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.
184 questions
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An ant crawling on a square donut
This puzzle takes place on the following square donut:
This object consists of eight unit cubes fused into a single ring. (Or, if you prefer, you can also think of it as a 3×3×1 box with a 1×1 hole ...
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16
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3
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Wrap a leafy plant onto a dodecahedron
The following leafy plant shape:
... can be folded onto the surface of a regular dodecahedron in a way that covers the entire dodecahedron with no gaps and no overlaps. How can this be done?
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A 3D Slitherlink
This is a Slitherlink.
Not a set of Slitherlink but one Slitherlink, just in 3D.
How it works
You have a block of 5x5x5 cubes sharing faces with their neighbors. Your task is to assemble some of ...
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11
votes
1
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Is it possible to pack an 11x11x11 cube using copies of the two given shapes?
Is it possible to pack (no overlaps, no gaps) an 11x11x11 cube using copies of the two shapes shown below?
Text description of the two objects in the above image:
Object 1: Middle layer has 5 unit ...
14
votes
1
answer
562
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Two points on a cube with exactly three shortest paths connecting them
This puzzle is on Tanya Khovanova's Math Blog, from a book co-written with Ivo Fagundes David de Oliveira and Yogev Shpilman.
Can you find two points on the surface of a cube such that there are ...
- 243
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4
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If 3-D is too easy, go 4-D
It is a well-known puzzle that one can take a cube and make a single planar cut through it so that the intersection of the cutting plane and the cube is exactly a regular hexagon.
One can do an ...
- 3,501
19
votes
10
answers
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What is the maximum number of faces of a cube that you can see at the same time?
First of all this puzzle is not mine. It was asked by a professor at a university class I was attending years ago. For some time now I have been asking my friends this puzzle and only one person got ...
- 963
7
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4
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3D Packing Puzzle: Can 17 Mixed-Size Blocks Fill a Cube?
You are given a cube-shaped box with dimensions 5×5×5. Your task is to determine whether the following blocks can be arranged to fit perfectly inside the box without any gaps or overlaps:
5 blocks of ...
- 377
4
votes
2
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271
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A three-dimensional triangle centre
A disphenoid is a tetrahedron whose faces are congruent acute triangles. Its opposite sides are the same length and it can be inscribed in a cuboid.
Given an acute triangle, form a disphenoid out of ...
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5
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Are the lines intersecting in 3D?
Consider the following picture of the regular compound of five tetrahedra.
Does the line $CD$ exactly intersect the line of intersection of triangles $A$ and $B$?
- 10.5k
8
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A puzzle for middle school students: cuboid or slice of cake?
A fixed volume of dough can be shaped into either a cuboid, or a slice of cake. Which shape should you choose, in order to minimize the total surface area of the dough?
Remarks:
The cuboid has six ...
- 6,136
3
votes
0
answers
122
views
How to solve wooden cross puzzle I found [duplicate]
I found a wooden cross puzzle but I don't know how to solve it.
The pieces I have are 12, 3,4, 20,19,17
- 31
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3
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places far away from each other but similar every now and then
What (approximately) is common to Paris, mid Mongolia and mid North Washington state border with Canada, and when was it manifested last time recently? Also, in what (approximately) do these places ...
- 3,530
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How to cut wooden beam into 4 parts that can be reassembled into a cube?
A wooden beam (which is a rectangular parallelepiped) with edges of 8, 8, and 27 inches is to be sawed into 4 parts out of which a cube can be made. Naturally, one should draw first and saw later.
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12
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A (not so) K₁₂ problem
The following map on the torus was devised by Peter Ungar and John Leech.
It has 7 mutually adjacent faces each homeomorphic to a disk. In addition, geometrically the whole map is face-transitive – ...
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