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.

Filter by
Sorted by
Tagged with
6 votes
4 answers
2k views

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 ...
  • 3,755
11 votes
1 answer
393 views

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 ...
  • 69.3k
0 votes
2 answers
733 views

Flow3rs fDr Charlie

Clues: [4 contextual images] Instructions: Name that serial killer _ a _ _ _ _ _ _ _ _ _ _ _ _
  • 427
3 votes
1 answer
289 views

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, ...
  • 6,764
15 votes
1 answer
405 views

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, ...
4 votes
2 answers
861 views

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: ...
  • 12.6k
8 votes
1 answer
240 views

Six loops of threads

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 ...
  • 7,199
13 votes
1 answer
2k views

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 ...
36 votes
2 answers
2k views

Can you refold a hyper plus sign into a cube?

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 ...
12 votes
1 answer
252 views

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 ...
0 votes
1 answer
227 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?
  • 411
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 ...
10 votes
1 answer
215 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) ...
  • 33.8k
8 votes
1 answer
254 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 ...
  • 71.5k
4 votes
1 answer
223 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 ...
  • 16.1k
4 votes
2 answers
604 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
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. ...
1 vote
1 answer
122 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
2 answers
260 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
1 answer
189 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 ...
  • 3,447
0 votes
0 answers
108 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 ...
  • 2,176
2 votes
2 answers
483 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 ...
  • 2,176
1 vote
1 answer
143 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
1 answer
291 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
1 answer
242 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 ...
  • 2,176
8 votes
2 answers
821 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 ...
  • 83
18 votes
1 answer
455 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&...
  • 69.3k
11 votes
2 answers
756 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 ...
  • 6,827
3 votes
1 answer
198 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 ...
29 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 ...
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 ...
1 vote
0 answers
137 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
1 answer
141 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 ...
  • 1,942
2 votes
1 answer
213 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
3 answers
549 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
1 answer
315 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 ...
  • 21
11 votes
1 answer
374 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 ...
  • 69.3k
4 votes
1 answer
192 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
1 answer
408 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?
26 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 ...
17 votes
1 answer
527 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
1 answer
297 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
1 answer
200 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 ...
  • 411
16 votes
1 answer
696 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?
  • 11.8k
8 votes
1 answer
197 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
1 answer
421 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 ...
  • 69.3k
10 votes
1 answer
316 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 ...
  • 69.3k
0 votes
2 answers
273 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 ...
  • 2,176
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 ...
  • 143k
1 vote
1 answer
289 views

Cut a cube into 5 objects

Cut a cube into 5 3D objects with 6 edges each. Hint:
  • 2,176