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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8
votes
3answers
545 views

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 ...
4
votes
1answer
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 ...
18
votes
6answers
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, ...
12
votes
1answer
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 ...
1
vote
2answers
773 views

Quadrilateral inside a square

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 (...
2
votes
8answers
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 ...
3
votes
1answer
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 ...
21
votes
10answers
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 ...
60
votes
5answers
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 ...
7
votes
5answers
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 ...
8
votes
1answer
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 ...
50
votes
11answers
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 ...
22
votes
7answers
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 ...
32
votes
3answers
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:
18
votes
4answers
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 ...
16
votes
3answers
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 ...
8
votes
2answers
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. ...
16
votes
1answer
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 ...
10
votes
2answers
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 ...
4
votes
3answers
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 ...
10
votes
2answers
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 ...
9
votes
8answers
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 ...
13
votes
6answers
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 ...
7
votes
5answers
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 ...
47
votes
3answers
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 ...
2
votes
4answers
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 ...
4
votes
5answers
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 ...
18
votes
3answers
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....
-1
votes
2answers
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.
12
votes
1answer
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 ...
17
votes
4answers
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....
3
votes
2answers
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 ...
20
votes
1answer
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 ...
1
vote
1answer
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 ...
7
votes
1answer
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 ...
9
votes
1answer
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: ...
36
votes
7answers
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, ...
17
votes
6answers
2k views

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 ...
15
votes
8answers
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 ...
12
votes
1answer
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): ...
16
votes
2answers
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 ...
8
votes
2answers
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 ...
2
votes
2answers
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 ...
10
votes
3answers
1k views

Do a barrel roll! (i.e. a Euclidean plane rotation puzzle)

One of my favorite Putnam problems due to a slick solution. $R$ is at $(3, 4)$ on the cartesian plane. To try to confuse $R$, the devious $S$ decides to rotate $R$ about the point $(1, 0)$ by $36^\...
-2
votes
6answers
1k views

Minimum number of steps required to cut this bar

What is the minimum number of steps required to cut this chocolate bar which is a single piece into at least 30 single pieces? 1)Image for chocolate bar 2)Image for single piece ...
2
votes
1answer
284 views

Skylark of Valeron [closed]

In E.E. 'Doc' Smith's classic Skylark of Valeron, Dick Seaton and party are beset in space by disembodied intelligences. These intelligences working as they do on the 6th order of forces are able to ...
7
votes
6answers
2k views

Partition a cube into 6 congruent tetrahedra

A tetrahedron is a solid shape with four triangular faces, not necessarily regular or identical. Show how to partition a solid cube into 6 tetrahedra that are congruent, meaning identical up to ...
11
votes
1answer
577 views

Ants on a Hula Hoop

There are $24$ ants scattered around a hula hoop of circumference $3$ meters . They each randomly, and independently, choose to face clockwise or counterclockwise, and then simultaneously start ...
-3
votes
2answers
136 views

Points following an axiom [closed]

Your aim: Mark any finite number of points on a plane. It should meet this axiom. Axiom: Original way of stating it: If a line (infinite) is drawn passing through exactly n (n>0) points, any line ...
12
votes
4answers
829 views

Pursuit Problem II: Surrounded in Marauders' Circular Cove

(This is the sequel to this puzzle. It has a similar setup, but believe me, the solution is very different. Be careful! The answer is counterintuitive. It shocked me at first.) You are a pirate. ...