Jump to content
BrainDen.com - Brain Teasers
  • 0

Where did all these dowels come from?


Prof. Templeton
 Share

Question

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.

post-9402-0-67175000-1349278237_thumb.jp

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.

post-9402-0-14372100-1349278259_thumb.jp

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

Link to comment
Share on other sites

Recommended Posts

  • 0

I count 34!

post-39441-0-25638700-1349385960_thumb.j

To alter the square one pair of angles has to get bigger while their adjacent angles get smaller.

Two of the triangle arms prevent the angle between them from getting bigger but the angle can get smaller. By using three arms this prevents the angles adjacent to each other in the square from getting bigger. Therefore the square can't alter shape.

Edited by curr3nt
Link to comment
Share on other sites

  • 0

Recreate it with a rhombus with angles of 60 and 120 instead of squares for an idea of how it can change.

Top square and bottom square are flattened and middle square's left side drops down.

I already tried that. Made some pretty patterns when I kept expanding it.

Link to comment
Share on other sites

  • 0

How thick and long is the dowel? Given the right proportions Rob may be a winner.

Note the triangle is not connected to the square as end needs to be connected to end but the triangle does not need to be connected to the square?

Note while if we assume infinite thinness of the dowel the triangle has to be larger than the square for this to work if the dowel has the right thickness this can be accounted for.

Link to comment
Share on other sites

  • 0

So... is it possible to get less than 34?

Yes. pg may be on the road to a more efficient solution with a small modifications to his current design. I'm glad to see he didn't make the common mistake of trying to join the connections (circled) on the bottom and eliminating a number of supports on the top.

post-9402-0-95969700-1350403692_thumb.pn
Link to comment
Share on other sites

  • 0

I see that other solutions have had the triangles impinge on the square, without connecting to it.

My question about the 33 solution is that I imagine the top and bottom squares collapsing to the left and right respectively, while still remaining pinched between the crab claws. So I think the squares are not actually firmed up.

Link to comment
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Answer this question...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

Loading...
 Share

  • Recently Browsing   0 members

    • No registered users viewing this page.
×
×
  • Create New...