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 process:
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 around the black squares.
Joy, it all worked! Here's the final cube, with some white "intentionally" showing through between the pieces, highlighting the borders:
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 from opposite sides have the same combined volume.
The solution for 7 pencils - without using the ends - was only recently discovered:
Seven mutually touching infinite cylinders - Sándor Bozóki, Tsung-Lin Lee, Lajos Rónyai. It was presented at "Gathering 4 Gardner" in May 2014, because the original 7-cigarette version, allowing the ends to be used, was popularised by a Martin ...
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 missed is that the message tells you to...
Which reveals the secret interior!
Zooming inside the model (back in solid form for visibility), shows the ...
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, laying on the original, this achieves 6:
You can also achieve an arrangement of 7 by making 3 V's of 2, an arranging them like a ninja star (not really sure ...
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 example Huffpost.
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 and folding.
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 spoiler:
The 3x3x3 version of this puzzle is very common, though almost all versions use the same configuration of straight and bent cubes. You can find out ...
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 ⁄2 or more of the cube’s volume.
So with a drop of lateral-thinking and...
Now the puzzle statement’s
“fill the cube with water ...
Throughout this, "north" refers to the topmost direction on the first picture.
The north of the outer ring.
The outer ring contains 30 stones spaced evenly in a circle. They have alien creatures carved out of them on the inside. The creature inside the southernmost stone is pointing left (clockwise around the circle).
Using the numbers on the pillars as starting points and travelling around the circle by the amount indicated on the stones below, we get:
END/HAT/HORN // RAIN/AUNT
OLD/RAIN/RIDGE/OWL // END/OTHER
(The groups separated by double slashes are on the same pair of pillars.)
Each of those groups
As is clearly ...