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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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 ...
6
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2answers
141 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 ...
5
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2answers
372 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 ...
7
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1answer
223 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
26
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1answer
535 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 ...
10
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3answers
402 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 ...
2
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1answer
93 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
307 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
189 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 ...
4
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3answers
299 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 ...
6
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3answers
840 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 ...
6
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0answers
248 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 ...
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 ...
14
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1answer
318 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?
8
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1answer
620 views

One piece of a destroyed chess board

Once I met a friend and he told me the following story: I recently cut my wooden 8x8 chess board into different rectangular pieces along the edges. Each square of the chess board has a length of one ...
7
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1answer
174 views

Cube Tubes & Cube Loops

Given a three dimensional n×n×n cube containing n^3 cubes of 1×1×1, Define a cube tube to be a sequence of 1×1×1 cubes from the n×n×n cube such that: 1) No cube appears in the sequence more than ...
15
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4answers
809 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. ...
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1answer
234 views

Locations on the Earth that are all separated by the same distance

What is the maximum number of distinct locations you can select on the surface of the Earth, such that the distance between every pair of locations is the same? Assume that the Earth is a perfect ...
19
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1answer
3k views

Is it possible to divide a square into convex pentagons?

I have seen this question on reddit (r/math's chatroom - to be specific). No one has answered it yet, so I thought I would pose the same question here. The only discovery I made that is worth ...
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 ;)
5
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1answer
227 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 ...
16
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1answer
616 views

A cube build with cuboids

You are given 27 pieces of 1x2x4 cuboids. Is it possible to build a 6x6x6 cube using those 27 cuboids?
9
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1answer
606 views

A famous dodecagon

A 12-sided polygon (Dodecagon) has the property, that neighbouring sides appear 4 times in a ratio of 1:1 and 8 times in a ratio of 7:6. Where can such a Dodecagon be found?
4
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2answers
408 views

Triparting a Garden

A gardener wants to trisect his rectangular garden into three parts, with the proviso that he can neither enter on the left and leave on the right AND nor can he enter at the top and leave at the ...
13
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4answers
696 views

Sharing a Cake with 7, 8, or 9

There may be 7, 8, or 9 guests at a party. The guests will share a round cake (shaped like a cylinder). Define a cut to be any plane or half plane that intersects the cake, i.e. straight cuts only. ...
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1answer
201 views

Connect 12 dots with 7 lines

Connect 12 dots with 7 lines such way that on each line there are 4 dots. Can anyone help me solve this quiz?
4
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1answer
178 views

A Box of Puzzle Blocks

A cubical box is required to contain a set of wooden blocks (N right parallelepiped solids that fits in without spaces) which have different edges and colors. No two blocks have the same edge linear ...
15
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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
242 views

What is the 'Three Cube Problem' in the Mega Test?

The now defunct IQ Mega Test had a problem which was considered it's 'most difficult' called the Three Cube problem. Does anyone know what it is?
7
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2answers
1k views

Two congruent triangles

Each triangle has 6 basic determinants: 3 line segments and 3 angles. Is it possible to have two triangles, which have 5 of the basic determinants in common, but are not congruent?
13
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1answer
463 views

Not Quite a Pipe Dream

Goal Complete the connection between the two red pipes using any of the pipe shapes provided below, using as few pieces as possible. This puzzle can be completed by placing just four extra pieces. ...
2
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0answers
110 views

Diving a polygon into 6 equal regions [closed]

You are given a convex polygon, ie all its internal angles are less than 180 degrees. Prove that you can always draw three straight lines through a point inside this polygon, such that they divide it ...
6
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3answers
1k views

Best angle to attack

Suppose a circle (O,R) and a point A within its area having distance r from O (0<=r<=R). Which points X of the circle minimize the angle between the line AX and the tangent on X? I was ...
30
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1answer
2k views

Dissecting the exotic bulbfish

Can you cut the following black shape into exactly three pieces, and then rearrange those pieces into a square?
8
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10answers
5k views

There are polygons with only right angles which have an odd number of corners

One of the interesting myths about a certain building in our university is that it has 13 corners. One way to dismiss this claim is to point out that a polygon with right angles must have an even ...
10
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2answers
800 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 ...
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1answer
88 views

In this cylindrical tank, by how much will the level of the water rise? [closed]

there. In the following picture is a puzzling question from a primary school math exercise booklet for selective high school exams in Australia. I don't think enough information is provided to solve ...
0
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4answers
144 views

Rectangles formed from every tetromino, tromino and domino

Can you form a 4x7 rectangle from every tetromino, tromino and domino? There are 5 different tetrominoes, 2 trominoes and 1 domino. Can you find different arrangements that are not mirrors/rotations ...
3
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2answers
208 views

10x10 divided into the most number of rectangles of different area

How can a 10x10 be divided into rectangles such that there are as many as possible and they all have different area? Can you find multiple solutions that are not mirror/rotation of each other? Good ...
0
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1answer
62 views

7x13 rectangle divided into 13 different rectangles

Can you divide a 7x13 rectangle into 13 rectangles all of different area? Can you find multiple solutions? Note that rotations and mirrors don't count as separate solutions. Here is a similar puzzle ...
0
votes
3answers
88 views

4x7 rectangle divided into 7 different rectangles

Can you divide a 4x7 rectangle into 7 rectangles all of different area? Can you find multiple solutions? Good luck! P.S. @Deusovi wanted me to make puzzles that have an "aha moment", so here is my ...
4
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1answer
166 views

Find the least expense?

You want to build a shop between three roads in the shape of an equilateral triangle. What would be the best location for the shop so that you can reach each road with the minimum transportation ...
0
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2answers
155 views

Bake and share Fair and square

The chef ask each of the 4 judges to make a single slice on the whole round cake, so they'll all have a 1/5th piece to take. How the judges do it for fairness sake?
6
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3answers
380 views

Line segments inside a square

A set of line segments inside or at the edge of a square with side length 1 should be positioned in such a way, that any straight line going through the square must touch or intersect at least one of ...
26
votes
6answers
8k views

Cut a cake into 3 equal portions with only a knife

You have to determine a way to cut a circular cake into exactly three portions of equal size. The only marking on the cake is a candle in the very center. All you have to work with is a knife that is ...
10
votes
4answers
2k views

Haselbauer-Dickheiser Test no. 3: Circle divided by lines between a blue dots

This is the test no. 3 from Haselbauer-Dickheiser Test. 3. These three circles below all have blue dots on their circumference which are connected by straight lines. These lines divide the ...
8
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1answer
518 views

Three lines through a square

Is it possible to draw 3 straight lines through a square such that they divide it into 7 equal-sized regions?

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