Questions tagged [geometry]

A puzzle related to shapes, geometric objects (polygons, circles, solids, etc.) of any number of dimensions, the relative position of figures, and the properties of space. Use with [mathematics]

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6 votes
2 answers
744 views

Make a square table top with the minimal needed amount of straight cuts

inspired by : Make a square table top with six (or fewer) pieces A carpenter has three pieces of beautiful wood, measuring 12 inches, 15 inches, and 16 inches square, respectively. They want to use ...
3 votes
1 answer
290 views

Build a slanted pyramid with ten L-shaped blocks

Consider the following L-shaped 3-dimensional object made up of three unit cubes joined at their faces: Use 10 of the above L-shaped pieces to make the following shape:
10 votes
2 answers
443 views

Make a square table top with six (or fewer) pieces

A man had three pieces of beautiful wood, measuring 12 inches, 15 inches, and 16 inches square respectively. He wanted to cut these into the fewest pieces possible that would fit together and form a ...
18 votes
1 answer
1k views

The Challenge Square

Q: Can you divide this shape into 4 equal parts, and then form a square? This puzzle was published by Henry Dudeney who received the puzzle from Edward B. Escott.
6 votes
5 answers
634 views

Circles crossing every cell of an NxN grid

What is the least number of circles you need to draw, such that every cell of an NxN grid is crossed? A circle crosses a grid cell if one of the points on its circumference lies completely inside the ...
6 votes
1 answer
255 views

April Fools Origami Update

Me (Sunny Lu) and Ωmega_3301 have made a special April Fools edition of origami puzzles. The objective is to fold a shape into a rectangle with uniform thickness. The thickness will be given to you. ...
13 votes
3 answers
2k views

Circles crossing every cell of an 8x8 grid

What is the least number of circles you need to draw, such that every cell of an 8x8 grid is crossed? A circle crosses a grid cell if one of the points on its circumference lies completely inside the ...
1 vote
1 answer
162 views

Recursive rhombic dodecahedron tiling

Say you have a single rhombic dodecahedron, call it "layer p0". If you then tile identical dodecahedrons around it so that it gets completely covered, the number of dodecahedrons on the ...
2 votes
1 answer
521 views

Is it possible to fill an arbitrarily large hex grid completely given these rules? #2

Based off of this. Lets say you have two players, Red and Blue, that alternate filling an arbitrarily large hexagonal grid of tessellated hexagons with pieces of their color. Hexagons can either be ...
4 votes
1 answer
494 views

Is it possible to fill an arbitrarily large hex grid completely given these rules?

Lets say you have two players, Red and Blue, that alternate filling an arbitrarily large hexagonal grid of tessellated hexagons with pieces of their color. Hexagons can either be filled or empty. A ...
7 votes
1 answer
418 views

origami WAVE t2

Fold the shape into a rectangle such that the rectangle is 2 layers thick everywhere. The grey part is not included in the puzzle; the purple part is the puzzle. Although solutions are not required ...
-4 votes
1 answer
123 views

Logic and Geometry Problem #6

Is it possible for a deadlock to occur in Necklace? Can there be a square on which neither Red nor Blue can place a stone? If it is possible, I need to see an example of that. If a deadlock is not ...
4 votes
1 answer
246 views

ORTHOGONAL origami FISH t8

Since the last puzzle got cheesed, we're adding a new restriction (in italics) Fold the shape into a rectangle such that the rectangle is 8 layers thick everywhere. All folds must be orthogonal ...
4 votes
1 answer
159 views

origami USHAPE t3

Fold the shape into a rectangle such that the rectangle is 3 layers thick everywhere. Although solutions are not required to be applicable in real life, using an actual sheet of paper is a great ...
12 votes
1 answer
482 views

origami FISH thickness 8

Fold the shape into a rectangle such that the rectangle is 8 layers thick everywhere. A puzzle for this type of orgami puzzle game made by Ωmega_3301, similar to this question.
7 votes
2 answers
518 views

One vs many. Can white force a draw?

On an infinite chessboard there's a single white king and N black kings. The nearest black king must be K moves away from the white king. Given N, white dictates the value of (finite) K, then black ...
4 votes
3 answers
319 views

Tiling rectangles with U pentomino plus rectangles

Inspired by Polyomino Z pentomino and rectangle packing into rectangle Also in this series: Tiling rectangles with F pentomino plus rectangles Tiling rectangles with N pentomino plus rectangles ...
7 votes
1 answer
271 views

Can 42 1x2x4 cuboids be packed into a 7x7x7 cube?

Can 42 1x2x4 cuboids be packed into a 7x7x7 cube without cutting any of them? Assume that all cuboids have their axes parallel to the axes of the big cube. I tried using https://www.jaapsch.net/...
9 votes
2 answers
270 views

How do I constrain a puzzle and keep a singular solution?

I am tinkering with a puzzle framework that has the following rules: In a 6x6 grid of squares, arrange 8 strips of connected squares such that there exists exactly one strip of every length (i.e. a ...
12 votes
1 answer
920 views

Anna tries to make triangles from broken sticks

Anna and Boris play a game with a red stick, a white stick and a blue stick, each of which is 1 meter long. Anna starts by breaking the red stick into three pieces. Then Boris breaks the white stick ...
24 votes
2 answers
4k views

A pizza dilemma

You are a waiter at a restaurant. The restaurant is known for its signature dish: the Donut Pizza. The Donut Pizza is a 5-inch square pizza with a 1-inch square hole in the middle. After several ...
12 votes
1 answer
634 views

Ernie and the Chocolate Bomb

Last week when I visited Ernie he complained that his trousers had shrunk in the wash. I suggested an alternate possibility – he was putting on weight. So he decided to go on a diet and to support him,...
9 votes
2 answers
833 views

Help! I lost my marble(s)!

Tomorrow is the annual meetup for the Northwest Region Marble Lovers Association. The day's festivities will include various marble games, admiring collections of marbles, a guest speaker who will ...
13 votes
4 answers
698 views

Pleasant Cuboids

A rectangular prism (or cuboid) made up of xyz identical unit cubes (x along its width, y along its length, and z along its height). Some of those cubes are internal, while the rest are external. Such ...
12 votes
1 answer
1k views

Pentominoes On the Edge

Archived Source Introducing Pentominoes! It's the same concept as tetrominoes except they use 5 tiles instead of 4. Discounting rotations and reflections, there are 12 different free pentominoes. (If ...
10 votes
5 answers
2k views

5 points on a ball, divide the ball into 2 halves so that one half as exactly 4 points

Suppose that you take a pen and mark five points on a ball. I claim that no matter where you draw those points, I can always slice the ball into two equal halves (two equal and closed hemispheres) ...
21 votes
3 answers
2k 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 a ...
32 votes
6 answers
4k views

Dissection Puzzle - The Umbrella Stand

You own a square-shaped table. You want to drill a small hole in the center to place an umbrella stand. Unfortunately, you're a little drunk: Alas. Fortunately, not all is lost. You are sober now, ...
16 votes
4 answers
1k views

Covering a 15x15 grid with rectangles

You are given a 15x15 grid and asked to cover it with rectangles whose dimensions are a power of 2. For example you can use rectangles 8x1 and 4x4, but not 2x3. The rectangles must cover every cell of ...
8 votes
2 answers
417 views

The shady puzzle that will keep you in the dark

The image below is the horizontal cross section of a room. The bulb shows the position of the single light source. When the light is switched on, one wall (marked in brown) remains completely in ...
14 votes
7 answers
3k views

Join six cities with roads

Warmup question: Each of five cities is connected to the others by four roads. Show that it is possible for the roads to intersect only once with exactly two roads crossing over at that single ...
8 votes
3 answers
1k views

Walking in a random direction

I walk $\pi$ km in one direction followed by $\pi$ km in another direction. In expectation how far am I now from my starting location? Both directions are chosen uniformly at random between $0^{\circ}$...
3 votes
4 answers
807 views

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 1 to ...
12 votes
1 answer
817 views

27 spaces, 27 curious places

Grid 1: Grid 2: Grid 3: Find the meaning behind these images. Hint 1: Hint 2: Hint 3:
13 votes
1 answer
707 views

An engineer, a mechanic and an athlete walk into a bar

...to exchange puzzles about the thing they talked about the other day and have a drink. The engineer showed these numbers: 2, 8, 14, 2, 99 2, 4, 0, 0, 1 The ...
18 votes
4 answers
6k 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 ...
6 votes
3 answers
534 views

Find the optimal dividing line

Consider the following grid of numbers: In machine readable form: ...
12 votes
0 answers
859 views

Dissecting a figure into 2, 3, 4, and 5 parts but not 6

This figure is divided in 2, 3 and 4 equal parts of same size and shape, but it is not possible to do it in 5 equal parts of same size and shape. Is it possible to find a figure that can be divided ...
17 votes
3 answers
3k views

What is the total area of the two quarter circles?

Puzzle by Catriona Agg. The yellow circle has radius 4. What’s the total area of the two quarter circles?
13 votes
5 answers
2k views

Capture a laser beam

Design a mirror box that can capture a laser beam, so that it will keep reflecting forever. The setup looks like in the following image: The goal is to design a box in a way, that the light beam will ...
-1 votes
1 answer
163 views

icosahedral net [closed]

The net of $20$ triangles shown to the right can be folded to form a regular icosahedron. Inside each of the triangular faces, write a number from $1$ to $20$ with each number used exactly once. Any ...
3 votes
2 answers
328 views

Find maximum circular array sum [closed]

Take this 10 by 10 grid of numbers. ...
1 vote
0 answers
229 views

Covering a Square Floor with Square Rugs [closed]

You are given a finite collection of axis-aligned square rugs. (You do not choose the collection of rugs that you receive and the rugs are not necessarily all the same size.) Your objective is to move ...
3 votes
1 answer
365 views

Longest cycle on a cube

What is the length of the longest straight path on the surface of a unit cube, such that it starts and ends at the same point? The path can cross itself and must be straight on every edge and face ...
5 votes
1 answer
183 views

Find the optimal partition in this matrix

Given a particular matrix of integers, the challenge is to draw a boundary line through the cells so that the sum of the numbers on the boundary line or above is as large as possible. In this case &...
-2 votes
1 answer
183 views

Deciding whether a set of points on a 2D plane has axial symmetry [closed]

The problem to solve: Let's say we have a set of $n$ points on the 2D plane. Determine whether it has axial symmetry. My attempt so far: For n=2 the answer is trivially "yes". For n=3 ...
10 votes
3 answers
1k views

A Sierpiński Carpet ratio

This math problem popped into my head and I wanted to share it with you: We have the Sierpiński carpet, which is a fractal built like this: Draw a square. Divide it into 9 equal subsquares arranged ...
2 votes
1 answer
268 views

Nimber mnemonic combinatorial puzzle

Please see my previous question for more background. The following represents an unfolded version of PG(3,2) with 1 as the center point: Given that each number must be an end point of a line which ...
8 votes
2 answers
2k views

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

The figure below consists of 5 equal squares in the form of a Greek 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 ...
21 votes
5 answers
3k views

Mishustin's circle problem

This problem was given to high school students by the Russian prime minister Mishustin. We have a circle. We are given some point on the circle and its diameter, as shown below. We are given a ...

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