Coins on a chess board

Discussion in 'Off-Topic' started by Dave, Apr 3, 2007.

  1. Dave

    Thread Starter Retired Moderator

    Nov 17, 2003
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    Here's a little conundrum that someone asked me the other day and it really demonstrates the power of the exponential.

    If you have a 64-square chess boards and an infinite supply of coins (if only) that are 1/8" (3.175mm) thick, and you placed 1 coin on the 1st square, doubled it and placed 2 coins on the 2nd square, doubled it again and placed 4 coins on the 3rd square, doubled it again and placed 8 coins on the 4th square, doubled it again and placed 16 coins on the 5th square, and continued doubling thereafter...

    ...How high would the pile of coins be on the final square?

    Now the trick here is to have a qualitative guess at the height, for example "as high as my house". Don't use software or maths to calculate the height, because that defeats the point of this.

    Dave
     
  2. m4yh3m

    Senior Member

    Apr 28, 2004
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    I remember reading about this somewhere... and my answer is:

    VERY FREAKIN HIGH! I can't remember if it was somewhere along the lines of a mile long or something to that extent.
     
  3. thingmaker3

    Retired Moderator

    May 16, 2005
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    As high as the appropriate parabola.:D
     
  4. Dave

    Thread Starter Retired Moderator

    Nov 17, 2003
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    So we have one guess at a mile.

    And in millimetres/inches/metres/feet/kilometres/miles that is?

    I reiterate to those reading don't calculate it on a computer then post up your "guess", the idea is to have a qualitative guess.

    Dave
     
  5. Salgat

    Active Member

    Dec 23, 2006
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    Somewhere in the vacuum of space.
     
  6. Papabravo

    Expert

    Feb 24, 2006
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    About the distance to a relatively close star. On the order of 1e18 meters
    Estimating 61 * log(2) = 18 * log(10)
     
  7. Distort10n

    Active Member

    Dec 25, 2006
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    This is similar to, would you rather have a million dollars or the money from 1 penny after it doubles everyday for one month.
     
  8. Salgat

    Active Member

    Dec 23, 2006
    215
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    Haha ya, I remember my teacher asking that in 8th grade. When your young it can be quite amazing how doubling something so small relatively few times can lead to quite a large value. Another one is the story of the man who asked the king for the amount of rice equal to 1 grain doubled for every square on the chess board.
     
  9. recca02

    Senior Member

    Apr 2, 2007
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    i believe uncle scrooge can answer that after he joins hands with bruce wayne and of course mr Bill Gates
     
  10. Dave

    Thread Starter Retired Moderator

    Nov 17, 2003
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    So higher than the atmosphere. Care to have a more accurate stab at it?

    Interesting approach to this. So we are saying somewhere near Proxima Centauri (the closest star)?

    This probably demonstrates why people get themselves into debt with culmulative interests on loans - but then this is a completely different question.

    Did he have enough rice?

    Funny you should mention Bill Gates, he lent me the infinite supply of coins I needed for this conumdrum :D

    Dave
     
  11. Salgat

    Active Member

    Dec 23, 2006
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    Haha I just said Outter space because I'm guessing its more than I can think in my head.:p
     
  12. Dave

    Thread Starter Retired Moderator

    Nov 17, 2003
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    To the Hubble Space Station? To the moon? To the Sun? To Mars? To Pluto? Beyond?

    There are no numbers required here, its a qualitative guess.

    Dave
     
  13. beenthere

    Retired Moderator

    Apr 20, 2004
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    Somewhere around Barnard's Star.
     
  14. Papabravo

    Expert

    Feb 24, 2006
    10,136
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    Yeah like 6 light years or so. 1e18 was inches not meters. My original estimate was only off by a factor of forty.
     
  15. thingmaker3

    Retired Moderator

    May 16, 2005
    5,072
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    I remember the last time my father and I were in the hardware store. He wanted to re-paint his living room, and was checking to see how many square feet a gallon of paint would cover. Once we had the number, we both started babbling - he in "old math" and I in "new math." We came to the same answer at the same time.

    It's how he taught me, it's how I do things. "Don't guess" he said, "you'll be wrong." If I'm not allowed to run the math (at least in my head) then I'm stuck at square one.:(
     
  16. kender

    Senior Member

    Jan 17, 2007
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    The cumulative mass of the coins will be comparable to that of Jupiter. The stacks of coins will colapse into a ball under their own gravitational pull.
     
  17. recca02

    Senior Member

    Apr 2, 2007
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    if one coin is 3.175mm thick
    so my guess is abt 3.1 light years ,
    lets go see it for ourself, your car got enough fuel
    i bought potato chips with the money on the 64th square.
     
  18. Gadget

    Distinguished Member

    Jan 10, 2006
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    Well, I know that if you fold paper over 50 times it will reach to the sun.. (Actually THAT is our closest star)... so accounting for the different thickness's and the extra 14 doublings, I would think Papabravo's estimate to be fairly close.
     
  19. recca02

    Senior Member

    Apr 2, 2007
    1,211
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    so thats why i saw something burning on sun that day. btw it was my million dollar lottery ticket that you folded and burned:mad:

    gadget san (jap for mr.),doesnt it has to be 13 extra doublings since first square is having only single coin (2^0) hence 64th sq will corr to (2^63)
     
  20. beenthere

    Retired Moderator

    Apr 20, 2004
    15,815
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    Hey man - spare change?
     
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