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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.

4
votes
1answer
72 views

Combine two squares into a square with the sum of the two

The red square is placed on top of a blue square The goal is to cut the red square into 4 pieces and assemble them with the blue square to create a larger square. The area of the resulting square is ...
90
votes
1answer
6k views

How can this shape perfectly cover a cube?

The following shape: can be folded onto the surface of a cube in a way that perfectly covers the entire cube with no gaps and no overlaps. How can this be done?
14
votes
1answer
1k views

Can you cover a cube with copies of this shape?

The following shape has an interesting property: It is possible to map multiple copies of this shape onto the surface of a cube in a way that perfectly covers the entire cube with no gaps and no ...
9
votes
2answers
1k views

Create a cube from identical 3D objects

The diagram is the outline of the surface of a 3D object. Several objects, like the one created from this given surface, may be used to create a cube. Let me know if you need more clarifications to ...
5
votes
5answers
334 views

Shortest time to meet

Three runners are located at the corners of an equilateral triangle, 100 meter a side. They run to a point inside the triangle and their goal is to do it as fast as possible. If they run at the same ...
6
votes
1answer
153 views

Polygon Construction for Specified Number of Interior and Boundary Lattice Points

Construct a simple polygon on a grid of equal-distanced points such that: all the polygon's vertices are grid points, there are exactly $i~(\geq 0)$ lattice points in the interior, and ...
2
votes
1answer
109 views

Shapes with 1/4 area of a quadrilatral

Given nine points connected as described by the black lines. G the middle of AC, I the middle of ED, and H middle of BF. By adding segments connecting points in the drawing, create shapes with area 1/...
17
votes
1answer
755 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 ...
8
votes
3answers
329 views

Four-in-a-line Puzzle

Disclaimer: This is an open-problem, I don't have a complete solution for this puzzle yet. We are playing a $2$-player game: you as a challenger and me as a judge. Initially, there is an empty ...
0
votes
3answers
172 views

Bisect the given shape

Given the shape below, the challenge is to bisect it by placing the two segments on the shape. All segments are length 6. The resulting two shapes need to have the same area but does not need to be ...
2
votes
2answers
197 views

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 ...
6
votes
1answer
607 views

Why are these shapes impossible to draw with the given rules?

The image above shows a group of shapes, all with lines leading to their center point. These shapes cannot be drawn with the following rules: You may not trace over over an already existing line. You ...
8
votes
1answer
115 views

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 ...
13
votes
6answers
318 views

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 ...
9
votes
3answers
1k views

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.
2
votes
1answer
96 views

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)?
13
votes
5answers
2k views

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 ...
2
votes
0answers
84 views

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, ...
12
votes
1answer
592 views

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 ...
3
votes
3answers
456 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 ...
5
votes
3answers
309 views

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.
15
votes
2answers
575 views

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 ...
3
votes
1answer
1k 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 ...
9
votes
3answers
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 ...
11
votes
2answers
337 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)...
2
votes
3answers
173 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,...
8
votes
4answers
768 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 ...
28
votes
3answers
3k views

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 ...
-1
votes
2answers
107 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?
25
votes
4answers
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 ...
6
votes
1answer
271 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 ...
24
votes
2answers
2k views

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. (...
11
votes
2answers
250 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 ...
4
votes
3answers
261 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.
48
votes
2answers
5k views

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 ...
6
votes
2answers
330 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 ...
3
votes
2answers
248 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 ...
5
votes
2answers
161 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 ...
11
votes
1answer
564 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 ...
13
votes
1answer
314 views

A small team doing their job

Find the unique solution to $$ 5\,ninja + retook + quarter + turn = \_\,\_\,\_\,\_ + \_\,\_\,\_\,\_\,\_\,\_\,\_\,\_\,\_\,\_ $$ where each unknown is a different _ _ _&#...
0
votes
2answers
152 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. ...
5
votes
3answers
229 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 ...
13
votes
4answers
593 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 ...
12
votes
2answers
294 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 ...
32
votes
10answers
3k views

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 ...
4
votes
2answers
163 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?
8
votes
7answers
2k views

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 ...
6
votes
3answers
151 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 ...
5
votes
3answers
189 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 ...
15
votes
4answers
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 ...