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Where did all these dowels come from?


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28 replies to this topic

#1 Prof. Templeton

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Posted 03 October 2012 - 04:33 PM

This may have been asked before since it was taken straight from bn’s playbook.

You have an unlimited supply of dowels all of the same length and they can only be connected at their ends. A triangle made by joining three dowels will be a rigid form, but a square made by connecting four dowels can be easily distorted into other shapes without breaking or bending a dowel or disconnecting the ends. As if the end connections were hinged. In three dimensional space the simplest way to brace the square would be to add eight more dowels the form an octahedron.

Octahedron.jpg

Let’s assume, however that we are limited to only two dimensions. Without bending, breaking or overlapping dowels, only connecting them at the ends and remaining on a two dimensional plane we can still brace the square by attaching triangles to it. Here is an example with 35 total dowels.
Spoiler for


The question is: What is the fewest number of dowels required to hold a square firm?
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#2 Faizaan

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Posted 04 October 2012 - 12:55 AM

I am sitting here with my homework tossed aside constantly rearranging a large number of tooth-picks in a desperate attempt to figure this out.
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#3 Faizaan

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Posted 04 October 2012 - 01:12 AM

ooh! ooh! WAIT!
Spoiler for I got


Arranged as such
Spoiler for peanutbutterandrazorblades


That was terribly crud(e).
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#4 Prof. Templeton

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Posted 04 October 2012 - 02:49 PM

ooh! ooh! WAIT!

Spoiler for I got


Arranged as such
Spoiler for peanutbutterandrazorblades


That was terribly crud(e).


I don't think that will hold, but applaud the effort.
Spoiler for morepeanutbutterthanrazorblades

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#5 curr3nt

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Posted 04 October 2012 - 05:35 PM

gah nevermind...

Edited by curr3nt, 04 October 2012 - 05:37 PM.

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#6 r8erred

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Posted 04 October 2012 - 09:47 PM

Spoiler for My guess


16.GIF
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#7 curr3nt

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Posted 04 October 2012 - 09:48 PM

Spoiler for would this work?


-edit-

*sigh* nope

Can I guess that 35 is the minimum?

Edited by curr3nt, 04 October 2012 - 09:51 PM.

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#8 curr3nt

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Posted 04 October 2012 - 10:32 PM

Spoiler for Ha! I got smaller than 35!

Edited by curr3nt, 04 October 2012 - 10:34 PM.

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#9 plainglazed

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Posted 04 October 2012 - 10:51 PM

Spoiler for can't quite visualize but would this work?

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#10 curr3nt

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Posted 05 October 2012 - 12:13 AM

Spoiler for sorry plain, no

Edited by curr3nt, 05 October 2012 - 12:14 AM.

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