Questions tagged [geometry]

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

6
votes
1answer
173 views

How many dimensions?

You have $n+1$ points in $n$-dimensional Euclidean space, such that the mutual distance between each pair of points is the same. Now imagine an $n$-dimensional generalization of a sphere, such that ...
15
votes
5answers
3k views

Mystery of the misprinted dice

Dan Hedfelt is a small gaming equipment manufacturer. Recently, he upgraded the machine that makes six sided dice, but the new machine started acting up, and he faced a production quality issue: the ...
14
votes
2answers
346 views

Hexominoes into 7 simultaneous congruent shapes

I came up with this puzzle 16 years ago, it was on Ed Pegg's Mathpuzzle site but nobody solved it AFAIK. The 35 hexominoes (which look like this): are to be arranged, in groups of five, into seven ...
6
votes
2answers
534 views

Three Right Triangles

There are three special right triangles, all of their edge lengths are positive integers. One of the triangles' longer leg, the other triangle's shorter leg and hypotenuse of the last triangle are ...
2
votes
0answers
72 views

How to Define the Intersection of a Rotated “Rectangle” in Spherical Coordinates [closed]

Can anyone tell me what is the intersection between the following two surfaces? The portion of a radius-1 spherical surface defined by four points: (r1, θ1, φ1), (r2, θ2, φ2), (r3, θ1, φ3), (r4, θ4, ...
6
votes
2answers
293 views

Independent Triangles with Straight Lines

Your task is to create independent triangles (which means they do not have the same edge) by drawing straight lines as exemplified below: In this example, there are $5$ lines and $5$ independent ...
6
votes
8answers
1k views

Measure the height of my neighbor's building

I'm standing on the roof of my building with nothing but a laser range-finder, and I want to know the height of my neighbor's home. Who can tell me how to do it with the least number of laser measures?...
0
votes
1answer
252 views

Triangle partial length of hypotenuse [closed]

How can I solve for X? What I did was solve for C, and then took (6/6+2)*C. It seems to work but I am not completely sure. Is there a better way?
4
votes
2answers
382 views

Turning the Horse Part 3

Here's the sequel to Turning the Goat Part 1 and Turning the Dog Part 2 As Hobble the horse stood on the hillside staring at the hurdle below, he wondered if he would ever have the courage and ...
1
vote
1answer
180 views

The smallest disc which could contain 11 coins

There are $11$ coins with $1$ unit radius and we are trying to put them inside a big disc with some radius. So What is the minimum radius of this disc? If this question was asked for $2$ coins, ...
3
votes
1answer
153 views

Is it possible to build this out of soma cube parts?

For those of you who dont know, these are soma cube parts: They can be assembled into a 3x3x3 cube. Is it possible to build a hollow cube with the extra little cube being on top, in the middle of ...
5
votes
2answers
544 views

Three Circles One Area

We have three circles where their centers are on the same line and PR is tangent to both small circles as shown below. If $|PR|=12$ unit, what is the area of blue part of the circle? Reference: A ...
3
votes
1answer
288 views

Two quadrilateral out of a hexagon

We have a hexagon shown as below with two quadrilaterals: Your task is: Slice hexagon into two pieces and combine these pieces to find shape $a$ Slice hexagon into three pieces and ...
13
votes
4answers
1k views

How many times does the coin turn around?

we have 10 coins, and we aligned 9 coins as shown below. The extra coin shown is being used to turn around the aligned coins. By turning it around like shown below, how many times would the coin ...
4
votes
2answers
359 views

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?
9
votes
2answers
278 views

Create a 1 meter measure

How many folding steps do you need to create a $1 \, \text{m}$ measure from an ideal DIN A0 sheet? This sounds easy, but consider that this paper has edge lengths of $\sqrt[4]{2} \, \text{m}$ and $\...
3
votes
2answers
159 views

Polygon neighbors

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 ...
48
votes
2answers
5k views

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 ...
6
votes
4answers
661 views

Radar towers in a military field

The military field has rectangle shape with the dimension of 16 km to 12 km and recently there are some drone activities around the area and drones are not welcome to the military region! Your ...
0
votes
1answer
153 views

Arrange six cigarettes in such a way that each cigarette touches every other cigarette [duplicate]

What are some ways to arrange six cigarettes in such a way that each cigarette touches every other cigarette?
28
votes
8answers
3k views

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 ...
4
votes
1answer
192 views

15 pawns on a chessboard

15 pawns are placed on the centers of distinct squares of a chessboard. Prove that there are three pawns which form a right triangle. In the example board below, a couple of right triangles are ...
10
votes
2answers
889 views

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 ...
8
votes
2answers
540 views

Help! I lost my marble(s)!

Tomorrow is the annual meetup for the Northwest Region Marble Lovers Association. The days festivities will include various marble games, admiring collections of marbles, a guest speaker who will talk ...
7
votes
2answers
791 views

Triangle with incircle [closed]

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 ...
9
votes
2answers
3k views

Rope between 2 poles

A 10 meter long rope with uniform mass-density and bending module is hanging between two poles. Given the fact that both ends of the rope are 5 meters higher than the lowest point of the rope, find ...
3
votes
1answer
403 views

8 Train Stations

You are going to build $8$ train stations and the railroads with it in an area. But you are asked to build these stations and their railroads in a very efficient way where there has to be the least ...
19
votes
9answers
1k views

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 ...
6
votes
2answers
1k views

Fold a standard paper to get a Rhombus

A follow up to the "Create a 3 inch measurement" post. Can you create a Rhombus ( a parallelogram with all sides equal AND which is not a square-- my restriction) using a standard letter size paper ( ...
11
votes
8answers
1k views

Prison Pizza Party

You are an inmate at Infinity Prison, where prisoners must work together to solve a challenging riddle every day to ensure their very survival. But today is your lucky break; the warden has decided to ...
8
votes
5answers
697 views

The distance between David and Eric

Alice and Bob are looking at each other, both turn $10$ degrees and now they both can directly see Claire. If they continue turning in their same directions before, Alice will directly able to see ...
9
votes
2answers
325 views

How to find the layout of the plots?

A peasant had a square garden of $100 × 100$ meters divided into $100$ equal square plots. In the testament, he left to each of his $7$ male grandchildren a connected region of $10$ plots, forming ...
3
votes
2answers
470 views

The farmer and the olive trees

A farmer has a rectangular ground of 100 m by 50 m, he wants to plant olive trees, in sufficiently spaced ways (to avoid exhaustion by the roots) at least 10 meters from each other. How much can one ...
3
votes
1answer
289 views

Floored and foiled

Scene 1 – A hallway There I was, in a corporate hallway 110 shaftments long (approximately 18 m or 60 ft) and unspooling a 100 -shaftment length of cable from a reel. All too ...
2
votes
2answers
121 views

Right angled triangle to all acute angled triangles

What is the minimum number of cuts needed to dissect a right angled triangle into acute-angled triangles ?
3
votes
1answer
215 views

How many combinations of pentagons can you make on a 4 by 4 dot grid?

Following on from: How many different non congruent polygons can you make on a 3x3 dot grid? How many combinations of pentagons can you make on a 4 by 4 dot grid? Since this is an even $n$ square ...
1
vote
1answer
135 views

Combinations of pentagons on a 3 by 3 dot grid - how to use Burnside's lemma?

In the accepted answer to How many different pentagons in this grid?, Jaap Scherphuis says: After reducing for symmetry, only 23 are left, which you can check using Burnside's lemma. How did they ...
7
votes
2answers
1k views

I cannot make any triangle with sticks

There are $13$ sticks with different lengths, and you try to form a triangle by using $3$ sticks (making every stick is a edge of a triangle) but somehow whatever $3$ sticks you choose, you cannot ...
15
votes
2answers
1k views

What's the missing pattern? 3x3 grid, dot pattern

What is the missing piece to this pattern? Got it as a quiz at work - no one here knows what it is!
19
votes
4answers
757 views

Ernie and the Uneconomical Flat-breads

When I arrived at Ernie's place last weekend I had some exciting news for him. "did you know", I announced "that a new Kzijekistanian fast-food shop has just opened in town?". "I did", Ernie replied, "...
0
votes
2answers
733 views

Unlimited paper folding

You have a squared piece of very thin paper. You can fold it and glue together to get a piece of paper with other shape. You can make it as many times as you want. Are there convex polygons, which you ...
-11
votes
2answers
542 views

What is the answer for the question 23 and 22 in the image below?

Source- NTSE Chattisgarh 2015. Sorry, didn't know I cannot post Exam questions.
-3
votes
1answer
202 views

Find the angle in the shape [closed]

I'm back again with another controversial puzzle for you. If you try this puzzle for yourself, you will notice that it does not seem possible at first. Please provide a proof for your solution. You ...
3
votes
2answers
416 views

Find the angle in this shape [closed]

The aim of this puzzle is to find the angle marked '?'. Answers must be in the format of exact values. You will have to assume some basic geometric constraints. e.g. points which look like they are ...
4
votes
1answer
207 views

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° ...
8
votes
12answers
2k views

Building a Square out of a rope

This was a challenge given to us in our Team Building exercise in an MBA course I took. Needless to say our team didnt do well. So I am asking the Stack community if there is a clear way. We were in ...
5
votes
4answers
491 views

What did Louis do to measure the cardboard box?

When Louis arrived at his apartment in Europe he found a note pinned to the wall in his study. The note was pinned on a 10 Euro bill. It was from his yankee roommate Jack, who always liked to play ...
7
votes
4answers
1k views

What's the most complex pattern to decipher if you have seen the pattern

I am trying to set a lock pattern for my phone with a snoopy guy behind. If he is able to see what my pattern looks like at the end, what is best possible sequence i can set so he will take maximum ...
5
votes
1answer
642 views

Can two colors ever be orthogonally adjacent in a flexi puzzle?

A flexi puzzle is a fun little toy, consisting of wood blocks and a string that runs through it. The pattern of colors is repeated twice; if a color is found at position $N$, it is found a second ...
6
votes
4answers
430 views

Constructing 0.35 Unit Length

The Problem The medieval equivalent of Bob the Builder has a new job offer: He is to build a box with the measures of $0.35$ units by $0.35$ units by $0.35$ units for a king. There is a little ...