# 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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### Separating the Pieces of a Rubiks Cube

I recall coming across this problem in one of my classes senior year of high school. (We only did the first part). Easy (and probably somewhere on the internet) Taking a standard 3x3x3 Rubik's ...
161 views

### Riddick and the Space Police [duplicate]

The next problem may be way too easy, but will post it anyway. Riddick, trying to escape from the space police, lands on a deserted planet. How many cops should the space police send to the ...
4k views

### How Can I Safely Double The Length of A Ladder?

I'm posting this from the roof of a building because I can't figure out a safe way down. I've scoured the roof for anything useful, and all I found was a coping saw. I also found a 100 foot ladder, ...
853 views

### Ernie and the Bubbles of Lucretia

"So, what do you know about milking spiders?", asked Ernie as he passed a fresh cup of coffee to me. Good grief!, I thought and gave an involuntary shudder as I glanced at the milk jug sitting ...
773 views

There is a square with a side length of 1. Inside this square there is a quadrilateral. Each vertex of the quadrilateral is on a side of the square. The area of the quadrilateral is bigger than half (...
766 views

### Optimal Rope Burning [closed]

You are given a single long rope of length L (ft) with radius R (in), a very sharp knife, and 2 matches. Your task is to completely burn the rope in the minimum amount of time. Calculate the total ...
241 views

### Painting a large sphere

An artist duo (Artist A and Artist B) were hired to make a large blue sphere resembling the earth. They decided to make it out of three sections, two spherical caps and one middle ring with the same ...
117k views

### Five Angles in a Star

In a regular pentagram (5-pointed star), the angle in each point is 36 degrees, so the angles in all five points sum to 180 degrees: What about an irregular pentagram, such as the following? Now the ...
11k views

### The Jeweller's Dilemma

You are well known as the best jeweller in Puzzovania; your shop is always well stocked and your pockets are always bulging. One day, the local 'godfather' of Puzzovania's organised crime comes into ...
2k views

### Cut up a cheese cube into $6$ equal parts with $5$ slices

Bob has a cheese cube and wants to cut it up into exactly $6$ equal pieces for his guests. These guests are professional cheese connoisseurs who will complain if they get less than anyone else. Bob ...
744 views

### Pretzel recipe with a twist

Browsing the geometry section in the local library you come across a flimsy book, seemingly misplaced: "The Pretzel Cookbook: Five More Patterns Using The Spoke Method" What's more, it's been ...
10k views

### Turning a goat?

This is a goat made up of 5 sticks. You have to move (change position) any one stick of them such that its head turns to the right side (above the right leg). Notice currently its head is on the left ...
3k views

### How much water do you need to cross the desert?

This question is inspired by Terry Pratchett's "Small Gods," in which an army crosses a vast desert by making multiple trips and caching water along the way. 1. Provide an answer. 2. I doubt I'm the ...
6k views

### Draw 4 straight lines to create 10 equal squares in this image

You can draw up to 4 straight lines in order to create 10 equal squares in the following figure:
1k views

### The 2 million, er, 20 dollar problem

Alfred is a guy who really likes solid shapes. He also really likes to keep his money in his wallet. What makes him the happiest? Getting a boxful of shapes at the Cheap Solids Store! The store has ...
3k views

### 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 ...
851 views

### Ghost Ship Collisions

There are five ghost pirate ships drifting on an infinite ocean in the spiritual realm. Each ship moves at a constant speed and never changes direction. No two ships are traveling in parallel paths. ...
882 views

### The Origins of a Confusing Maze

Behold a maze of fuses (the black dotted lines) laid out on a grid:         The fuses can be lit, causing sparks to burn along them at a perfectly uniform rate: one segment per ...
3k views

### Connecting blue dots to red dots

Suppose $n$ red dots and $n$ blue dots are arranged in the plane so that no three dots lie on a single line. Show that you can connect each red dot to a blue dot using a line segment so that no pair ...
1k views

### Fitting rectangles into square (optimal/perfect rectangle packing)

I gave the puzzle you can see on the image below to a friend of mine for christmas last year. I thought it would be fun to dump it out in front of him so he would not know the solution. Unfortunately ...
880 views

### hunting for treasure on an infinite grid

You are hunting for treasure located at some point on an infinite square grid. You have two tools: a pointer, which points toward the treasure; and a shovel, which you can use to dig for it. Here's ...
926 views

### Surviving the Shootout

$101$ gunmen stand in a field. At high noon, everyone shoots the gunman standing closest to him. If there are several gunmen who are equally close, they shoot the tallest one of them. No two gunmen ...
987 views

### Droning On in Circles

In the spirit of wizards and circular prisons: You have been imprisoned by an evil wizard in a perfectly circular prison cell of unknown size. You're shackled to the wall, unable to move about the ...
2k views

### The Fewest Strokes Golfer

A pro golfer has the amazing ability to consistently putt distances of 3, 5, 7, and 11 feet. Strangely enough, though, those are the only distances he can putt. Currently, our golfer stands on the ...
4k views

### The vicious wizard…and you!

The vicious wizard Neville has trapped you in the middle of a magical circle of radius $10000$, and you have to find a way out. Every time you want to take a step (of length $1$) in a certain ...
2k views

### Abstract image puzzle with a rotating arrow and a circle

What is the next image? I already found the rule for the circle. Which simply goes around clockwise in the corners. So, the correct choice is either C or D. But, I do not find such a rule for the ...
4k views

### Find the next image in this abstract reasoning puzzle

I have been looking for patterns for a while now, but could not find one. I found some rules: The middle column always points the same direction. The first two in the first row are always ...
2k views

### Cube made of 2x2x1 blocks which blocks all light

An Egyptian pharaoh wants to build a monument to the Sun God, Ra. He wants this to be a solid stone cube, which is $20$ hectocubits tall, long and wide. His engineers get right to work planning this....
5k views

### Can you make 2 squares and 4 rightangled triangles using only 8 straight lines? [closed]

Can you make exactly 2 squares and exactly 4 right-angled triangles using "only 8" that is exactly 8 straight lines? I am looking for 3 different answers.
547 views

### Enlarge the Square?

There are four stones, positioned on the ground at the vertices of a square. At any time, you may pick up a stone and "hop" it over another one so that it lands an equal distance beyond the hopped ...
5k views

### How do you walk across a 10' x 10' hole using two 9' boards?

Given a 10' x 10' hole which is very deep, how do you walk across the hole using two boards that are each 9' long? You can't jump, pole vault across, nail the boards together, or go around the hole....
9k views

### Cutting a cake into 7 pieces with 3 straight cuts - NO 3D

We want to have 7 pieces by only cutting our tasty cake with three straight and vertical cuts (maybe done with a katana :D), Sorry if it's repeated, but I couldnt find it here. Very similar to ...
3k views

### Shooting a Laser Between two Mirrors

There are two large mirrors standing upright and facing each other, both 10 meters long. They are not quite parallel: if you extended them, they would intersect at a $1^\circ$ angle. The distance from ...
246 views

### Find the optimal dot configuration

Rules: You have 9 dots, labeled A through I. You choose a layout (arrangement) for the 9 dots. You must connect the 9 dots with straight lines (no curves or extra lines). The object is to ...
840 views

### The Triangle Game

Take an equilateral triangle with dots at the vertices and at the midpoints of each side: There are a total of six dots. In the triangle game, you have the numbers 1, 2, 3, 4, 5, 6. Place one number ...
833 views

### Ernie and the Underground Network

I haven't seen Ernie for a few weeks - he's been on holiday in the People's Republic of Kzijekistan (PRK). But yesterday I got an e-mail and thought I would share it with you. It reads as follows: ...
5k views

### A Surprising Circle Packing

A grocery store has a long, skinny box, with no top, that it uses to display soda. The box is two soda cans wide and 200 soda cans long. You can neatly fit 400 cans in this box, using two rows of 200, ...
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### Points in a Rectangle

I was asked this question in an interview, so I am not sure what the optimal answer is. But here it goes: Given a rectangle with length l and breadth b, I pick 4 random points inside it. What is the ...
3k views

### Holes in the Table

I was asked this question in an interview and though I was able to answer a part or few parts I'm not really sure if what I gave was the optimal answer. So here goes the puzzle: A restaurant owner ...
379 views

### Croesus' Pizzas

This scrap of paper caught my eye, partially trodden in to a mush outside Bank tube station. It appears to be part of a pizza menu (illegible areas marked with square brackets): ...
882 views

### The Square's Center

The warden of the local prison was in a good mood - after a long winter, it was finally spring. The weather was warm and the sun shined over the prison. The warden decided, as is customary in the ...
923 views

### Overlapping Gang Territories

There are $7$ gangs in (a greatly simplified version of) Los Angeles. Each of them claims half of Los Angeles as territory. Let's say a place is "hot" if a majority of gangs claim it. How small can ...
228 views

### Is there a better solution to parallel segments problem?

There is a puzzle: Find a finite set of points with the following property: 1. Points are placed in space (not on a single plane) 2. If you take any pair of points A and B there are different ...
1k views