do you know geometry?

[RichD]

Start with a sheet of stiff paper, and a pen.
Draw an outline of a shape, such that when cut
out with scissors, it will fold into a cube.
You're permiited to draw interior folding lines.

Everyone here will regard this as trivial. But
I've tested it on 6 people, and only 2 got it
the first try. Try it on your friends and business
associates.

 

[Don Y]

It's obvious, or should be to any engineer. You just envision a box,
and unfold it in your head.

It's basically a Christian cross.

You can do it with a *square* piece of paper.

 

[George Herold]

Start with a sheet of stiff paper, and a pen.

Draw an outline of a shape, such that when cut

out with scissors, it will fold into a cube.

You're permiited to draw interior folding lines.



Everyone here will regard this as trivial. But

I've tested it on 6 people, and only 2 got it

the first try. Try it on your friends and business

associates.

Weird.. do they only do five 'pieces' a base and four sides?

 

[m II]

It's obvious, or should be to any engineer. You just envision a box,
and unfold it in your head.

It's basically a Christian cross.

My problems are the interior folding lines. When I try to draw them, I
don't have an interior anymore. There is something Zenish going on here.

mike

 

[m II]

Just be in the box.

So...you're implying that it's my *unfolding* of the box that causes the
interior to disappear...This three dimensional space of yours is
certainly taking getting used to.


mike

 

[Robert Baer]

Start with a sheet of stiff paper, and a pen.
Draw an outline of a shape, such that when cut
out with scissors, it will fold into a cube.
You're permiited to draw interior folding lines.

Everyone here will regard this as trivial. But
I've tested it on 6 people, and only 2 got it
the first try. Try it on your friends and business
associates.

Maybe because there are so many ways it can be done?
I thought of 2 ways in less than 2 minutes and quit because it is so
simple.

 

[Robert Baer]

It's obvious, or should be to any engineer. You just envision a box,
and unfold it in your head.

It's basically a Christian cross.

Check.

 

[Don Y]

Hi David,

It's that small a number only if you restrict yourself to those
configurations in which each face of the cube must consist of a single
square cut out from the original sheet, and joins can occur only at
the face-to-face edges of the cube. That's a limitation which was
*not* specified in the original statement of the problem.

Exactly. There was no mention as to how *complex* the folding
process was expected to be.

(Nor any mention as to whether or not the folded paper would *hold*
the shape of its own accord)

If even one face of the cube is allowed to be made from two or more
non-overlapping (but exactly-joining) sub-faces made up of non-square
portions of the shape that you cut out (i.e. these sub-faces meet in
the middle of one of the cube's faces), then there are an infinite
number of cutout shapes which will qualify.

Yes. I know of at least two different ways of folding a
perfectly *square* piece of paper into a cube (without the
benefit of scissors). I could probably come up with more
if pressed...

And, by extension, any rectangular piece of paper (I think all
I need is a right angle, somewhere).

You just have to NOT think in "pedestrian" turns. Think
outside the box -- er, *cube*! :>

 

[Martin Riddle]

Start with a sheet of stiff paper, and a pen.
Draw an outline of a shape, such that when cut
out with scissors, it will fold into a cube.
You're permiited to draw interior folding lines.

Everyone here will regard this as trivial. But
I've tested it on 6 people, and only 2 got it
the first try. Try it on your friends and business
associates.

How big is the cube going to be? Your light on design input

I got a 11 x 17" piece of paper here.....

Am I allowed to use a ruler?

Cheers

 

[Jasen Betts]

It's obvious, or should be to any engineer. You just envision a box,
and unfold it in your head.

It's basically a Christian cross.

there's several shapes that work

[]
[][][][]
[]

[]
[][][][]
[]

[]
[][][][]
[]

[]
[][][][]
[]

[]
[][][][]
[]


[][]
[][]
[][]


[][][]
[][][]

[]
[][][]
[][]

possibly posibly others too...

 

[Jasen Betts]

I stopped looking after finding 8

 

[Jasen Betts]

How big is the cube going to be? Your light on design input

I got a 11 x 17" piece of paper here.....

Am I allowed to use a ruler?

Even if you are it won't be a perfect cube, so presumably any
recognisable approximation is acceptable.

If you start with an acceptably rectangular piece of paper, by folding
it you can create a regular square grid. (fold a 45 degree angle to
translate east-west measure to north-south)

 

[Jasen Betts]

On Thu, 22 Aug 2013 16:23:38 -0700 (PDT), RichD

Start with a sheet of stiff paper, and a pen.
Draw an outline of a shape, such that when cut
out with scissors, it will fold into a cube.
You're permiited to draw interior folding lines.

Everyone here will regard this as trivial. But
I've tested it on 6 people, and only 2 got it
the first try. Try it on your friends and business
associates.

It's obvious, or should be to any engineer. You just envision a box,
and unfold it in your head.

It's basically a Christian cross.

there's several shapes that work

[]
[][][][]
[]

[]
[][][][]
[]

[]
[][][][]
[]

[]
[][][][]
[]

[]
[][][][]
[]


[][]
[][]
[][]


[][][]
[][][]

[]
[][][]
[][]

possibly posibly others too...

That can't be right. John Fields has declared that there are only six.

When covering the surface of a cube one must think outside the box

 

[Robert Baer]

---
Or:

_ _ _ _ _ _
| | | |
|_ _|_ _|_ _|
| |
|_ _|
| |
|_ _|
| |
|_ _|

Or:

_ _ _ _
| | |
|_ _|_ _|_ _
| | |
|_ _|_ _|
| |
|_ _|
| |
|_ _|


Or:

_ _ _ _
| | |
|_ _|_ _|
| |
|_ _|_ _
| | |
|_ _|_ _|
| |
|_ _|


Or:

_ _ _ _
| | |
|_ _|_ _|
| |
|_ _|
| |
|_ _|_ _
| | |
|_ _|_ _|


Or:

_ _
| |
|_ _|_ _
| | |
_ _|_ _|_ _|
| | |
|_ _|_ _|
| |
|_ _|

OR:
_ _
| |
_ _|_ _| <-- top
| | |
_ _|_ _|_ _| <-- front,right
| | |
|_ _|_ _| <-- left,bottom
| |
|_ _| <-- back

This gets rid of the boring 4-in-a-row design.

 

[Robert Baer]

Here is a collection of some of those given:


1A 1B 2A 2B
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
| | | | | | | | | | | |
|_ _|_ _|_ _| _ _|_ _|_ _ |_ _|_ _|_ _ |_ _|_ _|
| | | | | | | | | | |
|_ _| |_ _|_ _|_ _| |_ _|_ _| |_ _|_ _
| | | | | | | | |
|_ _| |_ _| |_ _| |_ _|_ _|
| | | | | | | |
|_ _| |_ _| |_ _| |_ _|


2C 3 var A var B
_ _ _ _ _ _ _ _ _ _
| | | | | | | | |
|_ _|_ _| |_ _|_ _ _ _|_ _| |_ _|_ _
| | | | | | | | | | |
|_ _| _ _|_ _|_ _| _ _|_ _|_ _| |_ _|_ _|_ _
| | | | | | | | | | |
|_ _|_ _ |_ _|_ _| |_ _|_ _| |_ _|_ _|
| | | | | | | | |
|_ _|_ _| |_ _| |_ _| |_ _|

var C
_ _
| |
|_ _|
| |
_ _|_ _|
| | |
|_ _|_ _|
| |
|_ _|
| |
|_ _|

 

[Jasen Betts]

Here is a collection of some of those given:


1A 1B 2A 2B
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
| | | | | | | | | | | |
|_ _|_ _|_ _| _ _|_ _|_ _ |_ _|_ _|_ _ |_ _|_ _|
| | | | | | | | | | |
|_ _| |_ _|_ _|_ _| |_ _|_ _| |_ _|_ _
| | | | | | | | |
|_ _| |_ _| |_ _| |_ _|_ _|
| | | | | | | |
|_ _| |_ _| |_ _| |_ _|


2C 3 var A var B
_ _ _ _ _ _ _ _ _ _
| | | | | | | | |
|_ _|_ _| |_ _|_ _ _ _|_ _| |_ _|_ _
| | | | | | | | | | |
|_ _| _ _|_ _|_ _| _ _|_ _|_ _| |_ _|_ _|_ _
| | | | | | | | | | |
|_ _|_ _ |_ _|_ _| |_ _|_ _| |_ _|_ _|
| | | | | | | | |
|_ _|_ _| |_ _| |_ _| |_ _|

var C
_ _
| |
|_ _|
| |
_ _|_ _|
| | |
|_ _|_ _|
| |
|_ _|
| |
|_ _|

I just thought up some more...
_ _ _ _ _ _
| | | | |
|_ _|_ _| |_ _|
| | | |
|_ _|_ _ _ _|_ _|_ _
| | | | | | |
|_ _|_ _| |_ _|_ _|_ _|
| | | |
|_ _| |_ _|

Having one tile different to "1B" and "2B" or "Var A" or "Var C"
I can's see how to classify them

That makes 11, I can't as yet complete the dozen, if that's possible.

 

[DecadentLinuxUserNumeroUno]

That can't be right. John Fields has declared that there are only six.

Maybe you should learn to read. I did not see where it was him making
that remark.

 

[DecadentLinuxUserNumeroUno]

That can't be right. John Fields has declared that there are only six.

Maybe you should learn to read. I did not see where it was him making
that remark.

 

[m II]

Nothing was said about doing a surface twice..

Mister Baer, please report to the Accounting office NOW!


mike

 

[Robert Baer]

I just thought up some more...
_ _ _ _ _ _
| | | | |
|_ _|_ _| |_ _|
| | | |
|_ _|_ _ _ _|_ _|_ _
| | | | | | |
|_ _|_ _| |_ _|_ _|_ _|
| | | |
|_ _| |_ _|

Having one tile different to "1B" and "2B" or "Var A" or "Var C"
I can's see how to classify them

That makes 11, I can't as yet complete the dozen, if that's possible.

Yep!
How about a strip of paper of uniform width (== box size)?
Use 45 degree fold after front, top, back, bottom are made - to allow
sides. Nothing was said about doing a surface twice..