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About bonanova

  • Rank
    Retired Expert
  • Birthday November 03

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  • Gender Male
  • Location New York
  • Interests Music [performing and directing], photography.

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  1. Drop two sticks

    It turns out to rational. When the two sticks lie close to the opposite diagonals they always intersect, when they're near the same diagonal they intersect with a very simple probability that I think can be proved geometrically
  2. The lion and the tamer

    Good thinking. Let's add the condition that the lion and tamer are point objects. Can they coincide? Also, could the lion reduce the radius of his circle to that of the lion and maintain any angular separation he might at some point have obtained? (Your solution prohibits this, but suppose the lion made one misstep and just for a moment he lagged the angle of the tamer.) This question has an amusing answer.
  3. The lion and the tamer

    Hi and welcome Chandra. Let's add the condition that the tamer (and the lion) can change/reverse directions instantaneously. Tamer can switch from CW to CCW at his pleasure.
  4. The lion and the tamer

    If a lion and his tamer can run at precisely the same speed without tiring, would the tamer be safe inside the lion's circular cage? Assume the lion sits on a stool at the center of the cage as the tamer enters though a door on the perimeter of the cage. You can also neglect the size of their bodies. i.e. consider the lion and tamer as points.
  5. Dangerous safari?

  6. 3 remarkable numbers

    The puzzle is interesting, especially for those who are into number theory. Last week I looked at this puzzle and decided I would not be able to find the connection among the numbers. So I searched OEIS out of curiosity. For some reason I didn't find it. (Strange.) Next I Googled the numbers themselves, and that turned up the football reference. <moderator hat on> I agree with Mike's sentiments. The Forum is for solving puzzles; it's not an Internet scavenger hunt. If you can't solve it, say so and maybe start a (spoilered) group effort. Or ask the OP for a clue. The spoiler function permits multiple users to have a go at solving a puzzle. So solutions belong there. (Even funny ones about football.) <moderator hat off>
  7. 3 remarkable numbers

    I'll bet this is not the answer you're looking for, but it does qualify as a remarkable matchup:
  8. What are these?

    Good one. But I can't identify all of the movies, either.
  9. Principal's age

    Assuming that they bought
  10. Drop two sticks

    In this puzzle, limits can lead us astray.
  11. In the case of 80 mph the fly, Ferrari and truck all meet on the fly's first and only collision. The OP asks the fly to move to the truck, back to the Ferrari, back to the truck and finally back to the Ferrari. Then, "upon returning from the second trip," the three collide. The 80 mph case has them colliding upon reaching the truck for the first and only time.
  12. Drop two sticks

    Yes. Sorry I didn't make that clear. In reply to your answer,
  13. Drop two sticks

  14. I think those equations describe the conditions described in the OP. But I don't think there is a solution that satisfies the OP. Maybe that is just what you are saying. But I don't think it's the fault of the equations; it's the claim in the OP that the three all collide at the conclusion of the second round trip of the fly. That just can't happen if all three have constant speeds. Consider the situation at time1 + time2 + time3, when the fly has hit the truck for the second time. The fly completes his trip by returning to the Ferrari. But it doing so it must perform an impossible task. (1) It must fly back to the Ferrari at a speed that is greater than the speed of the truck (it's at least the speed of the Ferrari), but (2) it must arrive at the same time that the truck arrives. That is not possible. The fly will arrive at the Ferrari before the truck does.
  15. Here's a simulation without actually writing the program: