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.

Filter by
Sorted by
Tagged with
7
votes
6answers
519 views

Tiling rectangles with N pentomino plus rectangles

Inspired by Polyomino Z pentomino and rectangle packing into rectangle Also in this series: Tiling rectangles with F pentomino plus rectangles Tiling rectangles with T pentomino plus rectangles ...
8
votes
3answers
571 views

Tiling rectangles with F pentomino plus rectangles

Inspired by Polyomino Z pentomino and rectangle packing into rectangle Also in this series: Tiling rectangles with N pentomino plus rectangles Tiling rectangles with T pentomino plus rectangles ...
14
votes
2answers
553 views

Tiling rectangles with W pentomino plus rectangles

Inspired by Polyomino Z pentomino and rectangle packing into rectangle Also in this series: Tiling rectangles with F pentomino plus rectangles Tiling rectangles with N pentomino plus rectangles ...
-4
votes
2answers
283 views

Random chord to a circle around a triangle

This puzzle is literally a math textbook question. Its only redeeming feature is that it also happens to be too broad in a surprisingly interesting way. The problem Given the circle $\mathbf O$ ...
10
votes
3answers
612 views

For n nodes that are connected to at most m and at least 2 other nodes, what values of n and m always allow the connections to not intersect?

I am trying to develop a puzzle game where $n$ nodes are generated and placed randomly on the screen. Each node is connected to at most $m$ and at least 2 other nodes by straight lines. This is an ...
5
votes
1answer
6k views

Is there only one solution to the “Ten Penny Puzzle” or more?

Not knowing the dimensions of the square in the Ten Penny Puzzle I ask if there is more than one unique solution that isn't a reflection/mirror of the one shown in the video, if you know the ...
24
votes
4answers
2k views

Four points with only two distances

Your task is this: Find all arrangements of four distinct points in the plane such that only two distances occur between them. When you have $4$ distinct points, you can measure the distance ...
22
votes
2answers
839 views

Slashes, Dashes, and Boxes: Oh My!

These riddles are really hard until you figure out how to look at them at the right angle. Sometimes it's hard to connect the dots at first. This riddle might contain a hint to my other riddle. Or ...
17
votes
4answers
2k views

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.
6
votes
3answers
232 views

Two puzzles about encompassing convex sets

Prove that any convex set of area $1$ is contained in a rectangle of area $2$. Prove that any convex set of area $1$ is contained in a triangle of area $4$. Notes: (1) is from "The Art of ...
6
votes
1answer
458 views

How many possible different shapes are there on a 4x4 dot grid?

Alright. This math required to do this is way beyond me, so please be patient. I edited this a lot to make the question more solvable and easier to understand, without making the answer less useful ...
1
vote
1answer
98 views

Ways to cut and reassemble a solid object [closed]

I have been puzzling over this for a few years and still have no answer. How many ways can a solid object like a cube or a ball be cut into pieces such that it is possible to take apart and put ...
18
votes
4answers
3k views

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?
2
votes
1answer
250 views

Make lots of squares with only 6 squares

You are going to draw $6$ congruent squares to make as many squares as you can! What is the maximum amount of squares (except the original squares) you can create by drawing 6 congruent squares? ...
27
votes
7answers
3k views

What's the perimeter of the hexagon?

Consider a hexagon which is equiangular but not equilateral: all angles equal to 120 degrees but four consecutive sides of length $a,b,c,d$ not necessarily equal. What is the perimeter of the hexagon? ...
2
votes
1answer
284 views

Wooden Snake Puzzle - logic behind solution

I refer to the wooden snake puzzle in this post: Wooden Snake Puzzle I notice that there are 6 solutions to the 4x4x4 snake, which start respectively as follows: FRB… (↗→↙…, which is also the ...
1
vote
2answers
163 views

Ugh! The extra SQUARE! [duplicate]

Can you split this figure into two congruent pieces with a line? The line need not be straight. :D
2
votes
1answer
151 views

Finding the equation among shapes

There is a relation between the shapes in the top equation on the left side. If we apply such an equation to the bottom shapes, which one from the right choices can fill the question mark? Source: ...
0
votes
1answer
134 views

Combining parts to make an square

In the following picture, if one puts some of the shapes A, B, C, D, and E together, they can make a square. Then which shapes would be redundant? Only A Only D Only E A and D Can you construct the ...
9
votes
4answers
1k views

Putting the pips on a d6

Using a blank cube and a bunch of circular stickers, an average person constructs a d6. A d6 is also known as a six-sided die, or sometimes, a dice. For the purpose of this puzzle, the average person ...
36
votes
4answers
5k views

Odd-looking circle

A man is told to make a circle He makes this: Where is the man?
7
votes
3answers
497 views

Laser Beams in Helsinki Skies

(The first two chapters are just for flavour, you can safely skip to the TL;DR near the end.) This puzzle in situated Helsinki for a reason: for the city's "200 years as capital" celebration, the ...
5
votes
2answers
328 views

Minimal-length curve guaranteed to intersect all secants of circle [duplicate]

Consider a unit circle C. The goal is to find a curve L such that: all secant lines of C intersect L; the length of L is minimal among those with property 1 above. Any closed curve containing C (for ...
3
votes
3answers
2k views

Old 6-piece wooden cross puzzle

I found this old puzzle and have no idea how to get it together. I have been trying to complete it for several hours now but to no avail. The pieces of the puzzle are as follows: Also sorry if it has ...
10
votes
1answer
363 views

Minimize the intersection area

You are given two identical pieces of paper of size $a \times \sqrt{2} a$, like the standard DIN A4 paper. Put one paper on top of the other, such that none of the corners is under or above the other ...
4
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 ...
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
votes
2answers
281 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
votes
4answers
389 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
votes
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
votes
1answer
624 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
votes
5answers
666 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
votes
2answers
292 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
votes
3answers
403 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
votes
1answer
337 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
votes
1answer
210 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
votes
1answer
216 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
390 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
558 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
326 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
353 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
428 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
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
167 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
votes
2answers
554 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
357 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 ...

1
3 4
5
6 7
15