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.
132
questions
0
votes
1answer
211 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?
31
votes
2answers
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 ...
10
votes
1answer
185 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) ...
8
votes
1answer
231 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
votes
1answer
205 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
votes
2answers
523 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
votes
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
100 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
187 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
177 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
votes
0answers
95 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
votes
2answers
472 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
vote
1answer
133 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
votes
1answer
239 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
votes
1answer
229 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
votes
2answers
548 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
votes
1answer
417 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
votes
2answers
666 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
167 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
votes
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
vote
0answers
131 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
votes
1answer
133 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
votes
1answer
207 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
522 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
295 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
318 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
157 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
371 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
438 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
238 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
186 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
666 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
184 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
368 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
270 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
196 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
236 views
6
votes
2answers
190 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
937 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
976 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
688 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
382 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
414 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
221 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
476 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
302 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 ...
