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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.

8
votes
3answers
115 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
83 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.
0
votes
0answers
56 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
79 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
588 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
297 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
171 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
765 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
325 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
106 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
2k 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
260 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
323 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
159 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
149 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
247 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
258 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
225 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
247 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
292 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
162 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
149 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
187 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 ...
15
votes
0answers
646 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
643 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
224 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
122 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,...
14
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
592 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 ...
15
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
461 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
78 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: ...
14
votes
1answer
330 views

Hidden numbers (hand drawn)

I like doodling and had an idea based on a flash game, where numbers are hidden in a picture, and it's ended up better than i expected. So have fun with it. And if you can give feedback on it that ...
6
votes
1answer
439 views

Where are the extra coins?

I am a manager of a coin casting foundry. We produce perfectly round coins with some (fixed) thickness and a diameter of exactly 1 inch. The working room is well-secured such that if any coin tries to ...
4
votes
2answers
204 views

Traverse a 3 × 3 × 3 cube; starting from the center [duplicate]

Consider a 3 by 3 by 3 cube — in essence, a Rubix cube — like the one pictured in the following image: Start from the cube in the middle, enclosed on all sides. Moving to only cubes that are directly ...
1
vote
3answers
110 views

Determining The Piangle

The Piangle is a unique triangle. Every circle has its unique Piangle. To create a Piangle, you cut a circle along its bottom radius, then you unroll the left side of the circle up and over to the ...
8
votes
2answers
191 views

What is the largest number of cubes that can be cut?

Consider a cube made up of 27 unit cubes. If you consider a plane going through the middle of the larger cube it cuts through a number of the unit cubes. The number of cubes that are cut depends on ...
14
votes
5answers
1k views

When did I make this puzzle?

I was flipping through some of my old puzzling notebooks, and I found an old puzzle of mine I don't quite remember. I tried to find when I made it (I put the date I made all of my puzzles on them), ...
5
votes
1answer
131 views

Horror Episode #1: Shapely Shedding Light

I shined my flashlight on a wall in terror. It was 2 in the morning at my place and I thought I heard a voice in my head. At first when I saw what was in my light, I jumped back because it looked ...
10
votes
4answers
564 views

Mirrored clocks

Triangulating for the simplest puzzle that is still at least somewhat interesting to solve.. On the left side wall in this picture, we have two particular clocks: 1: an analog clock with identical ...
9
votes
3answers
339 views

Special triangles in convex polygons

Given identical 30-60-90 triangles, what is the convex polygon with the highest number of sides that I can build from them? This seems a very easy task by first look, but I’m totally stuck right now. ...
1
vote
0answers
96 views

Golden Ratio plus 1 [closed]

There was an interesting puzzle by Presh Talwalker in 'MindYourDecisions' about finding the radius of a circle that was cotangent to two larger circles. https://www.youtube.com/watch?v=i0dZukEw1JY I ...