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Put a cork in it [original thread]


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19 replies to this topic

#1 bonanova

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Posted 07 September 2009 - 04:02 AM

A while ago we asked for a shape that fits snugly through three different holes: triangle, square and circle.

Actually, the answer is not unique. So now we ask:

What is the volume of the smallest shape that fits snugly through the holes?
The largest?

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
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#2 xamdam

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Posted 07 September 2009 - 04:25 AM

Spoiler for Hmmm

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#3 bonanova

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Posted 07 September 2009 - 04:47 AM

Spoiler for Hmmm


Spoiler for Consider

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
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#4 plainglazed

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Posted 07 September 2009 - 05:00 AM

Have to assume you're starting with the same 2" x 2" x 2" cube and by snuggly you mean the shape that, at a maximum, fits thru the hole in two dimensions while being the smallest volume? Dont know if that made any sense but it's late and I've just returned home after a night out.
Spoiler for it seems

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#5 bonanova

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Posted 07 September 2009 - 05:09 AM

Have to assume you're starting with the same 2" x 2" x 2" cube and by snuggly you mean the shape that, at a maximum, fits thru the hole in two dimensions while being the smallest volume? Dont know if that made any sense but it's late and I've just returned home after a night out.

Spoiler for it seems


Snugly means completely fills each of the hole cross sections at some moment as it passes through.
Of all the 3-dimensional shapes that do this, one has a maximum and another has a minimum volume.
The question is what are these volumes?

Been watching TV all evening, so you have the advantage on me. B))



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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#6 DeeGee

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Posted 07 September 2009 - 08:22 AM

A while ago we asked for a shape that fits snugly through three different holes: triangle, square and circle.

Actually, the answer is not unique. So now we ask:

What is the volume of the smallest shape that fits snugly through the holes?
The largest?


Spoiler for may be

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#7 DeeGee

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Posted 07 September 2009 - 08:40 AM

Oops, I just realised it was rather easy... so I decided to make sure what i understood was correct and that led me to the link to the previous question. So, now that I have realised that what I had previously understood was way off, pls ignore my previous post.

Although, for the shape with the smallest volume, I would still stick to the previous answer! Although the material would be wood and the shape could still be made by chopping and chiseling it to a very small breadth while keeping the length as 2".

Edited by DeeGee, 07 September 2009 - 08:46 AM.

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#8 DeeGee

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Posted 07 September 2009 - 09:18 AM

Spoiler for Post enlightenment - max volume

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#9 bonanova

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Posted 07 September 2009 - 02:23 PM

The shape[s] must pass completely through each of the holes.
Your cube will not pass through either the circular or triangular holes.

Consider them to be hole[s] in a wall separating two rooms.
The shape must pass from one room to the other, in turn, through
all three holes, fitting each hole snugly as it passes.

There are actually an infinity of 3-dimensional solids that will do this.
One has a largest and another has a smallest volume.

What are these volumes?

Refer to the figure in the referenced post for dimensions of the holes.
The circle has a 2" diameter; the square and triangle have 2" sides.
Since this puzzle asks a new question, it's fair game to look at the answers given there.


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#10 plainglazed

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Posted 08 September 2009 - 10:40 AM

Spoiler for considering

Edit: inches squared/inches cubed, what really is the difference?

Edited by plainglazed, 08 September 2009 - 10:43 AM.

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