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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]

A puzzle related to shapes, geometric objects (polygons, circles, solids, etc.) of any number of dimensions, relative positions of figures, and the properties of space.

Geometric puzzles include:

  • dissection puzzles
  • tangram puzzles
  • shortest-path puzzles

General geometry questions are considered off-topic but can be asked on Mathematics Stack Exchange with the geometry tags(search "geometry" in the list of tags for a full list of geometry tags).

1127 questions
55
votes
16 answers

Join all circles together only with 6 lines

In the below image, can you draw 6 straight lines that pass all the circles? As soon as you start drawing lines you can't take your pen up until you draw all six lines. hint: you don't have to keep the polyline inside the square. Edit: Best answer…
Masoud Mohammadi
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40
votes
5 answers

Blindfolded and disoriented near the Great Wall of China

You are blindfolded and disoriented, standing exactly 1 mile from the Great Wall of China. How far must you walk to find the wall? Assume the earth is flat and the Great Wall is infinitely long and straight.
dshin
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34
votes
3 answers

What is the minimum number of straight lines to connect all the dots on this grid?

Recently a question was posted with this picture of a 7x7 grid of dots, asking for a possible configuration with 12 lines where you can draw them without lifting a pencil. But is it possible with 11 lines? If so, what about 10? Just to be clear,…
warspyking
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34
votes
5 answers

Simple geometry. Or is it?

I've got a regular tetrahedron and a square pyramid. Every edge of the two solids has the same length. If I perfectly attach one face of the tetrahedron to one of the triangular faces of the square pyramid (I.E. every point of one face overlaps a…
Marco Bonelli
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32
votes
6 answers

Find 7 solutions

You have three flat pieces, as shown: Arrange them flat, without overlap, such that the shape formed by the black parts is congruent to the shape formed by the white parts. Rotation and reflection are allowed. Find at least 7 distinct solutions. If…
TheGreatEscaper
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31
votes
9 answers

Splitting a Plate into 4 Equal Pieces

You are stuck on an island and have been tasked by the natives with dividing a plate of chocolate into 4 equal pieces, one for each of the island's gods. Each god must have an equal share, or you go into the volcano. The plate is a perfect square.…
JonTheMon
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22
votes
1 answer

Find 10 triangles in a five pointed star using two straight lines

This puzzle consists of counting ten triangles (check three sides for each one, remember that there aren't exist triangles with more than three sides :P ) using two straight lines that cross the figure wherever you want. You can't count a triangle…
Mauro Bilotti
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21
votes
6 answers

Seven overlapping circles

The area of a circle of radius 1 is completely covered by seven smaller circles, all with the same radius as each other. (The circles can overlap - indeed they must!). What is the smallest radius the small circles can have so that it is possible to…
DavidButlerUofA
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21
votes
1 answer

Shooting a Laser Between two Mirrors

There are two large mirrors standing upright and facing each other, both 10 meters long. They are not quite parallel: if you extended them, they would intersect at a $1^\circ$ angle. The distance from the mirrors to this intersection point is also…
Mike Earnest
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20
votes
4 answers

What's the radius?

I have a book of puzzles from 1972 with the pretentious title, "Games for the Superintelligent" by James Fixx. One puzzle had me thinking for a couple of days: I drew it out, thought about different ways of attacking it, and eventually gave up and…
WhiteHotLoveTiger
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20
votes
2 answers

Staking Out the Integers

Suppose you're given six stakes and an unlimited length of string. Your objective is to plant the stakes in a flat patch of ground in such a way that you can wrap the string around the stakes in different ways to create simple polygons with integral…
COTO
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20
votes
10 answers

Cutting a cake into 8 pieces

Say, you are given a cake which you must share with 7 others. So, you must cut the cake into 8 pieces. But, you are only allowed to make 3 straight cuts. You cannot move pieces of the cake after the first cut.
d'alar'cop
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19
votes
9 answers

Point mass soldiers in Fogland

A troop of N immortal point mass soldiers (with N >= 3) are attempting to infiltrate Fogland (an infinite 2-dimensional plane covered in fog). They will jump out of an airplane and, after being buffeted by the winds, will each land in an independent…
sousben
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18
votes
4 answers

Draw a hexagon that can’t be divided into two quadrilaterals by a single straight line.

I’m kind of stumped. Logically if a hexagon has 6 sides and you split it and add one (the line) it will always result in two quadrilaterals. I may be off.
Mike
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18
votes
4 answers

What is the shape of the object?

There is a 3D object, so that when you look at it from 3 different angles, you can see the shape of a triangle, rectangle, or circle. What does it look like in 3D?
didxga
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