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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 ...
JKHA's user avatar
  • 6,135
12 votes
2 answers
1k views

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 ...
ApexPolenta's user avatar
  • 3,168
0 votes
2 answers
206 views

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, ...
Alexey Birukov's user avatar
4 votes
2 answers
253 views

Another four 3D masyu

This puzzle is inspired and descended from Brain-breaking 3D masyu Here the exact copy of rules, for convenience: This is a three-dimensional masyu puzzle.1 The five squares depict the layers of a $...
Alexey Birukov's user avatar
12 votes
1 answer
948 views

You won't believe what John's hostesses discovered

This is a three-dimensional crossword. The seven grids below depict the layers of a 7x7x7 cube. "Across" and "down" clues work like in normal crosswords, and "away" clues ...
Jafe's user avatar
  • 78.7k
3 votes
1 answer
336 views

Build a slanted pyramid with ten L-shaped blocks

Consider the following L-shaped 3-dimensional object made up of three unit cubes joined at their faces: Use 10 of the above L-shaped pieces to make the following shape:
Will.Octagon.Gibson's user avatar
7 votes
1 answer
344 views

Can 42 1x2x4 cuboids be packed into a 7x7x7 cube?

Can 42 1x2x4 cuboids be packed into a 7x7x7 cube without cutting any of them? Assume that all cuboids have their axes parallel to the axes of the big cube. I tried using https://www.jaapsch.net/...
mathlander's user avatar
  • 1,261
2 votes
2 answers
241 views

Filling a 5x5x5 grid

Inspired by this. On each line to the left is the position of a word, and to the right is the "snyptic clue" not a cryptic clue (duh) for the word, along with the word's length. The 5x5x5 ...
Sny's user avatar
  • 3,185
-1 votes
1 answer
136 views

Anyone up for a 3x3x3 Hidato?

So, I have been pretty evil with how I make Hidato puzzles lately, with there being no numbers. To make up for it, I have decided to make a 3x3x3 Hidato for you all. Yes you read that right. I made a ...
CrSb0001's user avatar
  • 2,423
13 votes
2 answers
716 views

A sudokey and 14 messages

This puzzle is part of the Monthly Topic Challenge #15: Multi Puzzle — two (or more) puzzles in one. Remarks: Feel free to post partial solutions. This is a multi-puzzle: If you found the titular 14 ...
Retudin's user avatar
  • 9,316
0 votes
1 answer
161 views

The Triangular Cannonball Problem [closed]

How many ways are there to stack an equilateral triangle of cannonballs into a tetrahedron of cannonballs? In other words, how many positive integers are both triangular and tetrahedral?
gyancey's user avatar
  • 519
2 votes
0 answers
98 views

Assemble n^3 cubes into n different n×n×n larger cubes [duplicate]

You might have seen this question before: Goal: Paint 27 cubes using three colors (for example, red, yellow, and blue), so that you can form a 3x3x3 cube with all surfaces in red (for example), a ...
Haspamelodica's user avatar
3 votes
1 answer
202 views

Packing a 3xMxN-box with copies of a single tetracube

There seems to be no solution for packing a 3xMxN-box with copies of this tetracube. Does anybody know of a proof that this is impossible or is this still an open question?
Werner Nickel's user avatar
27 votes
2 answers
2k views

12 piece cube packing puzzle

Consider the following hexacube (made from 6 unit cubes): GOAL: Pack a 3 x 3 x 3 cube using three of these hexacubes plus nine unit cubes. This puzzle comes from: https://puzzlewillbeplayed.com/333/...
Will.Octagon.Gibson's user avatar
5 votes
1 answer
874 views

Find all the objects from their shadows

In my previous puzzle I asked you to derive the 3D object that casts 3 different shadows: circle, square and an equilateral triangle. This is a more general version of the puzzle. If we limit ...
Dmitry Kamenetsky's user avatar
5 votes
1 answer
1k views

Find the object from its shadows

A 3D object is suspended in the air and it casts shadows on each orthogonal plane. The shadows are in the form of a circle, triangle and square, as shown in the diagram below. What is the shape of the ...
Dmitry Kamenetsky's user avatar
11 votes
3 answers
1k views

Can you pack these pentacubes to form a rectangular block with at least one odd side length other the side whose length must be a multiple of 5

This puzzle is part of the Monthly Topic Challenge #11: Now in 3D. Consider the following pentacube (made from 5 unit cubes): It is possible to pack four of these pentacubes to form a 2x2x5 ...
Will.Octagon.Gibson's user avatar
14 votes
1 answer
783 views

Re-producing the 3D Connecting Wall!

This puzzle is part of the Monthly Topic Challenge #11: Now in 3D. See Introducing the 3D Connecting Wall! for the original presentation of this puzzle type and further context. This post presents a ...
Stiv's user avatar
  • 146k
5 votes
1 answer
2k views

How many ways are there to solve the Mensa cube puzzle?

The Mensa cube is a puzzle in which a solid cube has been partitioned into $N=11$ rigid parts. The goal of the puzzle is to re-assemble the cube from its parts and place it back in its rigid box. See ...
fromscratch's user avatar
17 votes
1 answer
2k views

Introducing the 3D Connecting Wall!

This puzzle is part of the Monthly Topic Challenge #11: Now in 3D. A typical '2D' connecting wall puzzle (as made popular by the BBC quiz show, Only Connect) involves dividing a group of 16 seemingly ...
Stiv's user avatar
  • 146k
14 votes
1 answer
650 views

Brit’s Alphabet Block Cube

This puzzle is part of the Monthly Topic Challenge #11: Now in 3D. Please do not write a computer program to solve this by brute force. Use of existing online tools like anagram solvers or ...
Amoz's user avatar
  • 27.7k
1 vote
1 answer
182 views

Create a 3D object to demonstrate the pyramid volume equation [closed]

Under the assumption that every triangle area is given by the equation "S = constant X Base X height", with a simple drawing it is demonstrated that the constant is 1/2. Assuming that a ...
Moti's user avatar
  • 2,239
11 votes
1 answer
889 views

Odd solutions are in 3d

This puzzle is part of the Monthly Topic Challenge #11: Now in 3D. You are given a collection of sticks which are straight lines of length 1. Two such sticks can be attached to each other at their end ...
quarague's user avatar
  • 1,863
6 votes
1 answer
323 views

The Nine Gardens Of Eden

This puzzle is part of the Monthly Topic Challenge #11: Now in 3D. There are nine distinct known three-cell Garden of Eden patterns in the Life Without Death cellular automata, including the two well-...
Scratch---Cat's user avatar
1 vote
2 answers
269 views

Axis of Symmetry

Give an example of a 3D object with exactly $2$ axes of symmetries? Definition of Axis of Symmetry: Let $l$ be a straight line. If every point $P$ on object $O$ has a corresponding point $P'$ on $O$ ...
thisIs4d's user avatar
  • 1,083
7 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 ...
isaacg's user avatar
  • 7,158
11 votes
1 answer
491 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 ...
Jafe's user avatar
  • 78.7k
2 votes
2 answers
800 views

Flow3rs fDr Charlie

Clues: [4 contextual images] Instructions: Name that serial killer _ a _ _ _ _ _ _ _ _ _ _ _ _
Tyler's user avatar
  • 1,265
3 votes
1 answer
340 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, ...
Parcly Taxel's user avatar
  • 7,820
16 votes
1 answer
524 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, ...
plasticinsect's user avatar
4 votes
2 answers
886 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: ...
SlowMagic's user avatar
  • 13.8k
8 votes
1 answer
247 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 ...
WhatsUp's user avatar
  • 7,405
14 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 ...
plasticinsect's user avatar
40 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 ...
plasticinsect's user avatar
12 votes
1 answer
302 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 ...
noneuclideanisms's user avatar
0 votes
1 answer
233 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?
gyancey's user avatar
  • 519
34 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 ...
Beastly Gerbil's user avatar
10 votes
1 answer
233 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) ...
athin's user avatar
  • 34.3k
9 votes
1 answer
360 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 ...
Bass's user avatar
  • 77.9k
4 votes
1 answer
239 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 ...
loopy walt's user avatar
  • 21.3k
4 votes
2 answers
755 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 ...
Dmitry Kamenetsky's user avatar
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. ...
Евгений Павлов's user avatar
1 vote
1 answer
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 ...
Chris Steinbeck Bell's user avatar
0 votes
2 answers
365 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 ...
Chris Steinbeck Bell's user avatar
3 votes
1 answer
204 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 ...
Albert.Lang's user avatar
  • 6,205
0 votes
0 answers
114 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 ...
Moti's user avatar
  • 2,239
2 votes
2 answers
504 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 ...
Moti's user avatar
  • 2,239
1 vote
1 answer
146 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?
Pahom Bumbarani's user avatar
7 votes
1 answer
306 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 ...
ExecutionByFork's user avatar
4 votes
1 answer
257 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 ...
Moti's user avatar
  • 2,239