160

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 process:


79

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: ...


63

The shape can be folded like this


62

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.


52

These form a rebus-like clue. So the message is... So the solution is...


25

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 ...


23

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:


23

This can be done To figure out how to do it, Here are some images of the covering:


23

The cube can be covered by


21

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


18

The task is


18

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 ⁄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 ...


18

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:


17

Preliminary analysis. After some playing around with Acorn, I came up with the answer:


16

nonogram: this is depicting


15

The passphrase is: How to find it:


15

As the top view has 90° symmetry, a 90° side view... A 45° side view can be more interesting, ... The bottom view, for those interested, ... This can be constructed by...


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Transcription Throughout this, "north" refers to the topmost direction on the first picture. Outer Ring     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 ...


15

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 ZONE/PEN/PINE ICE/OTHER OLD/RAIN/RIDGE/OWL // END/OTHER EVEN/UPPER/END/INNER (The groups separated by double slashes are on the same pair of pillars.) Each of those groups As is clearly ...


15

My answer :


14

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:


14

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 ...


14

The six pyramids each have the same base area $b$, and can be partitioned into three pairs whose bases are opposing sides of the cube. For each such pair of opposite pyramids, the two heights' sum is the cube's edge length $e$. A pyramid's volume is $V = \frac{b h}{3}$, and thus $h =\frac{3 V}{b}$. Therefore, for a given pair with heights $h_A$ and $h_B$ ...


14

I think the answer is by Here's a visualization, thanks @JaapScherphuis for linking to the Wikipedia article:


14

My answer is to Then you have exactly the correct number of corner, edge, face-center, and center pieces for each cube.


14

The shapes are The filled grids are You get the shapes by


14

Deusovi beat me but here's the solution in Minecraft: Top to Bottom:


13

Let $n$ be an arbitrary positive integer. Start with a right cylinder with cross section a regular $n$-gon. To each of the bases, attach a pyramid (with regular $n$-gon base). The resulting polyhedron has $n$ rectangular faces and $2n$ triangular faces. If the cylinder and pyramids are tall enough, it will be impossible for the die to land on the triangular ...


13

Partial answer in progress. The first step is to In the safe, I found: In the monitor, I found: In the keyboard, I found: Inside the box, I found: In the dial, I found: We are also given 5 letters S, V, T, D, P in a separate image. Thoughts: Some trial and error


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