# 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.

630 questions
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### 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 ...
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### 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 ...
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### 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.
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### 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)?
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### 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 ...
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### 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 ...
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### 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, ...
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### 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 ...
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### What are the fewest weights you need to balance any weight from a triangular seesaw?

I saw this question: What's the fewest weights you need to balance any weight from 1 to 40 pounds? Suppose you want to create a set of weights so that any object with an integer weight from ...
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### 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.
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### What is the Universal Translator censoring?

Lieutenant, launch the polar probes! Launching probes, sir. Failure, sir. Probes did not land at the poles. Well!? Where are they? Unknown, sir. Somewhere off-axis. They did land on ...
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### Which of the six tiles is missing? — An IQ Test Question

Which of the six tiles below is missing? I honestly do not know the answer. I took a screenshot of this from an online IQ test a while back. If you know where it is from, please let me know, and I ...
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### 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 ...
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### 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)...
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### 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,...
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### 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 ...
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### Can you see out of the forest?

You are standing at the centre of a circular forest of radius 500 metres. The trees of this very regularly planted forest stand in a precise rectangular lattice on the plane, each 10 metres from the ...
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### 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?
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### 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 ...
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### 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 ...
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### The tilted labyrinth - Can you find the fastest path in this 3D-puzzle? (Simulator now included.)

This is a puzzle was inspired by the board game labyrinth, which I very much enjoyed as a kid. It either requires very good 3D-visualization skills in your brain or some paper & scissors work. (...
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### 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 ...
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### 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.
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### Six pyramids in a cube

This question is from the German mathematics competition Känguru der Mathematik. In this competition students have to solve 30 mathematical tasks like this in 90 minutes without calculator. Actually ...
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### 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 ...
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### 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 ...
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### 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 ...
563 views

### Blindfolded and disoriented near a space station

Following on from the recent blindfolded near the great Wall of China puzzle. Suppose you are floating in space a mile away from a huge space station (the death star perhaps). Assume that the death ...
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### A small team doing their job

Find the unique solution to $$5\,ninja + retook + quarter + turn = \_\,\_\,\_\,\_ + \_\,\_\,\_\,\_\,\_\,\_\,\_\,\_\,\_\,\_$$ where each unknown is a different _ _ _&#...
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### 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. ...
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### 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 ...
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### 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 ...
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 ...
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### Variant of lion and 100 zebras

Note: This problem remains unsolved, as of 4 Feb 2018, so do try it out This a variation of this question by @Gamow Suppose there are $100$ lions and $100$ zebras. The lions function together as a ...
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### 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?
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### Two Blindfolded and disoriented near the Great Wall of China

Following on from the recent blindfolded near the great Wall of China puzzle. This time, two wise guys are blindfolded and disoriented and standing together exactly 1 mile from the Great Wall of ...
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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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,...
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### 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 (...
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### A clock where the hour and minute hands are the same length

Your buddy Frankie sold you a shoddy clock: it keeps good time, but the minute and hour hands look exactly the same! Both of these hands move continuously, and there is no second hand. How many times ...