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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1
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0answers
46 views

Intersecting shapes on a flat surface

If I draw two circles and two triangles on a flat surface, how many bounded regions are created to the maximum? Try to answer with mathematical arguments.
6
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1answer
138 views

Move just 2 matchsticks to make three equally sized triangles

There are 9 equally sized matchsticks, move 2 to make 3 equal triangles
5
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1answer
99 views

Geometry optimization

Three equilateral triangles with side lengths 28 are placed in the position as shown in the picture above. All the contacts are perfect and a circle passes by exactly one vertex per triangle. What’s ...
8
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1answer
102 views

Table covering with tablecloths

In front of me stands a table with the shape of an equilateral triangle with side lengths 1. I can cover the whole surface with five identical circular tablecloths. What is the minimum radius for a ...
5
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1answer
111 views

A new Sangaku puzzle

A cyclic hexagon is inscribed inside a circle. The sum of two consecutive sides always equals 149. Then, we triangulate the hexagon into four triangles each containing an incircle, and surprisingly, ...
6
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2answers
172 views

The pond of symmetry

There is a $4$m by $4$m square pond. You have $3$ straight planks of wood, each exactly $2$m in length. You need to place the planks so that they go from one corner of the pond to the diagonally ...
24
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4answers
3k views

A COVID-19 puzzle: How large a class do you need to fit 30 pupils?

Some countries are proposing to reopen high schools soon. To ensure safety, they want to make sure that all pupils in a class are at least 2 m apart. To help them find the smallest room that can ...
5
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3answers
636 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 ...
10
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2answers
778 views

Bouncing ball on a billiard board

Consider a unconventional billiard board in the shape of an equilateral triangle (depicted below). An incredibly small ball (size in picture is increased for the sake of visibility on your screen) is ...
17
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1answer
2k views

Blue. Orange. Green. Magenta. What does this strange picture represent?

Is it text? Is it a face? Is it code? What is it?
4
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1answer
156 views

Cutting a Rectangular Board

There is an $m \times n$ rectangular board drawn on a graph paper. You need to cut it into $mn$ $1 \times 1$ squares by straight cuts along the grid lines. You are allowed to stack several pieces ...
8
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5answers
209 views

An $n$-sided polygon with area $n$

Here is a $10$-sided polygon which area is $23$ (i.e. it contains exactly 23 unit squares). Can you draw a polygon with: $6$ sides and area $6$? $8$ sides and area $8$? $12$ sides and area $12$? ...
4
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1answer
110 views

How can I cut a cube so that all its vertices except for two mutually opposite vertices are equally distanced from the plane of the cut?

A friend of mine has been struggling with a solid geometry problem and, knowing my imagination skills developed by playing gomokunarabe and renju, has asked me to help her, but the problem has proved ...
11
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1answer
183 views

Pythagorea Toughie

I recently happened upon a game called pythagorea. The idea is that you're given a 6x6 grid. You may click at any intersection to create a point and you may join any two points to create a line (that ...
11
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1answer
605 views

Perfect Golomb Circles

A Golomb ruler of order $n$ is a straight line with $n$ marks (at integer locations) such that no two pairs of marks are the same distance apart. We can extend the concept to circles. Place $n$ marks ...
7
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2answers
125 views

When is a robotic arm able to reach any point (closer than the length of the outstretched arm)?

In a plane, there is a robotic arm consisting of $n \ge 2$ segments of length 1, like this: The first segment is fastened to a single point ("origin"), but it can rotate freely around that point. All ...
10
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1answer
197 views

Interplanetary blips and bleeps

Things were quite different in 3000 AD. We'd discovered other planets with sentient life for instance. Five to be precise. Adam, Bill, Carl, Dave, and Eric we called them, and we used the lately ...
8
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4answers
2k views

Is there a simple algorithm for solving Kami 2 puzzles?

I'm finding my life has been consumed by Kami 2, partly because I seem to have achieved some "insight" and am able to solve the puzzles reliably, almost always on the first try. The rules are simple: ...
4
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3answers
171 views

The death prism

One day, you are caught by a evil wizard. He presents you with a prism, and says, "You can ask me to turn this prism to any $n$-angled right prism. Then you shall fill in $1$ to $3n$ with no ...
8
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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 ...
36
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12answers
3k views

Variant of lion and 100 zebras

Note: This problem remains unsolved, as of 19 April 2020, so do try it out. 400 rep bounty guaranteed for a correct answer This a variation of this question by @Gamow Suppose there are $100$ lions ...
9
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2answers
598 views

A rectangle in a rectangular hole

I have a carpet of 240 inches by 120 inches, but my floor, which it needs to cover, is 180 inches by 160 inches. How can I do this by cutting the carpet into exactly two pieces? Source: Rational ...
-1
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2answers
113 views

Can we visit each block of 4*4 exactly once? [duplicate]

A person is standing at a corner of $4\times4$ square, he would like to travel each block exactly once before exiting from the opposite corner. Is there a way?
12
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2answers
280 views

Goldman's Transformation Puzzle

In an old book (*) I found an advert with a puzzle I had never seen before. Unfortunately the book is very rare and it is hard to make out in the scanned photocopy above. I have redrawn it: It looks ...
2
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0answers
124 views

Ernie and the Chocolate Bomb

Last week when I visited Ernie he complained that his trousers had shrunk in the wash. I suggested an alternate possibility – he was putting on weight. So he decided to go on a diet and to support him,...
11
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2answers
2k views

Two Cannons - A Beginner's Physics Puzzle

Standoff Let's say we have two cannons aimed directly at one another ( as my horrible attempt shown in the image ). The Angles The cannon on top is aiming down towards the one on bottom right, ...
12
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2answers
2k views

Cut this shape into 3 pieces and fit them together to form a square

A shape is drawn on a sheet of squared paper as shown in the picture below. The shape is then cut from the sheet and given to you. You are asked to first make a straight cut across the shape and then ...
20
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11answers
3k views

Tiling a Hexagon with Diamonds

A regular hexagon is divided into a triangular grid, and completely tiled with diamonds (two triangles glued together). Diamonds can be placed in one of three orientations. Prove that, no matter how ...
4
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4answers
578 views

Rapunzel and the Prince

This is a simple mathematical puzzle, which I decided to improve a bit one year after posting. Some of the answers below consider slightly different, but equivalent setting of the problem. Rapunzel ...
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 ...
5
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2answers
378 views

How to obtain the 6- and 12-gon with 6 equal rectangles?

Let's say you have 6 equal business cards. How can you place them on a table to create these shapes: regular hexagon regular dodecagon Edit. Feel free to propose an answer for options: a) you have ...
6
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2answers
150 views

Squared, what is in the post-scriptum?

Just received an invitation from a fellow mathematician for a party. The invitation is quite clear: where I need to be at what time is clearly said in the invitation, but at the bottom of the ...
134
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8answers
35k views

How can 64 = 65?

Here is a interesting picture with two arrangements of four shapes. How can they make a different area with the same shapes?
7
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1answer
248 views

Picture-Puzzle. Find the number!

Make sense out of this picture below and find the two-digit number! Note: Pay attention to everything except the rounded rectangles
10
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3answers
464 views

Ten squares inside a rectangle

You are given 10 squares with side length of 1 to 10 units each. You want to put them in a rectangle such that there is no overlapping and no piece of a square is outside the rectange. The sides of ...
26
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1answer
543 views

You find a piece of paper in your bag

In your bag you find a piece of paper with a size of 5 x 5. You want to make it a 6 x 4 but you may only make 1 continuous cut and reposition the pieces. You are not allowed to bend or twist the ...
2
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1answer
105 views

Icosahedron-Wrapping Monstrosity

The following monstrosity of a shape: ... can be wrapped onto the surface of an icosahedron in a way that completely covers the entire icosahedron with no gaps and no overlaps. How can it be done?
12
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1answer
316 views

Tri-bladed Boomerang vs. Octahedron!

The following tri-bladed boomerang shape: ... can be folded onto the surface of an octahedron in a way that perfectly covers the entire octahedron with no gaps and no overlaps. How can it be done?
10
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2answers
192 views

Mark Two Points Which Have a Distance of $\sqrt{3.6}$

Here is a grid graph with $7$ horizontal and $7$ vertical lines which are $1$ unit apart. It is trivial to mark two points which have a distance of $\sqrt{36}$. Drawing at most two extra lines as ...
25
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1answer
2k views

A Slightly Moth-Eaten Integral Sign

The following slightly moth-eaten integral sign: ... can be folded onto the surface of a cube in a way that perfectly covers the entire cube with no gaps and no overlaps. How can it be done? (You ...
9
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5answers
6k views

How to make 4 triangles out of 4 lines

Use any drawing software like Paint or the like to draw 4 triangles using only 4 straight lines! Also, the borders of your drawing don't count ;)
4
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3answers
319 views

Two shapes that cover a 4x4 grid with any 1x2 missing

Can you find two geometrical shapes with the following property: If you remove any 1x2 rectangle from a 4x4 grid, then the remaining area can be exactly covered with the two shapes. What do these two ...
10
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2answers
810 views

Twelve Labours - #04 Erymanthian Bar

This puzzle is part of the ‘Twelve Labours’ series. Previous instalments can be found here: Prologue | 01 | 02 | 03 Now one crate lighter, Hercules made his way back up the road to the Erymanthian ...
6
votes
0answers
257 views

Looking for a kid's puzzle, cannot remember title

I'm looking for a kids' logical puzzle I saw in a Brazilian puzzle magazine several years ago. A farmer had a square farm with four houses and twelve trees and he wanted to divide it between his four ...
16
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4answers
974 views

My Mother's Dish Collection

From every trip she makes, my mother brings as a souvenir a well-decorated dish to hang in a wall. She now has a collection of 12 dishes, all disks, of radii 1, 2, 3, ..., 12 inches respectively. ...
6
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3answers
850 views

Cover 63 squares of a chess board, differently

In this other puzzle, ThomasL asks for three similar pieces which can be arranged to exactly cover all of an 8x8 chessboard, except for a single square — for any of the 64 possible single squares. I ...
17
votes
5answers
1k views

Universal dissection

Alice has a squared paper 8 by 8. She cuts out one 1x1 square from it, at row N, column M. Bob cuts the rest of the paper into pieces. Once he is done, Alice asks Bob to put the pieces together in a ...
43
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3answers
5k views

Cover 63 squares of a chess board

Can you find 3 similar geometrical figures (common shape but can be different sizes) A, B and C with the following property: If you remove any square from a 8x8 chess board, then the remaining area ...
5
votes
1answer
231 views

Brute-force solver for Gear Octahedron - flawed method?

I am working on a program to brute-force a LanLan Gear Octahedron I bought second-hand (and scrambled). I have no background in "cubing" and just fancied solving the problem. The structure comprises ...
14
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1answer
331 views

Wrapping a Galaxy Around a Cube

The following galaxy-like shape: can be folded onto the surface of a cube in a way that perfectly covers the entire cube with no gaps and no overlaps. How can it be done?

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