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.
677
questions
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
431 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
99 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 ...
9
votes
2answers
615 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
85 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
128 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
188 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
51 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
78 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
158 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
147 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
284 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
507 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
765 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
91 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 ...
7
votes
2answers
401 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!...
4
votes
1answer
156 views
Area of the square
Can you find the area of the following square given the known lengths?
Good luck!
7
votes
5answers
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 ...
0
votes
2answers
105 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 ...
5
votes
4answers
369 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:
1
vote
1answer
208 views
12
votes
1answer
699 views
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 ...
17
votes
5answers
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 ...
11
votes
1answer
302 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 ...
8
votes
2answers
992 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 ...
3
votes
2answers
240 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 ...
16
votes
1answer
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 ...
56
votes
2answers
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?
7
votes
1answer
219 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 - $S^2_x+S^2_y+S^2_z = S^2_d$
...
4
votes
1answer
123 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 ...
7
votes
2answers
274 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.
4
votes
0answers
110 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 ...
6
votes
3answers
508 views
Five 5-cent coins touching each other
Is it possible to position five 5-cent coins so that each coin touches the other four coins?
23
votes
1answer
607 views
How can this fractal shape perfectly cover a certain platonic solid?
The following fractal shape has a surprising property:
This two-dimensional shape can be folded onto the surface of a regular polyhedron (one of the five platonic solids) in a way that perfectly ...
8
votes
1answer
497 views
Combine two squares into a square with the sum of the two
The red square is placed on top of a blue square
The goal is to cut the red square into 4 pieces and assemble them with the blue square to create a larger square.
The area of the resulting square is ...
17
votes
1answer
1k views
Can you cover a cube with copies of this shape?
The following 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 cube with no gaps and no ...
110
votes
1answer
7k views
How can this shape perfectly cover a cube?
The following 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 this be done?
9
votes
2answers
1k views
Create a cube from identical 3D objects
The diagram is the outline of the surface of a 3D object. Several objects, like the one created from this given surface, may be used to create a cube.
Let me know if you need more clarifications to ...
6
votes
1answer
350 views
Polygon Construction for Specified Number of Interior and Boundary Lattice Points
Construct a simple polygon on a grid of equal-distanced points such that:
all the polygon's vertices are grid points,
there are exactly $i~(\geq 0)$ lattice points in the interior, and
...
3
votes
2answers
225 views
Shapes with 1/4 area of a quadrilatral
Given nine points connected as described by the black lines. G the middle of AC, I the middle of ED, and H middle of BF.
By adding segments connecting points in the drawing, create shapes with area 1/...
6
votes
5answers
362 views
Shortest time to meet
Three runners are located at the corners of an equilateral triangle, 100 meter a side. They run to a point inside the triangle and their goal is to do it as fast as possible. If they run at the same ...
1
vote
3answers
187 views
Bisect the given shape
Given the shape below, the challenge is to bisect it by placing the two segments on the shape. All segments are length 6. The resulting two shapes need to have the same area but does not need to be ...
8
votes
3answers
356 views
Four-in-a-line Puzzle
Disclaimer: This is an open-problem, I don't have a complete solution for this puzzle yet.
We are playing a $2$-player game: you as a challenger and me as a judge. Initially, there is an empty ...
8
votes
1answer
132 views
9x9 Map Path: In and out next to each other?
This isn't something I read in a book or anything, it's more of a puzzle I thought up for myself.
However, I am unable to find a solution.
Here's my problem:
If I create a 9x9 checkerboard, and ...
13
votes
6answers
373 views
Pulling Apart a Jigsaw Puzzle
Assume you have a jigsaw puzzle that is also a tessellation. This means every piece has an identical shape and can be assembled into a 2D pattern that fills the plane with no gaps. Such a jigsaw ...
