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]
922
questions
13
votes
2answers
917 views
Prove why this mechanical linkage for a triangle centroid works
I saw on Twitter this cool mechanical linkage for which the red dot corresponds to the centroid of the triangle defined by the blue dots:
Can you prove why this linkage works?
11
votes
0answers
692 views
Hidden message in rap text II: “Ya, a ray 'ave july joy!”
This puzzle is inspired by this one by @LukasRotter. Hopefully you don't mind me using similar (well, basically the same) format as yours, Mr. Rotter! ;)
The same rapper released another teaser for ...
12
votes
1answer
865 views
Four non-right angled triangles passing through every dot of a 5x5 grid
This puzzle was suggested by jwezorek in Three triangles passing through every dot of a 5x5 grid
25 dots are drawn as a 5x5 regular square grid. Can you draw 4 non-right angled triangles that pass ...
18
votes
1answer
1k views
Four triangles passing through every dot of a 7x7 grid
49 dots are drawn as a 7x7 regular square grid. Can you draw 4 triangles that pass through every dot? The corners of the triangles must lie on the dots, ie., they cannot lie outside the grid.
The 7x7 ...
15
votes
3answers
3k views
Three triangles passing through every dot of a 5x5 grid
25 dots are drawn as a 5x5 regular square grid. Can you draw 3 triangles that pass through every dot? The corners of the triangles must lie on the dots, ie., they cannot lie outside the grid.
-5
votes
2answers
150 views
Inscribing a cylinder within a sphere [closed]
Let's have a sphere with R=3. What is the trick to inscribe in this sphere a cylinder almost half
its volume? The circumferences of the two bases of the cylinder have to lie on the surface of the
...
8
votes
2answers
486 views
Largest rectangle from 20 Lego bricks
You have twenty 2x4 Lego bricks, like the one shown below
What is the area of the largest rectangle you can make satisfying the following conditions:
All bricks must be connected in a single ...
9
votes
3answers
736 views
Lines and Squares
This 'puzzle' is from the New York Times website, from its puzzles. I decided it was fun and so I would share it with you.
Question
Here are 10 straight lines and 17 squares.
Here are 9 straight ...
21
votes
7answers
4k views
Can you irrigate your lawn with 23 sprinklers?
You have a perfectly circular lawn with radius exactly 4 metres. Lately the grass has been turning yellow and quite rough, so you go to Stiv's Diabolical Instruments and describe your problem.
"...
5
votes
2answers
399 views
My special animal
The answer to this puzzle is an image not hosted on Imgur. The image host and the ID of the image on that host should become clear when solving the puzzle.
(SVG source of the above)
Exact coordinates ...
7
votes
2answers
121 views
Vertices of a regular $13$-gon and $14$-gon on a circle with center angle $< 1°$
All vertices of a regular $13$-gon and all vertices of a regular $14$-gon lie on a circle and divide it into $27$ circular arcs.
Is there always an arc, which corresponding center angle is less than $...
13
votes
3answers
981 views
A line not intersecting points in the plane
Is it possible to draw a finite or infinite set S of points in the plane, such that any line drawn in this plane neither intersects with exactly one point in S or an infinite number of points in S?
9
votes
1answer
269 views
Survive the infinite zombie attack II
Zombies are back again. Same as last time, You're at the origin, and zombies occupy the points $(100𝑖,100𝑗)$ for all integers $𝑖,𝑗$ except the origin, as shown below:
The ratio of your speed to ...
13
votes
2answers
689 views
Paint Eight Squares
Inspired by this question
Given a $5 \times 5$ grid of white squares, can you paint $8$ of the squares black so that each white square is orthogonally adjacent to exactly one black square?
1
vote
1answer
243 views
1 lion, with a zebra and a fixed enclosure
Background
See the puzzle Variant of lion and 100 zebras from @ghosts-in-the-code which remains unsolved years after it was posted.
Several times in the last couple of years I've started to write up ...
-1
votes
2answers
247 views
Filling up squares! ⬜ ⬛ [closed]
You have a white grid of size
a) 9x9
b) 10x10
and you are asked to paint some squares black. Your generous friend has given you a challenge:
Can you paint them so that each white square has only one ...
-2
votes
1answer
136 views
Trails on a grid filled with skinny tetrominoes
Let's have a 10x10 grid with 12 empty bases. The rest of the grid is filled with skinny tetrominoes. The 5 regular tetrominoes are marked with a red color and the 2 reflections are marked with a green ...
7
votes
6answers
2k views
Dividing a chocolate frosting cake [closed]
Mrs. Betty made a squared cake with chocolate frosting for his neighbors to the afternoon tea. However, first she sliced a middle piece for her two grandchildren and cut it in half:
There was no ...
6
votes
1answer
561 views
Flat share share
This is a sequel to Gentrification in Chessshire.
Due to the febrile state of the Chesster housing market you and your flat mates are forced to rent out half your place to another group of sharers.
...
2
votes
1answer
208 views
Rearranging the square
You are given a square piece of paper. You can cut it into pieces and rearrange them to form a new shape. You are allowed to rotate and flip pieces, provided that they are all used. Can you cut the ...
-3
votes
1answer
233 views
Open dice Problem
The following figure is folded to form a box. Choose from the
alternatives (A), (B), (C) and (D) the boxes that is similar to the
box formed.
Source: YouTube
Video
How to answer these type of ...
2
votes
2answers
159 views
A bear of a different colour [duplicate]
Here is a stunning new version of the famous bear problem. IT IS NOT A DUPLICATE, OR LATERAL THINKING. MATHEMATICS REQUIRED.
A photographer stepped out of their tent with a camera and walked:
1 km ...
10
votes
2answers
323 views
Gentrification in Chessshire
You can skip the back story and directly jump to the question.
Capitalism has arrived in suburban Chesster the community most famed for The Game, and with a vengeance. Rents have trebled in less than ...
1
vote
3answers
173 views
Test of Pentominoes
These are pentominoes, with letter codes:
Create 4 yes/no questions which uniquely classify each pentomino.
Examples of such questions are:
Does it have rotational symmetry?
Does it have reflection ...
1
vote
1answer
183 views
Catch the fugitive
The fugitive is at the origin. He moves at a speed of 100. You have a guard at every integer coordinate except the origin. A guard's speed is 1. The fugitive and your guards move simultaneously and ...
10
votes
1answer
282 views
Wraps and Loops—Which Sequences are Admissible?
If you take a non-intersecting closed loop on a torus (that is to say, a path which ends where it starts and does not cross over itself, drawn inside a square whose edges "wrap" left to ...
7
votes
5answers
638 views
What a coincidence or eighteen is not seventeen take two
Since I botched my first attempt at posing this puzzle, let me try again, this time hopefully closing all loopholes by dropping the packing angle and making this a purely geometric puzzle:
The figure ...
6
votes
2answers
2k views
Eighteen is not seventeen
This question is not the same as Adding coins inside a ring of coins
From a pile of equal size perfectly round coins take eighteen and make a perfect ring. Show that you can fit at least sixteen more ...
9
votes
1answer
225 views
Connect the dots to form a polygon
a) In each of these two grids of dots, 5 x 7 and 7 x 9, connect all of them so as to form polygons of 35 and 63 sides respectively (two consecutive segments can therefore not be collinear as they ...
-1
votes
2answers
117 views
Tessellation with nonagons and equilateral triangles
What type of convex nonagon is required to tesselate a plane with equilateral triangles and nonagons? All sides of the nonagons are equal.
NOTE: Partial tessellation of a plane should accompany your ...
5
votes
3answers
530 views
Another puzzle with area
Squares $ABCD, DCGH, BEFG$ and $ELKM$ are positioned as shown on the picture. Find the area of triangle $DGK$ if you know that the area of square $ABCD$ is $20$.
9
votes
1answer
166 views
Puzzle with the point inside paralelogram and area
We have a paralelogram $ABCD$ and point $P$ inside it. Halflines $BP$ and $DP$ cuts respectively lines $AD$ and $AB$ at $E$ and $F$. Why are the area of $ABPD$ and $CEPF$ the same regardles of the ...
10
votes
2answers
573 views
Adding coins inside a ring of coins
17 identical coins with diameter 1 are lying flat on a table, such that their midpoints build the vertices of a regular 17-gon (regular heptadecagon) and adjacent coins touch each other.
What is the ...
3
votes
0answers
206 views
One vs many. Can white force a draw?
On an infinite chessboard there's a single white king and N black kings. The nearest black king must be K moves away from the white king. Given N, white dictates the value of (finite) K, then black ...
7
votes
2answers
303 views
Can the fugitive escape?
A fugitive is surrounded by N police officers, with the nearest one at distance 1 away. The fugitive and the officers move alternatively.
In a fugitive move, the fugitive can travel no more than a ...
7
votes
1answer
219 views
The Extraordinary Sky of Saddlestania
The infinite country of Saddlestania has some very interesting geography: its elevation from the mathematically flat sea level exactly follows the equation $$\mathbf{z=x^2-y^2}.$$
After traveling ...
2
votes
1answer
97 views
“Physical” height of an infinitely distant joint point
When driving along long straight roads, this is what you would typically see:
Photo by Luke Stackpoole on Unsplash
As you're probably aware, the solid lines on the sides of the road are parallel, in ...
11
votes
3answers
361 views
Inhomogeneous circle packing
In the figure, what is the diameter of the smallest circle assuming the two parallel lines are one unit apart?
Note: There is at least one elegant, geometric proof.
Attribution: Mine, but wouldn't be ...
6
votes
2answers
792 views
A square covering a rectangle
You are given a rectangle with base b and height h with $h>b>0$.
What is the minimum side length of a square, which completely covers this rectangle?
13
votes
1answer
427 views
Folding a piece of paper with numbers in sequence
Divide a rectangular sheet of paper with a side length of 2 × 4 into eight 1 x 1 unit squares
and label them as shown in the sketch.
Then fold the sheet of paper along the boundaries of the square so ...
8
votes
1answer
337 views
Manual tiling with 8 dodecadudes
Here are 8 dodecadudes. (Drawn from the very numerous dodecadrafters, made from 12 half equilateral triangles, dodecadudes are a subset of 770 pieces with sharp points and narrow necks excluded). ...
2
votes
1answer
122 views
Painting cells on the diagonals of a grid rectangle
In a grid rectangle 20210 × 1505, two diagonals are drawn, and all the cells containing segments of diagonals are painted. How many cells are painted?
12
votes
1answer
400 views
Strange tiling pattern
Here is a simple pentagonal shape:
Using copies of this shape it seems that you can tile the plane, without even needing to flip over the tile.
But can you really?
-6
votes
1answer
87 views
3-Sliced Square [closed]
I remember this one time when my brother told me "with just 3 lines, how many shapes can you form in a square piece of paper?"
After 30 minutes, my 7-year-old brain thought that I could only ...
3
votes
1answer
197 views
Infinite beauty
This is a follow-up to Puzzle about 6 infinite cylinders in space
Question:
Given six identical infinite (no caps) cylinders is there a beautiful arrangement in space such that each touches each ...
4
votes
2answers
515 views
Cubes touching all other cubes
This question is based on this great puzzle: Puzzle about 6 infinite cylinders in space
What is the most number of identical cubes that can be placed, such that every cube touches all the other cubes ...
4
votes
2answers
444 views
A geometric puzzle. What is the angle?
This is a simply stated geometry puzzle. What is the angle p in this isosceles triangle?
Here's some information about the origin of the puzzle. Following any links therein may spoil the fun if you ...
14
votes
2answers
1k views
Puzzle about 6 infinite cylinders in space
You have 6 infinitely long cylinders (tubes) with the same radius R. Can you arrange them in space in a way that every cylinder touches the other 5? By touching, I mean have a common point or a line. ...
8
votes
5answers
1k views
A pentagon puzzle
Consider the following pattern made of regular pentagons:
If the pattern continued, will it form a complete loop or will the pentagons overlap?
-1
votes
2answers
113 views
Surrounding an equilateral triangle
You are given an equilateral triangle. What is the most number of such identical triangles you can place such that they do not overlap, but each one touches the original triangle?
