184
votes
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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 ...
- 148k
87
votes
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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 ...
- 77.9k
66
votes
65
votes
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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 ...
- 1,999
55
votes
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The brain-curdling eldritch horrors and the third dimension
These form a rebus-like clue.
So the message is...
So the solution is...
- 148k
40
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Two chunky pixelated X's locked in mortal combat!
The combined area of the X's is
The solution:
- 15.4k
37
votes
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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:
- 11.5k
36
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.
- 461
28
votes
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12 piece cube packing puzzle
What a great puzzle!
For me the key was to notice that
you will quickly run out of corners. Since there is only one other way (plus a zillion symmetries) to place the hexacube, this means that we ...
- 77.9k
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 ...
- 17.5k
26
votes
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Wrap a squashed, bullet-riddled lowercase lambda around a cube
Here is the cube I made:
Update:
- 14.6k
24
votes
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23
votes
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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:
- 54k
23
votes
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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 ...
- 54k
23
votes
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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:
- 4,992
23
votes
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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:
- 148k
23
votes
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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:
- 30.8k
22
votes
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Isometric Heyacrazy - Now In 3D!
I've been really enjoying these puzzles. This was the best one yet.
Reasoning:
22
votes
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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 ...
- 54k
21
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 &...
- 21.9k
21
votes
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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 ...
- 14.6k
21
votes
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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.
- 14k
19
votes
Fair d5 with as few faces as possible
Surely
will suffice for all n > 2.
Consider a symmetrical cone with an n-sided regular polygon as its base.
If we take a "stubby" one (of a shortish height) and a "pointy" one (...
- 77.9k
18
votes
Accepted
18
votes
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18
votes
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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
- 23.7k
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 ...
- 54k
18
votes
Accepted
17
votes
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17
votes
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