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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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?
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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 ...
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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?
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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/...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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-...
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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 $O$ ...
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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 ...
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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 ...
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Flow3rs fDr Charlie
Clues: [4 contextual images]
Instructions: Name that serial killer
_ a _ _ _ _ _ _ _ _ _ _ _ _
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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, ...
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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, ...
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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:
...
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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 ...
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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 ...
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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 ...
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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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 ...
