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]

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56
votes
8answers
5k views

Find a straight tunnel

There is a circular area with radius 1 km. And there is a tunnel, which is just under the surface, but invisible - unless you dig. It is known that the tunnel goes under the area (at least touches it ...
-4
votes
1answer
103 views

A Clear, Simple, Geometry Problem [closed]

Draw a shape consisting of all the points equidistant from a specific point. Furthermore, draw a segment passing through a side of the shape exactly twice, and draw another segment so that it also ...
-1
votes
2answers
134 views

Nested six-point stars: least number of cuts to dissemble

The puzzle is as follows: The figure from below represents a peculiar structure which consists in congruent triangles whose sides intersect and is made of an iron wire. How many cuts passing through ...
0
votes
1answer
163 views

Least cuts can be made in a metal grid structure to get 44 rods

The puzzle is as follows: Suppose that you have a metal structure made by brass wire. Assuming that you must get 44 rods of the same size each. What is the least cuts to be made using an electric ...
1
vote
1answer
109 views

Minimum cuts to make a rectangle into a square, allowing bending

The puzzle is as follows: Mike has a thin sheet of cardboard which is 96 centimeters large by 24 centimeters wide and a guillotine whose maximum cut length is 80 cm. Assuming this guillotine can cut ...
0
votes
1answer
94 views

Vowels, consonants and Mathematical Shapes

Your aim is first to select at least three different mathematical shapes. For instance, you could select "a losange", "a disk" and "two lines". You must then ensure that ...
3
votes
1answer
158 views

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 ...
9
votes
5answers
3k views

How many different non congruent polygons can you make on a 3x3 dot grid?

There is a 3×3 dot grid. How many different non-congruent polygons can you make on the grid? Rules: All vertices of the polygon must be on the grid Only non self intersecting polygons Only polygons ...
20
votes
7answers
4k views

All clock hands at equal degrees from each other

My dad once asked me: At what time will the second hand, minute hand, and hour hand on an analog clock all be 120° from each other? It's a simple question, but I thought it was a fun one to figure ...
0
votes
0answers
81 views

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 ...
0
votes
1answer
78 views

Number of turns for two wheels to bring edge-points together

The puzzle is as follows: We present you below this riddle. A certain mechanism opens a gate of a maximum security lab. It just happens that a glass lets you see the mechanism and you know the ...
2
votes
0answers
64 views

Fair and square island hopping [duplicate]

If amateur fiction is not your thing skip to the bottom. As IP (Implausible Physics) expert for DREAM, the Department for Reckless Engineering and Advanced Megalomania you have been tasked by sheikh ...
12
votes
4answers
2k views

How many matchsticks need to be removed so there are no equilateral triangles?

The puzzle is as follows [with minor copy edits for grammar]: By only using matchsticks of equal length a set of equilateral triangles has been built as indicated in the figure from below. With that ...
1
vote
2answers
146 views

How many lines are needed to connect all smiling toasters in a 4x4 grid?

The puzzle is as follows: How many straight lines do you need to draw the least possible to join all the smiling toasters if you should not raise the pen or go over any line already drawn? Remember ...
14
votes
3answers
411 views

Two integer sided equilateral triangles with integer distances

In this figure with two non-congruent equilateral triangles and three-fold rotational symmetry the distance between any two of the 6 vertices is an integer. Can you give a solution? I know only one ...
5
votes
3answers
246 views

A square in the plane with 4 vertices of the same color

Every point in the plane is colored either red or blue. Is it necessarily the case (i.e., is it true for all such colorings) that there exist some four points of the same color that are the vertices ...
5
votes
1answer
284 views

Brute-force solver for Gear Octahedron - flawed method?

I am working on a program to brute-force a LanLan Gear Octahedron I bought second-hand (and scrambled). I have no background in "cubing" and just fancied solving the problem. The structure comprises ...
0
votes
1answer
35 views

A rectangle with non-integer side lengths [duplicate]

Is it possible to build a gapless rectangle with non-integer side lengths using rectangles each with two integer side length and two non-integer side length? The rectangles are not required to be the ...
1
vote
2answers
79 views

No four cells forming a rectangle

You are given a 5x5 square grid with 25 cells. Can you paint 12 cells, such that no 4 painted cells form the corners of a rectangle with sides parallel to the edges of the grid? Good luck!
9
votes
3answers
1k views

No three points in a line

You are given a 4x4 square grid. It has 16 cells and 25 grid intersections. Can you place 10 points at grid intersections, such that no three points lie on the same straight line? Lines can be ...
6
votes
2answers
449 views

Covering a 15x15 grid with rectangles

You are given a 15x15 grid and asked to cover it with rectangles whose dimensions are a power of 2. For example you can use rectangles 8x1 and 4x4, but not 2x3. The rectangles must cover every cell of ...
5
votes
1answer
283 views

Triangles, rectangles, nonagons

Which is the nonagon with the least area and which fulfills the following conditions. The nonagon has to be made from 7 triangles and 3 rectangles, all having side-lengths that are integer numbers. ...
45
votes
5answers
2k views

What fraction of the larger semicircle is filled?

What fraction of the larger semicircle is filled? The two smaller semicircles are of equal size. This is a puzzle originally set by Catriona Agg, who is a puzzle setting genius.
4
votes
1answer
173 views

An angle between diagonals

The diagonals of a square intersect at a right angle. Is that true in three dimensions? I.e. would the two diagonals of a cube, each running from one corner of the cube to its opposite corner and ...
5
votes
1answer
225 views

Cryptic Geometry

An entry in Fortnightly Topic Challenge #48: Unusual tag mix I was trying to study some geometry, but I just can't seem to wrap my head around all this mathematical mumbo jumbo. Can you help me out? ...
10
votes
2answers
355 views

Concave quadrilateral with integer sides and integer diagonals

Which is the concave quadrilateral with integer sides and integer diagonals with the smallest possible perimeter? This puzzle is my own creation.
8
votes
2answers
279 views

Cutting a shape into two equal area shapes

Given the following shape - an hexagon ABCDEF of which a parallelogram CDGH is cut out. With a single cut divide the shape into two equal area shapes by means of an unmarked . You may draw lines and ...
27
votes
4answers
2k views

Ernie and the Pirates of the Caribbean

A few weeks ago, I dropped in to see Ernie to ask if he was willing to look after the cat while I was on holiday in the Caribbean. “No problem.” he replied then showed me an old leather-covered book, ...
-2
votes
1answer
122 views

Heptagon, nonagon

What is the trick to constructing a heptagon and a nonagon which have all their sides equal? The length of the side has to be a natural number. Your answer should include a drawing of the two polygons....
7
votes
4answers
592 views

Divided by Pie Squared. Aaahhh

I have a machine that can divide a square pie into 9 equal square pieces using 4 blades: The blades can be moved, but there is only one control - which defines the width of the blades in both ...
3
votes
2answers
90 views

A triangle inside a triangle

All sides of a triangle T1 are shorter than the shortest side of a triangle T2. Is it always possible to put triangle T1 completely inside triangle T2?
3
votes
2answers
448 views

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 ...
13
votes
1answer
411 views

What is a Vexed Word™?

This is in the spirit of the What is a Word/Phrase™ series started by JLee with a special brand of Phrase™ and Word™ puzzles. If a word conforms to a special rule, I call it a Vexed Word™. Use the ...
2
votes
2answers
301 views

Four touching circles

Three identical circles are placed such that they touch each other. A larger circle is drawn around the smaller circles such that it touches them, as shown in the diagram. Can you find the ratio ...
20
votes
3answers
1k views

An ant's walk in the Cartesian Plane

An ant lives in the origin of the Cartesian Plane. Every morning, at 6 am, it sets out on a 16-hour walk which gets her back home precisely at 10 pm. In the first hour the ant walks exactly one unit, ...
1
vote
3answers
154 views

Maximum number of triangles formed in a pentagon with equal area

All diagonals of a convex pentagon are drawn, dividing it in one smaller pentagon and 10 triangles. Find the maximum number of triangles with the same area that may exist in the division. The best I ...
0
votes
1answer
76 views

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?
0
votes
2answers
130 views

How do you find the perimeter of a set of odd looking squares and triangles?

The problem is as follows: The alternatives given in my book are: 76 cm 80 cm 92 cm 100 cm Upon the first inspection. I'm getting the idea that I have to make a system of equations. Assuming that ...
0
votes
0answers
69 views

Pinocchio and the board [duplicate]

Pinocchio has driven two nails into the board to secure them, so that if one of them falls, the other nail will prevent him from falling.(Maybe he wanted to stand on the board)The fox claims that he ...
7
votes
3answers
463 views

Put line segment the way they cover end points

Is it possible to place 1000 line segments on the page so that the two ends of each line segment are on the inner points of other line segments? (By the inner point of the line segment, we mean a ...
1
vote
1answer
81 views

Painting a plane!

Paint the points on a plane with three colors, so that the points on each line are a maximum of 2 colors, and all three colors are used. (Math Festival 1990)
11
votes
1answer
703 views

How many circles needed to pass through each of 5x5 lattice points?

You are given a 5x5 set of lattice points. What is the minimum number of circles, which pass through each of the 25 points at least once?
1
vote
1answer
103 views

Splitting figures on the Cartesian plane

What is the minimum number of lines to separate the sets? a) 2 b) 3 c) 4 d) 1 e) 5 Observe the graph below, it is possible to separate linearly with a line at least two of the classes? a) Yes, just ...
2
votes
0answers
112 views

Does anybody know the history of this star/triangle puzzle?

Does anybody know the history of the puzzle posted by Mario Bilotti? Who created this puzzle? Who deserves the credit? Find 10 triangles in a five pointed star using two straight lines
15
votes
6answers
1k views

Tommy's Train Tracks

Tommy just got a new train set. It only came with one type of train track piece, a quarter circle, all of which were the same size. $\hspace{2.5in}$ Prove that, whenever Tommy makes a closed loop ...
4
votes
1answer
221 views

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 ...
0
votes
2answers
74 views

Show that no lines need cross [closed]

There are n red points and n blue points in the plane. Show that you can always join all the red and blue points with straight lines so that no two lines cross. Each point can have exactly one line ...
1
vote
1answer
161 views

Assemble lozenges

You have a large number of 60° rhombi called "lozenges." Each lozenge has its edges marked with four distinct symbols drawn from an infinite alphabet. Lozenges may be rotated by 180° or ...
-2
votes
1answer
236 views

How many shapes can you form with squares? [closed]

There is a 6 by 6 dot-grid. You will draw two squares by joining the dots. The squares cannot have common dots/points or areas. Rotations or reflections of a drawing are considered distinct. In How ...
9
votes
3answers
366 views

A theorem about angles in the form of arctan(1/n)

There is a famous classical geometry puzzle about the angles formed by integer coordinates: What is the sum of angle A and B in the following image? Do not use any advanced mathematics such as ...

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