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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.

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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.
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 ...
182 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,...
782 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 ...
357 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)...
116 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?
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 ...
321 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 ...
334 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 ...
166 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 ...
157 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. ...
262 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 ...
268 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.
241 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 ...
258 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 ...
308 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 ...
169 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?
162 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 ...
264 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 ...
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 ...
785 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 ...
674 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 ...
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 ...
255 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. ...
128 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,...
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 (...
608 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 ...
1k views

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 ...
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 ...
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, ...
583 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 ...
83 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.
139 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: ...
375 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 ...
442 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 ...
259 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 ...
114 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 ...
226 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 ...
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), ...
141 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 ...
688 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 ...
397 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. ...
101 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 ...
823 views

### Cutting a cross made of 5 equal squares by 2 straight cut into 4 figure to together form a square

A figure consists of 5 equal squares in the form of a cross. Please show how to divide it with two straight cuts into 4 equal pieces which will fit together to form a square. A MSE told me I need to ...
438 views

### Which polygon is the one?

There is a unit-radius circle and you must form a polygon all of whose vertices are located on the circle, such as below: What is the biggest possible value of the sum of squares of side lengths of ...
314 views

### A small team doing their job

Find the unique solution to $$5\,ninja + retook + quarter + turn = \_\,\_\,\_\,\_ + \_\,\_\,\_\,\_\,\_\,\_\,\_\,\_\,\_\,\_$$ where each unknown is a different _ _ _&#...
2k views

### Matchstick Puzzles

Puzzle #1: There is a matchstick: | Add 2 more matchsticks to make the number, 11. Puzzle #2: There is a palace made out of 11 matchsticks: Move 2 matchsticks to make 11 squares. Puzzle #3: ...
2k views

### 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 ...
There is a regular tetrahedron with edge ledge of $2$ units. Your task is to put as many points within the volume occupied by the tetrahedron. But there is a condition: there has to be at least $1$ ...