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Everything posted by ThunderCloud

  1. A simple integration paradox?

    (removed... still thinking...)
  2. 3-color cube

  3. 3-color cube

  4. Twenty Questions

    I did not see this puzzle mentioned in the forum before: Twenty Questions by Don Woods. I was able to solve it by computer (I verified my answer with the author), but even that wasn't easy! I'd love to hear of others' experiences with it. ^.^
  5. 3-color cube

    This is a good point. I should clarify that for my answer, I assumed that if one configuration of colors can be transformed into another by rotating the cube, then they should not be counted as two distinct configurations.
  6. 3-color cube

    I think...
  7. How much white?

  8. Finding a function

    You asked for it...
  9. The lion and the tamer

  10. Really?

  11. Numbered Foreheads Concluded

    Although I believe the logic to answer the original problem was present, it was distributed among several postings... It did not seem right to mark any single post as the best answer. Therefore, here is the bonus round. If approached correctly, this version is not much harder than the original. The puzzle: Three perfect logicians had stickers placed on their foreheads so that none could see their own sticker but each could see one another's. They were told that each sticker has a single positive integer written on it (i.e.1, 2, 3, ...), and that the sum of the integers on all three stickers is either 1002 or 1003. They were then asked, in turn, to identify the number on their own sticker. Upon being asked, each logician would name their number if they were sure that they knew it, give up if they were sure that they would never know it, or otherwise 'pass' (or say "I don't know"). The question was repeated, again in turn, until EACH of the three logicians had either named their number or given up. All three stickers actually had the same number written on them. Who among the three logicians was able to deduce his number, and who among them gave up? (Furthermore, how did each answer?)
  12. combining the primes

  13. Find the flaw: Picard's Theorem

    It's a theorem in complex analysis, not in real analysis. Do you know about complex numbers? Ah, that was the part I missed. Thanks.
  14. Halloween Candy

    At a Halloween party, three boxes of candy were set out. Each contained 100 candies, individually wrapped in plain black wrapper. One box contained only chocolate candies, another contained only licorice candies, and the remaining box contained a blend (of unknown proportion) of chocolate and licorice candies. All three boxes were labeled, however, some prankster came by and swapped the labels on two of the boxes. How many candies would you have to sample in order to set the labels right again?
  15. Numbered Foreheads Concluded

    We know that A sees B=334 and c=334 - A CANNOT see B=335 and C=334. (Not to confound with: "As this information in not available to him, he ASSUMES he has 334 or 335.") So my first answer was correct. In the 2nd try, I got lost and could not correct quickly enough.
  16. Numbered Foreheads Concluded

    I think you are on the right track, and very close.
  17. Numbered Foreheads Concluded

    No. The logicians cannot agree upon a strategy in advance. However, you may assume each of them to be "perfect" in that they will deduce all that they logically can. You may further assume that each logician will assume the others to behave this way as well (i.e., that it is generally known that all three logicians are "perfect").