assigned to one hundred seats on an airplane. Al was first to board, and Bert was last. Strangely, the first 99 passengers ignored their boarding passes and took random unoccupied seats. Bert liked the seat he was assigned and is not happy with the situation. If he's lucky, his seat is unoccupied and there's no problem. Otherwise, he insists the passenger erroneously occupying it move to his own assigned seat. The displaced passenger must then move, possibly displacing another person. This process continues until all passengers are seated. What is the probability that Al must move?
  9. Random passengers

    This was my take.
  10. Random passengers

    Nice. One thing I liked about this puzzle is that it's open to clear thinking. Even tho at first it seems too complex.
  11. Comparing a rectangle to a circle

    But actually ...
  12. Comparing a rectangle to a circle

    It certainly should. It clearly fails a units check. Good catch.
  13. Poisoned Needles

    Do any of the clues imply that the indicated needles are adjacent? I would take "on the left side of" to imply that "pain" is adjacent to "seek," while "to the left of" simply means "the other pain" is not to the right of "interesting little creation." But I'd like to be certain of that. Also, is "interesting little creation" one of the needles? If so, you have described nine, not eight, needles. Thanks.
  14. You have 10 sets of ten coins. One set of the ten is counterfeit, the others are genuine. The genuine coins weigh exactly 0.10 ounces. The counterfeit coins are exactly a 0.01 ounces off, making the entire set of ten coins 0.10 ounces off. You may use an extremely accurate digital scale only once. How do you determine which set is counterfeit?
  15. Two boys

    I ask people at random if they have two children and also if one is a boy born on a tuesday. After a long search I finally find someone who answers yes. What is the probability that this person has two boys? Assume an equal chance of giving birth to either sex and an equal chance to giving birth on any day.
  16. Recently we considered the shortest roadway that connects the four corners of a square. Here we seek the shortest set of line segments, one attached to each of a square's corners, that need not connect with each other. Instead, what we ask of the line segments is that is they will block any ray of light attempting to pass through the square.
  17. a^b x c^a = abca

    Find a, b, c. ab x ca= abca , a 4-digit number
  18. Random passengers

    Clue.
  19. Two boys

    @ThunderCloud you're homing in on it, but now you're a little high. @BMAD It's certainly true that if the FIRST child was a boy born on a tuesday, then it's just the prob that the second child is a boy. But ... the OP does not tell you that. That is, "one is a boy" does not imply "my oldest child is a boy." So your "second" child simply means the "other" child.
  20. a^b x c^a = abca

    Not that I know of. Tables of powers, or spreadsheet where different abc values can be simply typed in, or inspired guesswork? It's not my fav type of puzzle, but some like this type.
  21. Two boys

    @ThunderCloudThat's close, but a bit low.
  22. The Most Wonderful Prince

    The King has decreed that his daughter the Princess shall marry the most wonderful Prince in all the land. One hundred suitors have been selected from their written applications, and on a certain day the King arranges for them, in turn, to interview the Princess. Each suitor must either be chosen or eliminated on the spot. If the Princess does not choose any of them, she will marry the last Prince to speak with her. You have been chosen as the Royal Advisor to the Princess and tasked with implementing her best strategy to choose the Most Wonderful Prince of the realm. You devise an evaluation scheme by which the princess can assign a unique "wonder number" to each prince as she meets him. The strategy then is to have the Princess reject, but record the highest score of, the first N princes that she meets. The Princess will then choose the first Prince that she subsequently interviews whose score exceeds that recorded score. That's it. The puzzle is basically solved. Except, of course, to decide on the optimal value of N. It requires some thought. If N to too high, the most wonderful prince is likely to be eliminated at the outset, and she ends up with the last guy. If N is too small, the Princess will likely settle for a fairly undistinguished prince. What value of N optimally balances these two risks? What is the probability that the Most Wonderful Prince will be chosen? Disclaimer: I recall this puzzle being posted before, with different flavor text. And it's somewhat of a classic. To give it a fair play here, I'll ask not to post any links and not to just give the answer if you know it, at least not without "showing your work."
  23. The Most Wonderful Prince

    So this guy Thomas Bruss solved the general stopping problem.
  24. Salesman in a Square

    Al made sales calls at a number of cabins, which lay in a square field, one mile on a side. He drove his car to the first cabin, then visited the remaining cabins and returned to his car on foot, walking several miles in the process. If Al had had a map and perhaps a computer, he could have picked the shortest route to take, (traveling salesman problem). Lacking these amenities, Al simply chose to visit (after the first one) the (un-visited) cabin closest to his current location. If there were 6 cabins in all, how might they be placed, so that using Al's nearest-neighbor algorithm, and selecting the worst initial cabin, Al would be forced to walk the greatest distance; and what is that distance? Examples: 2 cabins: diagonal corners, starting at either: 2 x sqrt(2) = 2.828... miles. 3 cabins: any three corners, starting at any of them: 2 + sqrt(2) = 3.414... miles. Check out n=4 and n=5 as a warm-up.
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