# Questions tagged [three-dimensional]

This tag is used for geometric puzzles, if one wants to stress that the setting is not 2-dimensional but 3-dimensional.

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### Identical cubes in a sphere

Suppose that you have a sphere of radius 10cm. At most how many cubes of side 1cm can you fit in the sphere such that: A cube can touch another cube (share a face, an edge or a point) but cannot ...
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### Packing 25 three-dimensional N pentominoes into a 5x5x5 cube

The puzzle contains 25 identical pieces that look like this: To be explicit, the piece is composed of five cubes. In the picture, three cubes form the base, and two cubes form the overhang. The goal ...
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### Dramatic follow-up 3D masyu problem

This is follow-up problem for Another four 3D masyu Your little dog has been abducted by aliens, and they will do unthinkable things to it. That is unless you provide solutions for problems C and D, ...
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### Fair d5 with as few faces as possible

Challenge: design a polyhedral die that will always give one of five outcomes, each with equal probability. While achieving that, minimize the total number of faces of the die. Think of the die as ...
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### Multidimensional Travel

This is part 11 of the puzzle series Around the World in Many Days. Each part is solvable on its own. Deаr Puzzling, This is a three-dimensional crossword. The five squares in the picture represent ...
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### Flow3rs fDr Charlie

Clues: [4 contextual images] Instructions: Name that serial killer _ a _ _ _ _ _ _ _ _ _ _ _ _
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### Seven octahedral nets to cover an octahedron

After solving Cover a single cube with FIVE identical cube nets I had the idea for this puzzle, which may be regarded as a natural generalisation to triangular grids. Find two different nets, A and B, ...
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### Cover a single cube with FIVE identical cube nets

Start with five identical cubes: Your challenge: Cut and unwrap all five cubes into five identical cube nets. Show how to re-fold these five cube nets to form the surface of a single larger cube, ...
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### D&D dice for literary people

Put a letter on each face of an icosahedron such that a five-letter word can be read clockwise around each vertex. Specifically, these words: ...
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The puzzle: Put six loops of threads together, in such a way that they cannot be separated from each other, but if any one of the loops is cut, then all threads can be separated from each other. As ...
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### Turn two cubes into one!

Here are two identical cubes: Your challenge: Start with two cubes of exactly the same size. Cut the surface of each of these two cubes along its edges and unfold the surface into a 2D shape. (So ...
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If you take a cube, and grow a new cube out from each of its six faces, you will get a "hyper plus sign": This 3D solid has an interesting property. It can be sliced along its edges and ...
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### Variety Gridlocks

Gridlocks is a word puzzle genre invented by my friend sus. Here's how it works: You are given 3x3 crosswords to fill in. Two of the crossword clues clue 3-letter words that must be entered down the ...
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### When a Cube Loves a Circle [closed]

Align the center of a unit cube to the origin, and one of its long diagonals to the z-axis. In terms of r and h, what proportion of the circle {x^2 + y^2 = r^2, z = h} is inside the cube?
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### Sudoku on a Mobius Strip

Well we've done sudoku on keyboards, so the next step is obviously putting a Sudoku on a Mobius strip... of course... I present, the world's very first MOBIUS SUDOKU: Now this sudoku is going to be a ...
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### 3D Tapa - Count to Five

Rules of 3D Tapa: The grid is a 3-dimensional cubes, represented here by layers of cubes from top to bottom. Shade some cubes such that all shaded cubes form a single orthogonally (in 3-axis) ...
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### The Extraordinary Sky of Saddlestania

The infinite country of Saddlestania has some very interesting geography: its elevation from the mathematically flat sea level exactly follows the equation $$\mathbf{z=x^2-y^2}.$$ After traveling ...
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### Infinite beauty

This is a follow-up to Puzzle about 6 infinite cylinders in space Question: Given six identical infinite (no caps) cylinders is there a beautiful arrangement in space such that each touches each ...
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### Cubes touching all other cubes

This question is based on this great puzzle: Puzzle about 6 infinite cylinders in space What is the most number of identical cubes that can be placed, such that every cube touches all the other cubes ...
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### Puzzle about 6 infinite cylinders in space

You have 6 infinitely long cylinders (tubes) with the same radius R. Can you arrange them in space in a way that every cylinder touches the other 5? By touching, I mean have a common point or a line. ...
1 vote
137 views

### How to arrange a set of cubes to get a tower of two?

The puzzle is as follows: Assume that you have this peculiar toy. This toy is composed by many plastic pieces which is shown in the figure from below, all of them are cubes. You can use as many as ...
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### How many L-shaped pieces will not be used to make cubes?

The puzzle is as follows: The figure from below belongs to a didactical toy which is comprised of 32 congruent wood pieces as indicated in the figure. Each piece is made up by three cubes whose edges ...
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### Universal bisectors

A bisector is something that cuts some other thing into two equal pieces. More concretely, assume we are given a reasonably well-behaved (for example, compact) 3D object and we are looking for planes ...
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### Bisecting a 3D object into two equal volume objects - 2

Given the following 3D object and means of an unmarked ruler to draw lines on its surface define a straight cut that will split it into two objects with the same volume. Hint: It seems to have at ...
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### How to fill 1/3 of the cylinder?

You are given 3 containers - pictured in this order below: a box with side 2, height 1, and a cone with base radius 1 and height 1 in the middle. a box with side 2, height 1, and a half sphere with ...
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1 vote
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### Fill big box with smaller boxes

Let's say we have a big box with inner edges with the lengths 2m, 1.5m, 1.4m. Can we fill this with smaller boxes with the edge lengths of 3dm, 5dm and 1m, without any gaps?