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.
707
questions
12
votes
2answers
1k 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
votes
2answers
137 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
votes
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
votes
1answer
221 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
votes
1answer
532 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
votes
3answers
397 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
votes
1answer
91 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
votes
1answer
305 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
votes
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
votes
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
votes
3answers
298 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
votes
3answers
839 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
votes
0answers
247 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
votes
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
votes
1answer
316 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
votes
1answer
617 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
votes
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
votes
4answers
806 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.
...
-2
votes
1answer
233 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
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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. ...
-1
votes
1answer
200 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
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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
votes
2answers
799 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 ...
0
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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
votes
3answers
376 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
votes
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?
8
votes
1answer
814 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....
4
votes
2answers
96 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 ...
