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bonanova

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Everything posted by bonanova

  1. It might be solvable, iteratively. I once posted a puzzle, here or elsewhere, that went as follows: But in that puzzle information was added as the constraints were iteratively applied. Here it seems it must all be determined in one shot. So maybe that's not possible.
  2. "Determine the rate of change to second base once the runner reaches halfway to first base." Determine the time rate of change of the distance between the runner and 2nd base when the runner is halfway between home plate and first base, running at 24 ft/sec on a path that is a straight line from home plate to first base. If these two statements ask for the same information, then
  3. Of his position? Of his velocity? Most runners going to 2nd base will swing wide to round out the corner and keep a constant speed.
  4. Agreed. Quite a bit off. Upon further review my guess (of a cosine relationship of line angle to wall angle) was wrong.
  5. Yes I agree. If the coin centers follow different-length paths, the shorter path will be traversed first. And since the radii are not zero, then even if the sine wave is in light-years the coin following the concave side of the curve will arrive first. (See my "In any case" post.) In the limit as the ratio of radius to amplitude goes to zero, however, the paths of the centers (and their transit times) coalesce. I just wondered if there were a reason to give units to the diameters (and not the amplitude of the sine wave.)
  6. Nice puzzle, jasen. Do you have more like this?
  7. Here's a refutation based on the impossibility of having chests whose value has uniform probability across the real numbers (or integers.)
  8. I'll give a refutation by symmetry. Mainly because Bayesian formulas are opaque to me. (Read, I tried to understand a priori distributions once.) Your first choice is random. If you switch you end up the the choice you would have made, with 50% probability, without switching. Your expectation for either envelope is $1.5x, where $x is the lesser of the two amounts. OK, yeah, the faulty argument in my post above presumes a uniform probability on the real numbers for $x. Anyone who thinks $2 and $Graham's Number have equal probability needs to immediately make a random deposit into my checking account. (Account number supplied upon request.)
  9. Please do not post advertising links.
  10. This is a classical paradox. I like this answer the best:
  11. I assume "surrounded by" means "adjacent to." So do diagonals count?
  12. Before reading the file I immediately thought of one method.
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