Posers and Puzzles

Posers and Puzzles

  1. Standard memberroyalchicken
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    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. Donationrichjohnson
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    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 memberroyalchicken
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    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 memberroyalchicken
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    22 Mar '03 15:09
    I've solved it. Anyone else? Ideas...?
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    24 Mar '03 21:07
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  6. Standard memberroyalchicken
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    24 Mar '03 21:54
    Erm...no. How did you arrive at that?
  7. Donationbbarr
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    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 memberroyalchicken
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    25 Mar '03 01:151 edit
    Actually, ingenuity and trigonometry suffice. Are you guys going to give it a go, or wait around for Acolyte 😉?
  9. Donationbbarr
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    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 memberroyalchicken
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    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 memberroyalchicken
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    28 Mar '03 19:33
    No takers? Acolyte?
  12. DonationAcolyte
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    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 memberroyalchicken
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    30 Mar '03 02:081 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?
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    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 memberrandomperson
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    06 Apr '03 18:05
    can't u just fit them into a hexagon and let them be any size?
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