# 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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### What is the largest number of cubes that can be cut?

Consider a cube made up of 27 unit cubes. If you consider a plane going through the middle of the larger cube it cuts through a number of the unit cubes. The number of cubes that are cut depends on ...
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### 6 piece mystery puzzle help!

So I have NO CLUE how to put this back together. I don't even remember what it looks like or what it's even called. I took it apart 3 years ago and it's still driving me crazy. Anyone have any ideas?!?...
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### Maximal-volume cube net from unit square paper

Given a square piece of paper (say 1x1), what is the largest cube net you can cut out of it? ('largest' meaning with maximal volume; 'net' meaning it's possible to fold into a cube (somehow)) This ...
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### Six-piece, two-tone wooden puzzle

We've had this puzzle for ages and I can't find a solution anywhere. I have vague memories of it being a cross but can't be sure. I've searched everywhere online and in the house for a solution, can ...
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### How many $2 \times 2 \times 1$ blocks can you put in a $3 \times 3 \times 3$ cube?

How many $2 \times 2 \times 1$ blocks can you put in a $3 \times 3 \times 3$ cube? And what is the way to put them? Of course the blocks can't overlap. I just remembered this nice simple ...
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### Wooden Snake Puzzle - logic behind solution

I refer to the wooden snake puzzle in this post: Wooden Snake Puzzle I notice that there are 6 solutions to the 4x4x4 snake, which start respectively as follows: FRB… (↗→↙…, which is also the ...
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### Laser Beams in Helsinki Skies

(The first two chapters are just for flavour, you can safely skip to the TL;DR near the end.) This puzzle in situated Helsinki for a reason: for the city's "200 years as capital" celebration, the ...
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### You go wherever you go today

A conclusion to my entries in the Fortnightly Topic Challenge #32: Grid Deduction Hybrids. This metapuzzle incorporates the three previous puzzles in this series: Desert Irrigation Project I am an ...
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### Improve my 3D puzzle to have a single solution

3D View of one solutions http://autode.sk/2Dg4FWx I designed a 4x4x4 soma cube in AutoCad and then built it with wood cubes. There are twelve pentacubes and one tetracube. Each piece is unique and if ...
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### Knight's Tour on a cube surface

You are doing a knight's tour, but this time, it's on the surface of a cube with chessboard faces. If you move to a square on the same face you started, everything works just like on a normal ...
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### These alien safes have no end

Well, I could solve the last safe, but what did it buy me? Just another instant-teleport and boom... here I am again! In a single room with very few things around me, most notably a safe, and no door ...
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### How many cubes are crossed by the diagonal (if HCF is not 1)?

There is a big cube of dimension 110 * 154 * 385 made up of smaller 1 * 1 * 1 dimension cubes. A body (main) diagonal is drawn. How many smaller 1 * 1 * 1 cubes will it cut?
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### Six pyramids in a cube

This question is from the German mathematics competition Känguru der Mathematik. In this competition students have to solve 30 mathematical tasks like this in 90 minutes without calculator. Actually ...
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### A hungry ant on a matchbox

A hungry ant is standing on the top of an empty matchbox cover (without its drawer) and has detected the smell of a drop of honey on the floor of the cover as shown in the figure below. What is the ...
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### Wooden Snake Puzzle

I have a wooden snake puzzle in my collection that has been unsolved for years. I wondered if any of you might be interested. I have fiddled with it, but think it might need dynamic programming or ...
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### Sometimes force is the solution [RTFM]

This time we are investigating a well secured safe. Simply breaking it is not possible (I've tried). We need to find the right combination! Can you help me open it? Along with the ...
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### Stonehenge - the true purpose

During the last year I've been working on solving the mystery behind these funny stones in Wiltshire, England. Now I'd like to have you join in on the fun and hope you enjoy discovering the true ...
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### Engineering drawing put to some good use

In engineering, objects/machine parts are often expressed using orthogonal projection, in which line drawings are created for their front/side/top views as seen from planes that rest 90° ...
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### Pulling strings...not legs?

What happens to the two strings - of the logo of G20 Summit (currently happening in Germany)-if pulled either side (in opposite directions, away from the center) at the same time ? Your options are:...
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### How many cubes are crossed by a diagonal?

A cuboid is composed by $81 \times 125 \times 128$ cubes. How many cubes are crossed by a (main) diagonal of the cuboid? (note: I chose the numbers for the sides so that the case of the diagonal ...
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### Every Fourth Wormhole

An entry in Fortnightly Topic Challenge #33: Surface Geometry Mazes
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### Martin Gardner's "The Twiddled Bolts"

This is a puzzle of Martin Gardner, taken verbatim from My Best Mathematical and Logic Puzzles: Two identical bolts are placed together so their grooves intermesh. If you move the bolts around each ...
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### Is there a common way to solve tetris like cube puzzles

I have a cube puzzle similar to bedlam puzzle. It is 4x4x4 and has 12 pentacubes, 1 tetracube. Is there a simple way to solve them? I hope tags are correct :)
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### A simple alien safe

Oh no!! Abducted by aliens and put into a labyrinth for ability testing - again! There is (obviously) no deeper meaning behind this all, but can you help me open this safe, as it undoubtedly contains ...
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### Eight identical spheres fit inside a cube

Eight identical spheres fit inside a cube with side length of 1 unit. What is the largest possible radius for a sphere which would fit between those 8 spheres (in the center)? There are no gaps ...
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### Find the side view and simple 3d [closed]

Find the side view and simple 3d associated with these views.It is given that there are no hidden lines (lines which are not visible from the side or top view).
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### Space Spectrums

Three interstellar stations have observed a distant cluster of luminous spheres or gas clouds. The elements detected emits either red, blue or green wavelength but some of the gas clouds with another ...
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### Measuring Water with a Holey Cube

You have been given a transparent glass cube, which has a small hole at the center of one of the faces. How can you fill the cube with water occupying exactly one third of its volume? Edit: The ...
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### A cube with colors

There's a word encrypted in this mysterious cube. Can you find out what it says? (See end of post for 3D model) >>SPOILER: Now that the puzzle has been solved you may have this 3D model<<
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### The Mechanical Octopus

The mechanical octopus is to light up all the glow orbs that forms the 8 corners of a cube. To do that it could use its laser pen and mirrors by passing a continuous beam of photons once through the ...
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### What puzzles can I make out of origami?

I recently made and solved a soma cube puzzle out of origami. What other puzzles can I make out of origami?                &...
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### Need help solving 3d wooden cross puzzle

I'm trying to solve this puzzle and need some help with the solution: These are the pieces: The size is: 60mm x 40mm x 10mm. Any help appreciated. How do you solve this?
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### Red Herring Bonkers In The Red Herring Bunkers

Please help me! Last weekend I hosted a hell of a party at my workplace (I'll invite you next time, promise). Of course, my boss didn't know about it. The next morning I entered the building and ...
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### Arranging cubes

You are asked to arrange 42 identical cubes such that exactly three of each cube's faces completely overlap another cube's face each. Is this task possible? If not, why not?
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### Escape the "bowl" above the abyss [closed]

You are at the bottom of this sphere section. You know the two given measures. The “bowl” is above and in the middle of circular opening of an abyss. The opening is circular with a radius of 4.87. The ...
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### The brain-curdling eldritch horrors and the third dimension

We're in the year 2016 so it's finally time to take puzzles to the 3rd dimension! So let's see what those beautiful times bring us today: (click to enlarge) Everyone of you clever sods could as ...
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### A-maze-ing Dice

This is an entry to the 12th fortnightly challenge "So you have escaped my labyrinth of words, and now you think you are free, do you? Well, I have news for you: Think again! Ha Ha Ha Ha" ...
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### Various cross-sections of platonic solids

We're going to take the 5 platonic solids (tetrahedron, cube, octahedron, dodecahedron, and icosahedron) and suspend them in various ways (we'll assume that they are solid and of uniform density). ...
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### Two potatoes and a loop of wire

You are given two potatoes. You want to make a finite loop of wire so that you can put it on either of them at some location at your choice, so that there are no gaps between the potato and the wire. ...
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### Points on a cube

Professor Halfbrain has spent his entire weekend by placing colored dots on the surface of a huge wooden cube. His objective was to find large groups of dots that form the vertices of a regular ...
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### Fair n-sided dice

I have recently bought a fair $10$-sided dice for generating equally distributed random numbers from the range $1,2,\ldots,10$. Let me describe this dice in some more detail. Consider a regular 5-gon \$...
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### Polygon wrapping a cube

A polygon is folded to perfectly wrap a cube, covering all of its surface area with no overlap. Show that the polygon had at least two equal angles.
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### Smallest number of matchsticks for a 3D structure with 6 matchsticks at each vertex

Make an as small as possible three dimensional structure of matchsticks, all of which have equal length, such that the end of each matchstick meets exactly five other ends. A matchstick is not allowed ...
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