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Posers and Puzzles

Posers and Puzzles

  1. Standard member royalchicken
    CHAOS GHOST!!!
    20 Mar '03 22:24
    Suppose you wish to place 7 equally-sized cylinders of length l and diameter d in such a way that they all touch each other. What is the largest value of l/d such that this is impossible?
  2. Donation richjohnson
    TANSTAAFL
    21 Mar '03 18:12
    Originally posted by royalchicken
    Suppose you wish to place 7 equally-sized cylinders of length l and diameter d in such a way that they all touch each other. What is the largest value of l/d such that this is impossible?
    Do you mean that they all touch at least one other cylinder? or that they each touch every other cylinder?
  3. Standard member royalchicken
    CHAOS GHOST!!!
    21 Mar '03 18:25
    Each touches every other. I haven't even tried this puzzle yet, and I don't know the answer, but I think I'll give it a go.
  4. Standard member royalchicken
    CHAOS GHOST!!!
    22 Mar '03 15:09
    I've solved it. Anyone else? Ideas...?
  5. 24 Mar '03 21:07
    20
  6. Standard member royalchicken
    CHAOS GHOST!!!
    24 Mar '03 21:54
    Erm...no. How did you arrive at that?
  7. Donation bbarr
    Chief Justice
    24 Mar '03 22:08
    Originally posted by royalchicken
    Erm...no. How did you arrive at that?
    Perhaps Fregean 'flash-grasping' of necessary truths?
  8. Standard member royalchicken
    CHAOS GHOST!!!
    25 Mar '03 01:15 / 1 edit
    Actually, ingenuity and trigonometry suffice. Are you guys going to give it a go, or wait around for Acolyte ?
  9. Donation bbarr
    Chief Justice
    25 Mar '03 02:09
    Originally posted by royalchicken
    Actually, ingenuity and trigonometry suffice. Are you guys going to give it a go, or wait around for Acolyte ?
    Not me, the only interest I have in mathematics consists in its reduction to first-order logic with identity and set-theory. I'm a foundational type of guy.
  10. Standard member royalchicken
    CHAOS GHOST!!!
    25 Mar '03 21:50
    Ah. Pity. You'd be good at it. My chief interest in mathematics is currently analytic number theory. They don't teach THAT in school .
  11. Standard member royalchicken
    CHAOS GHOST!!!
    28 Mar '03 19:33
    No takers? Acolyte?
  12. Donation Acolyte
    Now With Added BA
    29 Mar '03 09:05
    Originally posted by royalchicken
    No takers? Acolyte?
    Erm... I don't have the dexterity to construct a physical model with biros, and I can't really picture how the 7 cylinders are arranged, much less prove that they have to be arranged in a particular way.
  13. Standard member royalchicken
    CHAOS GHOST!!!
    30 Mar '03 02:08 / 1 edit
    A wee hintie: 7 cylinders is the largest number for which this can be done (easy to prove), and there is only one configuration (consider that as fact; it is). To visualize it, use unsharpened pencils, or cigarettes, or just draw them (that's what I did-probably the easiest). Figure out 3, then 4, etc. Then look at limiting positions.

    What is a biro?
  14. 06 Apr '03 17:55
    Originally posted by royalchicken
    A wee hintie: 7 cylinders is the largest number for which this can be done (easy to prove), and there is only one configuration (consider that as fact; it is). To visualize it, use unsharpened pencils, or cigarettes, or just draw them (that's what I did-probably the easiest). Figure out 3, then 4, etc. Then look at limiting positions.

    What is a biro?
    A biro is a very cheap pen, a ballpoint oen
  15. Standard member randomperson
    Ruler of Insanity
    06 Apr '03 18:05
    can't u just fit them into a hexagon and let them be any size?