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.

9
votes
3answers
531 views

Tiling a rectangle with just the Y pentomino

Inspired by this question series, which was inspired by this question. They give rise to beautiful pictures (at least in the eye of the beholder mathematician) and some nice generalizable solutions. ...
11
votes
1answer
430 views

6 nails String Art

String art is an arrangement of thread strung between nails to form geometric patterns or representational designs such as a ship's sails, sometimes with other artist material comprising the remainder ...
12
votes
1answer
449 views

Ernie and the Case of the Singing Sisters

On my way to work each morning I pass a news-agency that usually has a sandwich-board displaying the latest headlines of a somewhat disreputable tabloid newspaper (not that I would ever buy such a ...
2
votes
1answer
134 views

Tile a square with five rectangles with 10 distinct edges

The baby brother of: Cutting a square into seven rectangles Tile a square with five rectangles. Select the lengths of the edges of the rectangles from the set $1$ through $10$, with no length ...
5
votes
2answers
213 views

20 right isosceles triangles into a square

Similar: Unlucky tiling: Arrange thirteen right isosceles triangles into a square Five graded difficulty isosceles right triangle into square tilings Two difficult "Seventeen right isosceles ...
18
votes
2answers
2k views

Maximal-volume cube net from unit square paper

Given a square piece of paper (say 1x1), what is the largest cube net you can cut out of it? ('largest' meaning with maximal volume; 'net' meaning it's possible to fold into a cube (somehow)) This ...
2
votes
2answers
139 views

Two difficult “Seventeen right isosceles triangles into a square” tilings

Similar to: Unlucky tiling: Arrange thirteen right isosceles triangles into a square Five graded difficulty isosceles right triangle into square tilings V.hard problem, 20 right isosceles triangles ...
5
votes
2answers
193 views

Five graded difficulty isosceles right triangle into square tilings

Similar to: Unlucky tiling: Arrange thirteen right isosceles triangles into a square Two difficult "Seventeen right isosceles triangles into a square" tilings V.hard problem, 20 right ...
12
votes
2answers
257 views

Unlucky tiling: Arrange thirteen right isosceles triangles into a square

Link to next puzzle in this series:Five graded difficulty isosceles right triangle into square tilings Two difficult "Seventeen right isosceles triangles into a square" tilings V.hard ...
6
votes
3answers
276 views

Tiling rectangles with X 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 ...
6
votes
2answers
239 views

Tiling rectangles with V 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 ...
3
votes
3answers
191 views

Tiling rectangles with U 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 ...
8
votes
2answers
221 views

Tiling rectangles with T 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 ...
7
votes
6answers
451 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 ...
7
votes
3answers
478 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
504 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
234 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
549 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
2k 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 ...
21
votes
4answers
1k 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
820 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 ...
16
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
224 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
271 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
97 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
243 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? ...
26
votes
7answers
2k 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
262 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
155 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
147 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
131 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 ...
33
votes
3answers
5k views

Odd-looking circle

A man is told to make a circle He makes this: Where is the man?
7
votes
3answers
448 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
325 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
1k 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
335 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
205 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
188 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
260 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, ...
5
votes
4answers
384 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
397 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
609 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 ...
6
votes
2answers
225 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
339 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
388 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
268 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
173 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 ...