# 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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### 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 ;)
132 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 ...
247 views

### Is Every Obtuse Angle A Right Angle?

The Journal of Irreproducible Results once posted an article saying that every obtuse angle is a right angle. Their argument follows below: Given the obtuse angle $x$, we make a quadrilateral $ABCD$ ...
592 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?
586 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?
398 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 ...
668 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. ...
155 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?
168 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 ...
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?
226 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?
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?
443 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. ...
104 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 ...
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 ...
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?
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 ...
660 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 ...
87 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 ...
136 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 ...
204 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 ...
57 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 ...
82 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 ...
161 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 ...
148 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?
296 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 ...
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 ...
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 ...
511 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?
776 views

### Venn diagram with 7 equal regions

Can you draw 3 overlapping circles (Venn diagram) such that all 7 of the formed regions have the same area? For the case of two circles and 3 equal regions I found this answer: https://math....
95 views

### Pentagon with sides, diagonals and area that are distinct integers

Can you find a convex pentagon (5 sides) such that all its sides, diagonals and area are distinct integers? Note that a polygon is convex if all its internal angles are smaller than 180 degrees. A ...
405 views

### Quadrilateral with sides, diagonals and area that are distinct integers

Can you find a convex quadrilateral such that all its sides, diagonals and area are distinct integers? Note that a polygon is convex if all its internal angles are smaller than 180 degrees. Good luck!...
159 views

### Area of the square

Can you find the area of the following square given the known lengths? Good luck!
2k views

### Minimum number of lines to draw 111 squares

Find the minimum number of lines to draw 111 squares. For example, you can draw a single square using 4 lines i.e 2 vertical and 2 horizontal. Similar, you can draw a 2 square in the grid using 5 ...
109 views

### How many pyramids in a cube?

Knowing that a pyramid volume is computed as 1/3 of base multiplied by the height, how many pyramids may be constructed by connecting the corners of a cube to create pyramids with volume 1/3 of the ...
372 views

### What's wrong with this D20?

Here's a D20 I produced by 3D printing and finishing. Something is wrong with it relative to the intended design. What is wrong and how did it get to be that way? Hint:
213 views

### Cut a cube into 5 objects

Cut a cube into 5 3D objects with 6 edges each. Hint:
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### Ernie and the Superconducting Boxes

I was in anticipation all last week. Ernie, who had been travelling for several months, was finally coming home. So over the weekend I dropped in on him. He was bursting with news. "Some wonderful ...
3k views

### Help me, I hate squares!

There is $5$x$5$ equidistance matrix dot given as below; You need to remove dots from the figure where it will be impossible to form a square by drawing lines between dots at the end. So what is ...
304 views

### You could help me, couldn't you?

Introduction I am an enthusiastic geometry student, preparing for my first quiz. Yet while revising I accidentally spilt my coffee onto my notes. Can you rescue me and draw me a diagram so that I ...
1k views

### 3D? No-no! 3 Sides

Introducing the Isometric Nonogram! α) "Boar"ing Definition [oink] Column: Blue Part + Green Cell Row: Yellow Part + Green Cell Adjacent/ Continuous cells: Purple Cell + any of the Orange ...
246 views

### Coin around shapes: A Geometric paradox?

Here is a circular coin with diameter D Figure A From its starting position the small coin goes completely around a bigger circular body of diameter 4D without slipping, always in contact ...
1k views

### Cover a cube with four-legged walky-squares!

This is a four-legged walky-square: This shape has an interesting property: It is possible to map multiple copies of this shape onto the surface of a cube in a way that perfectly covers the entire ...
6k views

### Can you perfectly wrap a cube with this blocky shape?

The following blocky 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?
226 views

### Unfold a right angle pyramid into a square

This puzzle refers to a feature of right angle pyramid: The relation between the areas of the three perpendicular faces and the diagonal surface area is given as - $S^2_x+S^2_y+S^2_z = S^2_d$ ...
129 views

### The ultimate conversion of a square into right angle pyramid

This is a follow up of other puzzles. Here a general case of which the other cases are a subset. Given a square of any size, cut it into four pieces to be reassembled into a right angle pyramid (the ...
280 views

### A pyramid from a square

Given a square piece of paper. Cut it into 4 pieces that could be used to create a right angle pyramid - the 4 pieces are the faces of the pyramid.
112 views

### Run to a point in a triangle in shortest time [closed]

This is a generalization of a puzzle that dealt with an equilateral triangle. Assume three runners with the following speeds - 4.5, 6.2, and 8.7 meters/sec. They are at the corners of a triangle with ...