# Penny bridge

PBE6
Posers and Puzzles 07 Nov '07 19:45
1. 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. 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. sven1000
Astrophysicist
08 Nov '07 07:23
http://www.fincher.org/CoinStacking/HowTo.shtml
5. 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 09:441 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. 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... ðŸ˜•
10. joe shmo
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. uzless
The So Fist
08 Nov '07 19:431 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.ðŸ˜‰
12. wolfgang59
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.ðŸ˜‰
thats a minimum of 226 coins (I think)

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

ðŸ™„
13. PBE6
Bananarama
08 Nov '07 21:031 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!

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

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. wolfgang59
08 Nov '07 21:31
Originally posted by PBE6
Easy there, Frank Lloyd Right...I'm pretty sure he meant 7 coins... ðŸ™„

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.
ðŸ˜²

5 COINS is not worth posting about!!! I assumed a 5 coin width!
15. uzless
The So Fist
08 Nov '07 21:49
Originally posted by wolfgang59
ðŸ˜²

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