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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11 votes
1 answer
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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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0 votes
1 answer
217 views

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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33 votes
2 answers
3k views

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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10 votes
1 answer
201 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) ...
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8 votes
1 answer
235 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 ...
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4 votes
1 answer
215 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 ...
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  • 11.6k
4 votes
2 answers
543 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 ...
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14 votes
2 answers
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. ...
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1 vote
1 answer
108 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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0 votes
2 answers
222 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 ...
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3 votes
1 answer
181 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 ...
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0 votes
0 answers
101 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 ...
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  • 2,166
2 votes
2 answers
475 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 ...
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  • 2,166
1 vote
1 answer
135 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?
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7 votes
1 answer
251 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 ...
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4 votes
1 answer
234 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 ...
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  • 2,166
8 votes
2 answers
625 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 ...
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17 votes
1 answer
425 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&...
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  • 67.3k
11 votes
2 answers
699 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 ...
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  • 4,767
3 votes
1 answer
180 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 ...
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25 votes
3 answers
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 ...
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25 votes
1 answer
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 ...
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1 vote
0 answers
133 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 ...
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0 votes
1 answer
138 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 ...
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2 votes
1 answer
209 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 ...
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7 votes
3 answers
536 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 ...
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2 votes
1 answer
307 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 ...
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  • 21
10 votes
1 answer
343 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 ...
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  • 67.3k
4 votes
1 answer
165 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?
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12 votes
1 answer
379 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?
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25 votes
1 answer
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 ...
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16 votes
1 answer
462 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?
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10 votes
1 answer
259 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 ...
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7 votes
1 answer
191 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 ...
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  • 411
16 votes
1 answer
681 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?
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  • 11.5k
8 votes
1 answer
188 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 ...
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12 votes
1 answer
382 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 ...
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  • 67.3k
10 votes
1 answer
291 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 ...
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  • 67.3k
0 votes
2 answers
226 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 ...
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  • 2,166
20 votes
1 answer
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 ...
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  • 136k
1 vote
1 answer
248 views

Cut a cube into 5 objects

Cut a cube into 5 3D objects with 6 edges each. Hint:
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  • 2,166
6 votes
2 answers
198 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 ...
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  • 67.3k
16 votes
2 answers
946 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 ...
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  • 67.3k
12 votes
1 answer
183 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 ...
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14 votes
2 answers
1k 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 ...
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  • 67.3k
9 votes
2 answers
699 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 ...
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  • 67.3k
8 votes
2 answers
541 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 ...
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  • 67.3k
11 votes
1 answer
445 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 ...
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  • 67.3k
11 votes
1 answer
222 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 ...
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  • 67.3k
14 votes
2 answers
483 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 ...
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  • 67.3k