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.
7
votes
1answer
446 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 ...
14
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 ...
92
votes
1answer
6k 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
157 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
...
2
votes
1answer
112 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
345 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 ...
0
votes
3answers
173 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
332 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
119 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
318 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 ...
2
votes
1answer
96 views
Two rectangles for the price of one
Can you re-arrange these rectangles to form another rectangle, but with different dimensions (dimensions commute in this case)?
9
votes
3answers
1k views
Find the area of the rectangle
The image below shows a half circle, and a rectange DBFE. Your task is simply to calculate the area of the rectangle, based on the information given in the image.
2
votes
2answers
198 views
The Tiled Labyrinth Returns
This is a variant on The Tiled Labyrinth.
The rules are the same, except that the goal has changed.
You will probably want to use this script which was created for the initial puzzle but applies ...
13
votes
5answers
2k views
Find the unknown area, x
The image below shows one large rectangle, with smaller rectangles inside it. Your task is simply to calculate the area of the red rectangle, marked with an x.
Note that I have deliberately made the ...
2
votes
0answers
84 views
Flea on infinite chessboard jumping with irrational vector eventually changes square color [closed]
Question from Engel's Problem Solving Strategies: An infinite chessboard consists of $1 \times 1$ squares. A flea starts on a white square and makes jumps by $\alpha$ to the right and $\beta$ upwards, ...
12
votes
1answer
592 views
Reflections in a Square
An ideal billiards table (no friction, ideal reflections off of the walls, no pockets) is shaped like a square. From the bottom-left corner, shoot a point-sized cue ball at some angle.
What is the ...
5
votes
3answers
316 views
Can't figure this one out.. What is the missing box?
I've been stuck on this for ages, and can't figure this out.
What is the missing box, and the logic behind the answer?
This was taken from a Korn Ferry Leadership Assessment practice trial.
9
votes
3answers
2k views
That's an odd coin - I wonder why [closed]
Around the world, there are several roughly polygonal coins. Here's an example:
One thing you'll notice is that they all have an odd number of sides. It turns out that this is universally true for ...
2
votes
3answers
173 views
Make the largest box from a cardboard sheet Chapter #2
Please see:
Make the largest box from a cardboard sheet
Thanks to his older brother's friends: @Oray, @Weather Vane and @mlk, the boy managed to make as large cardboard box as possible. Unfortunately,...
8
votes
4answers
768 views
Make the largest box from a cardboard sheet
A boy in order to tidy his room asks his parents for a cardboard box to store lots of small toys. Unfortunately they didn't find any but only a raw cardboard sheet of dimensions ...
11
votes
2answers
338 views
Geometry From Hell
You’re locked in a room with nothing but a pencil, a math compass, and paper. You do not have a straightedge. Your captors have informed you that you cannot leave until you construct (the endpoints of)...
-1
votes
2answers
107 views
Can this be drawn in one line without going over the line?
Can this image be drawn in one line and without going over any lines?
25
votes
4answers
3k views
What is the most triangles you can make from a capital “H” and 3 straight lines?
So start with an upper case H, and then draw $3$ straight lines. What is the greatest number of closed triangles that you can form? For example:
Note that triangles inside of triangles only count ...
6
votes
1answer
277 views
Geometry haberdasher problem - square to equilateral triangle variation
Let me remind the haberdasher's problem, proposed in 1907 by the puzzle composer Henry Dudeney. Dissect an equilateral triangle to a square, with only three cuts.
I would like to propose the ...
6
votes
2answers
330 views
Find the Rogue with AOE
You are playing World of Warcraft which is well known an old MMORPG game. You are in arena where you play against another player. You are a mage and the opponent is a rogue which can hide while moving ...
5
votes
2answers
161 views
What's the perimeter of this poorly specified triangle? [duplicate]
Generalizing a puzzle from Mind Your Decisions, here's something that I found to be rather neat.
Suppose that AB$=c$, AC$=b$, and BC$=a$. What's the perimeter of $\triangle$CDE?
Clue: The coveted ...
0
votes
2answers
152 views
Finding a line on a plane
Imagine you are on an (in)finite 2d-plane (and confined to walk on it). There's a straight line somewhere on the plane, but you don't know where it is and neither can you find it by looking from afar. ...
11
votes
2answers
252 views
Pentomino solution maximizing straight lines length in rectangle - wood cutter problem
Recently in my free time I cut from wood with my scroll saw two pentomino sets. One set made from 10x6 pattern, and then the other set 20x3 pattern. Think of wood cutter difficulties. I would like to ...
4
votes
3answers
261 views
What is the maximum total possible number of rectangles in the picture?
Your objective for this puzzle is to find the maximum total number of rectangles in the pictured four overlapping squares. I believe it may be more than 36.
5
votes
3answers
229 views
Four squares into many squares
You are given four unit squares and your task is to form as many rectangles as possible out of it starting from 1 square (by overlapping every squares into each other) to N, one by one (2,3,4...). So ...
3
votes
2answers
248 views
Enumerate the ways of putting six armies of queens on a humongous chessboard
This is a sort of a sub-problem of the open puzzle Peaceful Encampments, for high numbers of armies.
Consider a chessboard with an astronomically large number of vanishingly small squares, on which ...
12
votes
2answers
295 views
Pucks in the arena
Two identical pucks of radius 10 cm are placed in a round arena of radius 1 m. They are positioned 50 cm away from the center of the arena on opposing sides. Assuming no energy losses during sliding ...
4
votes
2answers
164 views
Proving the count of symmetric configurations of pentagon
In a 3 × 3 dot grid, there are 5 configurations of symmetric pentagons. I am confused about how to prove that it is really just 5. Can anyone enlighten me?
6
votes
3answers
152 views
Discrete Peaceful Encampments: Player 4 has entered the game!
Here's a variation of Discrete Peaceful Encampments: Player 3 has entered the game! (which itself is a variation of Peaceful Encampments).
You have 3 white queens, 3 black queens, 3 red queens, and ...
5
votes
3answers
190 views
Discrete Peaceful Encampments: Player 3 has entered the game!
Here's a variation of Discrete Peaceful Encampments: 9 queens on a chessboard (which itself is a variation of Peaceful Encampments).
You have 4 white queens, 4 black queens, and 4 red queens. Place ...
15
votes
4answers
1k views
Discrete Peaceful Encampments: 9 queens on a chessboard
Here's a discrete variation of yesterday's puzzle Peaceful Encampments.
You have 8 white queens and 8 black queens. Place all these pieces onto a normal 8x8 chessboard in such a way that no white ...
17
votes
1answer
756 views
Peaceful Encampments
This math puzzle is due to Donald Knuth (as far as I know; maybe he got it from someone else) circa 2014.
Consider a plain represented by the unit square. On this plain we want to “peacefully ...
12
votes
4answers
652 views
Ray reflection inside the cube
Here's a seemingly interesting puzzle that i currently can't solve. Any ideas are highly appreciated. I was told that it's a middle school level problem but it's definitely not the simple one. At ...
13
votes
3answers
1k views
Spider and fly on a cube
A spider and a fly play a game with a cube of side length $s=1$ and with a positive real number $d$.
First, the spider picks its starting point $S$ somewhere on the surface of the cube.
Then the fly ...
5
votes
3answers
238 views
Fill $N$ by $M$ grid with numbers in such a way that any given cells' neighbors are different
Create an $N$ by $M$ grid with numbers in such a way that satisfies following conditions:
numbers should be integers that range from $1$ to $r$.
for any cell $C$, all its adjacent neighbors (i.e. ...
4
votes
1answer
123 views
What's the most triangles you can make with 4, 5 or 6 straight lines?
All the triangles can stick together. The triangles counted is the independent triangles, triangles made up of two shapes, a triangle made up from 3 shapes, or the outline of the shape consisting of 4,...
15
votes
7answers
3k views
The Lazy Laser Physicist
You have a setup like in the image above. But it seems like detector A does some weird things. You should better check it with detector B. What is the minimum number of mirrors you have to move (...
13
votes
4answers
595 views
Color the cubes, then assemble them to form a larger cube
Goal: Paint 27 cubes using three colors (for example, red, yellow, and blue), so that you can form a 3x3x3 cube with all surfaces in red (for example), a 3x3x3 cube all in yellow, and a 3x3x3 cube all ...
19
votes
4answers
1k views
What's the radius?
I have a book of puzzles from 1972 with the pretentious title, "Games for the Superintelligent" by James Fixx. One puzzle had me thinking for a couple of days:
I drew it out, thought about different ...
16
votes
12answers
1k views
A man is trapped in a cage and wants to escape but doesn't, even when given the keys. Why? [closed]
Note: I have invented this puzzle myself as far as I know. I'm certainly not aware of having read it anywhere else. I have no idea whether it will be hard or easy.
A man is imprisoned in a strong ...
10
votes
4answers
2k views
Where does the emperor sit and why the earplugs?
The Emperor is annoyed that the crowd routinely chant out of step at the Empire's largest circular amphitheatre. For example, they are supposed to shout phrases in unison such as "Hail to the Emperor, ...
7
votes
5answers
488 views
Cutting a Slice of Cake Into Two
Driven out of a serious question, when sharing a slice of cake in a coffee shop how can my two friends split it without going down the middle (the cake is likely to crumble if you do this!)
Given a ...
0
votes
1answer
80 views
What is the area of the shaded region? (Overlapping areas) [closed]
What is the area of the region poly1 formed by the arcs 'cdke'. The square is of sides 10 units long. The region poly1 is formed by four overlapping quadrants.
4
votes
1answer
135 views
Dystopian Tax Collection
The year is 2081, and... oh, what can I say? Dystopian stories have been done to death.
I have a much more practical problem, though. I need to... gasp... pay my taxes.
I owe five different taxes: ...
