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.

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votes
0answers
210 views

2018 January Challenge: Geometry [closed]

Considering it's the beginning of a new year, I have created the following challenge. I hope to make one every month until December 2018! Here goes: Show that $AD-AB>AC^3$. Do not use scale ...
4
votes
1answer
200 views

Two similar hand tiling puzzles

Make a square from each of these lists of aspect ratio $1:2$ rectangles 1, 4, 5, 6, 7, 9, 11, 12, 13, 14, 15, 17 ...
7
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2answers
282 views

Dissect a square into 3:2 non-congruent integer-sided rectangles

(Similar to the recent 3:1 rectangle question) Tile a square completely with rectangles which have aspect ratio 3:2, integral side lengths and all different sizes. In other words selected from 2x3, ...
4
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4answers
392 views

Another geometrical puzzle! [closed]

After the mind-boggling Dissecting Square puzzle, here is yet another geometrical puzzle. But a lot easier. In the figure $AE = 111$ and other lengths are unknown. What is the value of $AB^2 + BC^...
2
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4answers
1k views

Draw ten dots that are all the same distance apart

I am wondering, is it possible to draw ten dots so that every dot has the same distance to every other one? And how many possibilities are there?
7
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1answer
629 views

4 identical shapes that touch each other?

It is known that one can have 4 shapes in a plane all touching each other, and not 5. You can add requirements to the 4 shape problem: Can you do it with 4 equal triangles? (No) Can you do it with 4 ...
9
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5answers
667 views

Dissect a square into 3:1 rectangles

I am being known for Geometrical and Topological Puzzles, So continuing with the trend here is another one. Completely dissect a square into the lowest number of different sized rectangles with ...
7
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2answers
294 views

Teacup geometry

Inspired by the three utilities puzzle from prog_SAHIL I'm now posting a similar puzzle that makes use of the topology of a cup with a handle: The question is: How many distinct points can you ...
3
votes
3answers
353 views

Make me a room-filling pattern!

So I need a new knitting pattern, but I figured this might be a nice puzzle. I'm looking for a pixelated 2D-shape that can be used in a room-filling pattern (rotation and flipping allowed). The ...
17
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3answers
405 views

Is $s$ larger than the radius of circumscribed circle?

In the figure, showing a square and an equilateral triangle, is $s$ larger or smaller than the radius of the circumscribed circle?
6
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1answer
347 views

Cannot solve Ubongo Extreme B-38 purple puzzle

Today, I was playing Ubongo Extreme and I could NOT solve the following puzzle: B-38, purple colour. Let me know if you can solve it!
5
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1answer
217 views

A minor rearrangement of the one sided hexominoes in 12 simultaneous shapes

Here are the one sided hexominoes arranged into 12 congruent shapes. But there are one or two flaws: The dark blue hexominoes, which are the symmetric ones, may not occur more than once each in a ...
6
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1answer
219 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 ...
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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
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2answers
392 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
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2answers
562 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
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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
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2answers
328 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
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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
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1answer
359 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
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2answers
439 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
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1answer
187 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
168 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 ...
6
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2answers
555 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
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1answer
368 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
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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
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2answers
504 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?
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2answers
315 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
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2answers
165 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 ...
49
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2answers
6k 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
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4answers
680 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 ...
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1answer
180 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?
29
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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 ...
5
votes
1answer
200 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 ...
15
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2answers
1k 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
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2answers
594 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
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2answers
909 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
4k 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
426 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
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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
2k 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
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8answers
2k 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
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5answers
786 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
332 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 ...
5
votes
3answers
646 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
301 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
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2answers
125 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
237 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
153 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
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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 ...

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