# Building a bridge

PBE6
Posers and Puzzles 27 Oct '09 18:26
1. PBE6
Bananarama
27 Oct '09 18:26
Imagine you have a supply of perfectly uniform bricks of length 1, and you'd like to build a freestanding bridge of sorts. How far could this bridge theoretically extend if it is composed of bricks placed on top of once another in a single strip?

For example, a bridge made of 3 bricks resting on the ground would look something like this from the side:

. . . . ____
. . . ____
. . ____
**************(ground)
2. joe shmo
Strange Egg
27 Oct '09 20:40
it could go forever, given the proper placment.
3. PBE6
Bananarama
27 Oct '09 20:57
Originally posted by joe shmo
it could go forever, given the proper placment.
Of course, the real question is can you prove it?
4. joe shmo
Strange Egg
27 Oct '09 22:07
Originally posted by PBE6
Of course, the real question is can you prove it?
no, I cant prove it.
5. joneschr
Some guy
27 Oct '09 22:57
Originally posted by PBE6
Of course, the real question is can you prove it?
Sure, just give me some bricks and some mortar.
6. uzless
The So Fist
28 Oct '09 02:51
Originally posted by PBE6
Imagine you have a supply of perfectly uniform bricks of length 1, and you'd like to build a freestanding bridge of sorts. How far could this bridge theoretically extend if it is composed of bricks placed on top of once another in a single strip?

For example, a bridge made of 3 bricks resting on the ground would look something like this from the side:

. . . . ____
. . . ____
. . ____
**************(ground)
reverse cantelever every other brick.

lay one brick down
place the next one 2/3 of an overhang.
place the next one 1/3 hanging back the opposite way
place the next one 2/3 of an overhang

etc etc
7. uzless
The So Fist
28 Oct '09 02:521 edit
an easier way would be to just build your bridge in the shape of an arch but i'm not sure if this is what you had in mind when you said one strip.
8. PBE6
Bananarama
28 Oct '09 15:33
Originally posted by uzless
reverse cantelever every other brick.

lay one brick down
place the next one 2/3 of an overhang.
place the next one 1/3 hanging back the opposite way
place the next one 2/3 of an overhang

etc etc
Nope, that only works for the first brick or the first 3 bricks. After that, it falls over.
9. PBE6
Bananarama
28 Oct '09 15:35
Originally posted by uzless
an easier way would be to just build your bridge in the shape of an arch but i'm not sure if this is what you had in mind when you said one strip.
That's a good point, actually. I should have used the word "staircase" instead of "bridge".
10. joneschr
Some guy
28 Oct '09 17:14
It can grow infinitely, but, you need to counterbalance each brick with enough weight, so that no one brick tips.

So, every brick must have more weight on the overlapping part beneath it, than the part standing free (or else the obvious happens).

So, you just need to make sure that you add additional weight to compensate for all the bricks that you add to the right.

So, your "bridge" looks something like:
|
|
| |
| |
| __
|__
__
__

It's a funny looking bridge, but it can get as long (and high at the same time) as you want it to.
11. PBE6
Bananarama
28 Oct '09 17:28
Originally posted by joneschr
It can grow infinitely, but, you need to counterbalance each brick with enough weight, so that no one brick tips.

So, every brick must have more weight on the overlapping part beneath it, than the part standing free (or else the obvious happens).

So, you just need to make sure that you add additional weight to compensate for all the bricks that you ad ...[text shortened]... a funny looking bridge, but it can get as long (and high at the same time) as you want it to.
I think you're hovering around the right idea, but you don't need extra weight on the back end of the staircase to balance everything. The greatest length bridge can be achieved with one brick per level, no back-weighting.

HINT: Each subset of bricks must balance on that subset's foundation brick...try starting with the smallest subset and see what happens!
12. joe shmo
Strange Egg
28 Oct '09 18:59
Originally posted by PBE6
I think you're hovering around the right idea, but you don't need extra weight on the back end of the staircase to balance everything. The greatest length bridge can be achieved with one brick per level, no back-weighting.

HINT: Each subset of bricks must balance on that subset's foundation brick...try starting with the smallest subset and see what happens!
It might have something to do with the fact that the series

Sum(n=1,infinity)1/n is a divergent series.
13. PBE6
Bananarama
28 Oct '09 19:17
Originally posted by joe shmo
It might have something to do with the fact that the series

Sum(n=1,infinity)1/n is a divergent series.
It may indeed. ðŸ˜‰
14. sonhouse
Fast and Curious
14 Dec '09 13:59
Originally posted by PBE6
That's a good point, actually. I should have used the word "staircase" instead of "bridge".
of course if that butterfly that changed the weather in Brazil were to land on top....