Questions tagged [geometry]
A puzzle related to shapes, geometric objects (polygons, circles, solids, etc.) of any number of dimensions, the relative position of figures, and the properties of space. Use with [mathematics]
1,348 questions
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Cover a cube with hugs and kisses!
The following set of eight shapes (which sort of looks like XOXOXOXO if you squint with your brain a little):
... can all be folded onto the surface of a single cube in a way that covers the entire ...
- 6,361
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Given six hexagons, cut three of them and reassemble into an equilateral triangle
Six congruent regular hexagons are given. Cut three of them into two parts such that the nine parts obtained (three hexagons and six "halves") can be used to compose an equilateral triangle.
...
- 34.7k
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Arrange 11 (or fewer) squares that will be colored
This puzzle is related to the Four Color Theorem.
Arrange 11 (or fewer) non-overlapping unit squares on the plane such that, for any coloring of these squares in three colors, there exist two ...
- 34.7k
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Grouping and routing puzzle: can these circles be partitioned into triples and connected by a single non-crossing path?
I’m interested in whether the following puzzle has a valid solution.
You are given a fixed arrangement of circles in a plane (see attached image). The task is to:
Partition all circles into groups of ...
11
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2
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Minimize the total cut length for a 7x8 rectangle
A 7x8 rectangle is cut from a sheet of graph paper. Cut this rectangle into polygons consisting of no more than 5 squares each in such a way that the total length of the cuts is minimized (the cuts ...
- 34.7k
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Cutting an 8x8 grid into 3 pieces and then reassembling them [duplicate]
Consider an 8x8 square grid of 64 unit squares from which one arbitrary unit square is missing. Show that you can dissect this grid into exactly three pieces that could be assembled to form another ...
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S1E4: Mirror Law
S1E3: Black Sundial
After solving the next puzzle, Coloseshi enters the Caucasus Mountains.
He is confronted by Sister Parallela, whose Stand Mirror Law enforces perfect symmetry. Uneven terrain ...
- 895
11
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2
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Are infinite loops possible in the game Sublimergy?
I'd like to know if infinitely repeating sequences of moves (i.e. cycles) are possible in the following game:
Sublimergy is a two-player game played on the spaces (cells) of an
initially empty ...
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3
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1
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S1E3: Black Sundial
Previous puzzle: S1E2: Paper Metropolis
After the puzzle reveals a safe route, Coloseshi crosses the Central Asian steppe by train.
Red Kestrel attacks using Black Sundial while Coloseshi is resting ...
- 895
3
votes
1
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S1E2: Paper Metropolis
Previous puzzle: S1E1: Steel Current
After escaping the port city, Coloseshi travels inland toward China by rail.
In Shanghai, he confronts Liáng Fēn, wielder of Paper Metropolis, who folds streets ...
- 895
4
votes
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S1E1: Steel Current
My next puzzles will all be part of a story. I will post the next puzzle when this is solved.
After solving the first puzzle in Tokyo, Coloseshi Cōkonawa uncovers evidence that GIO has already left ...
- 895
9
votes
2
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Horizontal to vertical rectangle via dissection and translations
What’s the minimum number of pieces that an m × n rectangle should be cut into so that they can be rearranged into an n × m rectangle by only translating the pieces?
Here’s an example with a 2 × 3 ...
- 23.9k
13
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Triangle Dissection
Behold these four triangles. They are isosceles right triangles rotated 0, 90, 180, and 270 degrees.
Your challenge is to split any one of these triangles into pieces so that they can be rearranged ...
- 895
10
votes
2
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Scalable Dissection
Given a square and a circle, can you dissect the square into pieces such that, using only similarity transformations, these pieces can be reassembled to form the circle?
Clarifications:
YOU CANNOT ...
- 895
8
votes
1
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Octagon surface
This one should be not too hard ...
Below crafted octagon features my PSE profile image.
It is designed using eight identical grey scaled squares.
The white vertices of all these squares have ...
- 3,183