177 votes
Accepted

How can this shape perfectly cover a cube?

The shape Using this, we can make a guess for how the cube might be folded: Once that fold is done, the shape looks more like this: A drawing of the finished product: And an animation of the whole ...
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  • 139k
84 votes
Accepted

Can you perfectly wrap a cube with this blocky shape?

This seems to work: Below, I printed out the shape, and cut off the excess. The white parts are for glueing; if everything works out as planned, all of them will be covered by the coloured bits ...
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  • 69.3k
64 votes
Accepted

Six pyramids in a cube

The answer is because the volume of a pyramid is proportional to its height, and we know that each pair of opposite pyramids together has the same total height. Therefore, all three pairs of pyramids ...
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63 votes

Can you perfectly wrap a cube with this blocky shape?

The shape can be folded like this
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  • 10.9k
55 votes
Accepted

The brain-curdling eldritch horrors and the third dimension

These form a rebus-like clue. So the message is... So the solution is...
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  • 139k
36 votes

Two chunky pixelated X's locked in mortal combat!

The combined area of the X's is The solution:
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35 votes
Accepted

Can you refold a hyper plus sign into a cube?

Phew! To start, After much trial and error, I got a net that looks like this:
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30 votes

How do I arrange pencils so they all touch each other?

The solution for 7 pencils - without using the ends - was only recently discovered: http://arxiv.org/abs/1308.5164 Seven mutually touching infinite cylinders - Sándor Bozóki, Tsung-Lin Lee, Lajos ...
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  • 401
29 votes

Two chunky pixelated X's locked in mortal combat!

Here's a diagram showing both the parts of the shape that make up each face of the cube in its own colour, and trying to give some indication of how they meet up when folded.
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  • 391
26 votes

The brain-curdling eldritch horrors and the third dimension

I think that others have found the answer and not realized it! They're just missing the meaning of the faces. Here's the breakdown of each face as others have already found: The key that others have ...
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25 votes
Accepted

Wrap a squashed, bullet-riddled lowercase lambda around a cube

Here is the cube I made: Update:
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  • 10.9k
24 votes
Accepted

Cover a cube with four-legged walky-squares!

The cube can be covered by
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  • 10.9k
23 votes
Accepted

How do I arrange pencils so they all touch each other?

You need 2 layers. First arrange 2 pencils that spread outwards touching by the erasers, like a V, then slide one with the pencil tip in between. Then you can repeat the process with 3 more, sideways, ...
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  • 14.2k
22 votes
Accepted

Maximal-volume cube net from unit square paper

The largest cube net I can cut out of a 1x1 square paper has a volume of Using the following cutout: Comparison of volumes from different methods:
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  • 4,952
22 votes
Accepted

Can you cover a cube with copies of this shape?

This can be done To figure out how to do it, Here are some images of the covering:
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  • 139k
22 votes
Accepted

Isometric Heyacrazy - Now In 3D!

I've been really enjoying these puzzles. This was the best one yet. Reasoning:
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22 votes
Accepted

Puzzle about 6 infinite cylinders in space

There has been some mathematical research done on this subject, and it turns out that: as shown in this paper by Sándor Bozóki, Tsung-Lin Lee, and Lajos Rónyai. The paper was also discussed in for ...
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21 votes
Accepted

Wooden Snake Puzzle

I have the same snake cube puzzle, except that its cubes don't alternate in colour. On mine they are coloured so that the finished cube consists of 2x2x2 blocks. Drawing of the solution is under the ...
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21 votes
Accepted

How can this fractal shape perfectly cover a certain platonic solid?

Preliminary analysis. After some playing around with Acorn, I came up with the answer:
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  • 20.8k
21 votes
Accepted

A Slightly Moth-Eaten Integral Sign

I made folds like this: These puzzles are getting harder and harder. In this case it was impossible for me to eyeball where any face would be, and it only started to make sense once I started cutting ...
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  • 10.9k
20 votes
Accepted

Measuring Water with a Holey Cube

As the other answers show, it is easy to fill 1/6th of the cube: You can now use this to work out how far much further to fill the cube:
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19 votes

Measuring Water with a Holey Cube

Tried looking at volumes obtainable by lining up a fill level with at least 3 well-defined points (vertices and/or the hole) but only found ways to fill 1 ⁄6, 1 ⁄4, 1 &...
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  • 21.5k
18 votes
Accepted

Arranging cubes

The task is
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  • 2,684
18 votes
Accepted

Two chunky pixelated X's locked in mortal combat!

As I don't have a camera handy, I have had to unfold my (pink) cube before I could show it to you. Its sides are Sqrt(52) = Sqrt(4^2+6^2) units long.
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  • 12.6k
18 votes
Accepted

Sudoku on a Mobius Strip

First, build a spreadsheet. This has links surrounding it so that I can see where things will be relative to each other. Then
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  • 22.3k
18 votes
Accepted

Turn two cubes into one!

I have found several solutions. There are three cube nets that cover the same-shaped half of the larger cube surface, so you can choose any two copies of those (the same or different) and combine them ...
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17 votes
Accepted

Red Herring Bonkers In The Red Herring Bunkers

The passphrase is: How to find it:
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  • 17.9k
17 votes
Accepted

Martin Gardner's "The Twiddled Bolts"

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17 votes
Accepted

3D nonogram, beginner's edition

nonogram: this is depicting
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16 votes
Accepted

Every Fourth Wormhole

That was a fun maze! Answer: It would take too long to go through every step but it was possible to complete it without guessing. Here are some steps along the way:
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  • 7,584

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