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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10
votes
1answer
167 views

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) ...
7
votes
1answer
219 views

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 ...
3
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1answer
197 views

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 ...
4
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2answers
515 views

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 ...
14
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2answers
1k views

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
1answer
87 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 ...
0
votes
2answers
171 views

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 ...
3
votes
1answer
174 views

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 ...
0
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0answers
88 views

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 ...
3
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2answers
469 views

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 ...
1
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1answer
132 views

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?
7
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1answer
235 views

Expanding on a classic

From the simple caesar to the seemingly uncrackable elliptic curve, there are countless ways to obscure - and even hide - a sensitive message. Cryptography is quite interesting in this way. I find the ...
4
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1answer
223 views

Bisecting a 3D object into two equal volume objects

Given the following object - box of which a rectangular pyramid is removed. By means of unmarked ruler, draw lines on the surface of the object to guide cuts of the object into two objects with the ...
8
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2answers
523 views

Strategy for solving a 3D maze

Given enough time, you can solve a large 2D maze by simply following a wall. Is there any similar strategy for solving a 3D maze that can be used (no marking/memorizing places you've seen in the maze ...
17
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1answer
405 views

3D cryptic brain melter

An entry in Fortnightly Topic Challenge #43: Variety Crossword Grids This is a three-dimensional cryptic crossword. The seven squares in the picture depict the layers of a 7x7x7 cube. The "away&...
12
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2answers
639 views

Chain Puzzle: Tabletop Games #7 - Maze

This is the seventh Chain Puzzle in the Tabletop Games series, in which all puzzles are themed around board games, card games, tile games, and the like. The answer to this puzzle is a thematic word or ...
3
votes
1answer
161 views

Permutation Puzzle Swap Cubies

I've recently launched an online puzzle RAVEL. It's a 3D array of cubes that must be arranged in color-order. A legal move is to slide a row, column, or lane any number of spaces. The cubes that are ...
25
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3answers
3k views

Two chunky pixelated X's locked in mortal combat!

In this dramatic image, we witness two rather chunky pixelated letter X's (having recently fattened themselves up for the approaching winter) locked in mortal combat, fighting to the death for the ...
25
votes
1answer
1k views

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

The following rather squashed and bullet-riddled lowercase lambda: ...can be wrapped onto the surface of a cube in a way that perfectly covers the entire cube, with no gaps and no overlaps. How can ...
1
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0answers
128 views

Building a cube from small bricks such that no lines can be pushed through between the seams

There is a puzzle on fault-free rectangles tiled by dominoes. It is rather known (it is described in Martin Gardner’s “Mathematical puzzles and diversions”, see here) and rather old (it is known at ...
0
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1answer
131 views

Concerning Tetrahedra

As a pyramid with a triangular base, the volume of a tetrahedron, like all pyramids, is $(1/3)*BH$, where $B$ is the base area and $H$ is the height. If one had $3$ square $45$ degree pyramids (square ...
2
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1answer
202 views

An exam question testing your spatial sense. (Is it worded correctly?)

I recently got the following question from a friend. This kind of question was asked in one of her exams (it really doesn't matter what kind of exam that was). I after trying to solve said question ...
7
votes
3answers
517 views

Balance the nails

Someone I know handed me this puzzle, I have seen a couple of solutions for it that follow the instructions and don’t involve bending the nails, etc. Can you figure out how to balance the 6 nails on ...
2
votes
1answer
294 views

Help! My Ring & Post puzzle is stuck

I have a fairly basic Ring and Wooden Post puzzle that I can usually solve. However, at a recent family gathering (pre-Covid); the ring was tangled into a weird spot and I cannot figure it out. Here ...
9
votes
1answer
310 views

Nurikabe minicubes: the Boondoggle, the Lollygag, the Dillydally

These are three-dimensional Nurikabe puzzles. In each case, the four squares represent the layers of a $4\times4\times4$ cube. The goal is to shade some cells in each layer so that the resulting space ...
4
votes
1answer
154 views

Icosahedron-Wrapping Monstrosity

The following monstrosity of a shape: ... can be wrapped onto the surface of an icosahedron in a way that completely covers the entire icosahedron with no gaps and no overlaps. How can it be done?
12
votes
1answer
367 views

Tri-bladed Boomerang vs. Octahedron!

The following tri-bladed boomerang shape: ... can be folded onto the surface of an octahedron in a way that perfectly covers the entire octahedron with no gaps and no overlaps. How can it be done?
25
votes
1answer
2k views

A Slightly Moth-Eaten Integral Sign

The following slightly moth-eaten integral sign: ... can be folded onto the surface of a cube in a way that perfectly covers the entire cube with no gaps and no overlaps. How can it be done? (You ...
15
votes
1answer
428 views

Wrapping a Galaxy Around a Cube

The following galaxy-like shape: can be folded onto the surface of a cube in a way that perfectly covers the entire cube with no gaps and no overlaps. How can it be done?
10
votes
1answer
215 views

3D Slitherlink (Slithersurface)

Here is a 5 x 5 x 5 cube filled with numbers. It's a 3D adaption of standard slitherlink puzzles. You must create a solid 3D object such that the number in each sub-cube matches the number of adjacent ...
7
votes
1answer
185 views

Cube Tubes & Cube Loops

Given a three dimensional n×n×n cube containing n^3 cubes of 1×1×1, Define a cube tube to be a sequence of 1×1×1 cubes from the n×n×n cube such that: 1) No cube appears in the sequence more than ...
16
votes
1answer
657 views

A cube build with cuboids

You are given 27 pieces of 1x2x4 cuboids. Is it possible to build a 6x6x6 cube using those 27 cuboids?
8
votes
1answer
178 views

Say “Herru” to Spatial Golf

Have a try with this 3D Herugolf puzzle! Rules of Herugolf: (Adapted from @Stiv's adaption of Nikoli) Move (hit) all circles (balls) one or more times, and bring them to a cell with a red ...
12
votes
1answer
362 views

Masyu keep making those 3D puzzles?

This is a three-dimensional Masyu puzzle. The five squares depict the layers of a $5\times5\times5$ cube. The goal is to make a single loop in 3D space which fulfills the following properties: The ...
9
votes
1answer
259 views

Nurikabe minicubes: the Headache, the Panache, the Apache

These are three-dimensional Nurikabe puzzles. In each case, the four squares represent the layers of a $4\times4\times4$ cube. The goal is to shade some cells in each layer so that the resulting space ...
0
votes
2answers
184 views

How many pyramids in a cube?

Knowing that a pyramid volume is computed as 1/3 of base multiplied by the height, how many pyramids may be constructed by connecting the corners of a cube to create pyramids with volume 1/3 of the ...
20
votes
1answer
1k views

Isometric Heyacrazy - Now In 3D!

This is a Heyacrazy puzzle on an isometric grid. Rules of Heyacrazy: Shade some cells of the grid. Shaded cells cannot be orthogonally adjacent; unshaded cells must be orthogonally connected. When ...
1
vote
1answer
231 views

Cut a cube into 5 objects

Cut a cube into 5 3D objects with 6 edges each. Hint:
6
votes
2answers
189 views

Yajilin minicubes: the Poppycock, the Balderdash, the Gobbledygook

These are three-dimensional yajilin puzzles. In each puzzle, the four squares depict the layers of a $4\times4\times4$ cube. Shade some cells on each layer. The numbered cells show how many shaded ...
16
votes
2answers
933 views

3D cryptic featuring Mao, Stalin and Simba's uncle

This is a three-dimensional cryptic crossword. The eleven squares above represent the layers of a $11\times11\times11$ cube. Across 21. Tribunal's way to imprison you in the old days (10) 25. Sir ...
12
votes
1answer
176 views

A Cryptic Not-so-mini Cube

A quick teaser, enjoy! Across 3 Dance bores serious (5) 6 Light angry look (5) 11 Finally asked it to agree (5) 12 Rails - cunning homes of thieves (5) 15 Trap saner design (5) 16 Kingdom with real ...
14
votes
2answers
953 views

Flood on the top floor

There has been a water incident on the top floor of a building, and one apartment has suffered some water damage. As in, a lot of water damage. The entire apartment is filled waist deep with ...
9
votes
2answers
682 views

Yajilin minicubes: the Hullabaloo, the Brouhaha, the Bangarang

These are three-dimensional yajilin puzzles. In each puzzle, the four squares depict the layers of a $4\times4\times4$ cube. Shade some cells on each layer. The numbered cells show how many shaded ...
8
votes
1answer
371 views

Mixed-breeds are puzzles too!

This is a three-dimensional mixed-breed puzzle. The five squares depict the five layers of a $5\times5\times5$ cube. The goal is to solve the odd-numbered layers as yajilin and even-numbered layers as ...
11
votes
1answer
405 views

Volcanic 3D masyu

This is a three-dimensional masyu puzzle. The six squares depict the layers of a $6\times6\times6$ cube. The goal is to make a single loop in 3D space which fulfills the following properties: The ...
11
votes
1answer
217 views

3D devilry, DIY edition

This is a diagramless three-dimensional cryptic crossword. Solve the clues and then fit the answers into a three-dimensional grid. The numbering of the clues starts from the #1 (nearest) layer. On ...
14
votes
2answers
473 views

A cubeful of three-dimensional devilry

This is a three-dimensional cryptic crossword. The seven squares represent the layers of a $7\times7\times7$ cube. The clues are a mix of Printer's Devilry and normal cryptic clues. Across 13. While ...
10
votes
1answer
299 views

A Difficult Rhombicosidodecahedron Slitherlink

This is the evil older brother of this puzzle. I'm posting it more out of scientific curiosity than because it is a fun puzzle, because it is not a fun puzzle. It's just really hard. I wrote a ...
7
votes
1answer
354 views

3D Statue Park: Daggers and dashes

This is a three-dimensional Statue Park puzzle.1 The five squares in the below image depict the five levels of a $5\times5\times5$ cube. The goal is to fit inside it the eight pieces shown in the ...
8
votes
2answers
478 views

3D Statue Park: U shapes

This is a three-dimensional Statue Park puzzle.1 The five squares in the below image depict the five levels of a $4\times4\times5$ cuboid. The goal is to fit inside it the four three-dimensional ...