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Quantum.Mechanic

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Everything posted by Quantum.Mechanic

  1. Please specify the number of games in the group round. Might as well specify the number of possible matches in the knockout tree. I'd also like to know the rules for swapping players, etc. I have no experience with fantasy sports, though the puzzle sounds interesting.
  2. The log of a sum is not the sum of the logs. The problem stated that this worked for all N, but only 1 X. Where's your X?
  3. Just for my education, is there a closed form solution for the infinite sum (1 + y + y^2 + ...) ???
  4. But we know that 1 minute does eventually end. And 1km has an end. It's very close to Zeno's Paradox about Achilles and the Tortoise.
  5. Every point on an infinite line can be taken as the midpoint. Each half-line is equally long. Note that a half-line is "just as long" as a whole infinite line, even though a 1:2 mapping can be constructed. Infinity = 2*Infinity = 3*Infinity = ...
  6. Your arrays are very regular, and not balanced with equal counts of the numbers 1-10.
  7. Rhythm has 2 syllables, so is 'm' a vowel too?
  8. What does grammar have to do with it? Whether it's hyphenated or not doesn't change the meaning. Hyphenation would simply allow quicker identification, and avoid confusion with similar words where sub- was not a prefix. (Examples?) And if it needs to be hyphenated, you could make a case that bookkeeper should be "book-keeper" or even "book keeper" (ignoring the common usage card).
  9. Bonus points for your self-deprecating style, persistence, and -- the best part -- fresh and interesting puzzles.
  10. Hrmmm...What defines which side is the black side and which side is white? Is it not the starting position? Since all normal cues are missing, something else must decide "Black's Pawn Movement Direction", etc. (I'm assuming there are no coordinates on the board, like there are in game discussions.) So, given no hints, Black can "assume the position" at either end. Under normal chess rules this would determine the pawn direction, would it not?
  11. 1) Can the Guards' side start off in check? That is normally against the rules, but is worth stipulating here. 2) I understand the assumption that the Guards will start in the normal starting formation if possible. However, it seems to be a strategic blunder to do so if they form up last.
  12. To add to bonanova's reply... You would only be replacing one sequence of bits with another. To compute a given bit, the parity of <the given bit and all remaining bits> is combined with the parity of <all remaining bits>. An interesting twist on the puzzle: If each prisoner could only see the one immediately in front of him, and allowing for some simple (binary) communication, is there a solution?
  13. What if a + b + c isn't the smallest sum? To brute force it, you need to generate the sums for each permutation, count the unique ones (8), and check that max-min = 7. It only takes a minute or two on my machine to generate compute all of these, including the rotations and reflections. (It's debatable whether it takes longer to filter out the rotations and reflections, or just compute them all and filter the results.)
  14. Followup for you: Determine all possible pair(s) (F, G, H) of positive integers, with F > G >= H, such that: FF+HG = GG+HF
  15. "positive" integers?
  16. BTW, Tigers can swim.
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