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Posers and Puzzles

Posers and Puzzles

  1. Standard member PBE6
    Bananarama
    07 Nov '07 19:45
    What is the longest single-penny width bridge you can make by stacking pennies on top of each other on the edge of a table?
  2. Standard member sven1000
    Astrophysicist
    08 Nov '07 07:14
    Is that a theoretical or practical question?
  3. 08 Nov '07 07:17
    Idk. I know it's infinite for cards. You can experiment with cards if you like. Get a stack of cards, with length unit 2. Then push the top card out 1 unit, the next 1/2, the next 1/3. ect.

    Since 1+1/2+1/3.... is infinity, then the length is infinite.
  4. Standard member sven1000
    Astrophysicist
    08 Nov '07 07:23
    http://www.fincher.org/CoinStacking/HowTo.shtml
  5. Standard member sven1000
    Astrophysicist
    08 Nov '07 07:26
    Originally posted by Dejection
    Idk. I know it's infinite for cards. You can experiment with cards if you like. Get a stack of cards, with length unit 2. Then push the top card out 1 unit, the next 1/2, the next 1/3. ect.

    Since 1+1/2+1/3.... is infinity, then the length is infinite.
    Well, ok, that is a theoretical result. I'd like to see someone try to successfully use that to bridge even 5 units of length (2.5 units from each side).

    The website above shows a practical success of a three penny distance, using some counterbalance techniques. Counterbalance with your cards would probably make bridge building much easier.
  6. 08 Nov '07 07:48
    1+1/2+1/3+1/4... never reaches 9.
  7. 08 Nov '07 08:55
    Originally posted by doodinthemood
    1+1/2+1/3+1/4... never reaches 9.
    Yes, it does. The series 1/1+1/2+1/3+...1/n is asymptotic to ln(n); ln(n) reaches 9 for n=8103-and-a-bit.

    Richard
  8. 08 Nov '07 09:44 / 1 edit
    Originally posted by doodinthemood
    1+1/2+1/3+1/4... never reaches 9.
    It does. The easy way to look at it is this:

    1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9 + ...

    > 1 + 1/2 + (1/4 + 1/4) + (1/8 + 1/8 + 1/8 + 1/8) + (1/16 + ...) + ...

    = 1 + 1/2 + 1/2 + 1/2 + 1/2 + ...
  9. Standard member PBE6
    Bananarama
    08 Nov '07 16:50
    I got a different result. My series ended up being the inverse factorial series, not the harmonic series. Have to double check the calculations...
  10. Subscriber joe shmo On Vacation
    Strange Egg
    08 Nov '07 18:34
    Originally posted by mtthw
    It does. The easy way to look at it is this:

    1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9 + ...

    > 1 + 1/2 + (1/4 + 1/4) + (1/8 + 1/8 + 1/8 + 1/8) + (1/16 + ...) + ...

    = 1 + 1/2 + 1/2 + 1/2 + 1/2 + ...
    Is this like exponential decay?
  11. Standard member uzless
    The So Fist
    08 Nov '07 19:43 / 1 edit
    Originally posted by PBE6
    What is the longest single-penny width bridge you can make by stacking pennies on top of each other on the edge of a table?
    So far i've made it up to 5 but I've got the shakes after too many beers last night. I might be able to get to 7 when my hands settle down.
  12. Standard member wolfgang59
    Infidel
    08 Nov '07 20:45
    Originally posted by uzless
    So far i've made it up to 5 but I've got the shakes after too many beers last night. I might be able to get to 7 when my hands settle down.
    thats a minimum of 226 coins (I think)

    7 will take ... a MINIMUM of 1655 coins (I think) and a steady hand!

  13. Standard member PBE6
    Bananarama
    08 Nov '07 21:03 / 1 edit
    Originally posted by wolfgang59
    thats a minimum of 226 coins (I think)

    7 will take ... a MINIMUM of 1655 coins (I think) and a steady hand!

    Easy there, Frank Lloyd Right...I'm pretty sure he meant 7 coins...

    OK! Found the glitch in my calculations. I get the harmonic series now, too. More specifically, the position "L" of the furthest edge of the top coin is given by:

    L = sum(i=1...n) 1/(2i) = (1/2) * sum(i=1...n) 1/n

    This series is divergent, so the theoretical length of the bridge is infinite.
  14. Standard member wolfgang59
    Infidel
    08 Nov '07 21:31
    Originally posted by PBE6
    Easy there, Frank Lloyd Right...I'm pretty sure he meant 7 coins...

    OK! Found the glitch in my calculations. I get the harmonic series now, too. More specifically, the position "L" of the furthest edge of the top coin is given by:

    L = sum(i=1...n) 1/(2i) = (1/2) * sum(i=1...n) 1/n

    This series is divergent, so the theoretical length of the bridge is infinite.


    5 COINS is not worth posting about!!! I assumed a 5 coin width!
  15. Standard member uzless
    The So Fist
    08 Nov '07 21:49
    Originally posted by wolfgang59


    5 COINS is not worth posting about!!! I assumed a 5 coin width!
    Far be it for anyone to post a bit of humour. I got up to 10 before they crashed onto the carpet and rolled down the office hallway