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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11
votes
1answer
645 views

Ernie and the Superconducting Boxes

I was in anticipation all last week. Ernie, who had been travelling for several months, was finally coming home. So over the weekend I dropped in on him. He was bursting with news. "Some wonderful ...
17
votes
5answers
3k views

Help me, I hate squares!

There is $5$x$5$ equidistance matrix dot given as below; You need to remove dots from the figure where it will be impossible to form a square by drawing lines between dots at the end. So what is ...
11
votes
1answer
235 views

You could help me, couldn't you?

Introduction I am an enthusiastic geometry student, preparing for my first quiz. Yet while revising I accidentally spilt my coffee onto my notes. Can you rescue me and draw me a diagram so that I ...
8
votes
2answers
950 views

3D? No-no! 3 Sides

Introducing the Isometric Nonogram! α) "Boar"ing Definition [oink] Column: Blue Part + Green Cell Row: Yellow Part + Green Cell Adjacent/ Continuous cells: Purple Cell + any of the Orange ...
3
votes
2answers
214 views

Coin around shapes: A Geometric paradox?

Here is a circular coin with diameter D Figure A From its starting position the small coin goes completely around a bigger circular body of diameter 4D without slipping, always in contact ...
15
votes
1answer
1k views

Cover a cube with four-legged walky-squares!

This is a four-legged walky-square: This 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 ...
54
votes
2answers
6k views

Can you perfectly wrap a cube with this blocky shape?

The following blocky 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 it be done?
5
votes
0answers
153 views

Unfold a right angle pyramid into a square

This puzzle refers to a feature of right angle pyramid: The relation between the areas of the three perpendicular faces and the diagonal surface area is given as - $S^2_x+S^2_y+S^2_z = S^2_d$ ...
4
votes
1answer
111 views

The ultimate conversion of a square into right angle pyramid

This is a follow up of other puzzles. Here a general case of which the other cases are a subset. Given a square of any size, cut it into four pieces to be reassembled into a right angle pyramid (the ...
7
votes
2answers
262 views

A pyramid from a square

Given a square piece of paper. Cut it into 4 pieces that could be used to create a right angle pyramid - the 4 pieces are the faces of the pyramid.
4
votes
0answers
104 views

Run to a point in a triangle in shortest time [closed]

This is a generalization of a puzzle that dealt with an equilateral triangle. Assume three runners with the following speeds - 4.5, 6.2, and 8.7 meters/sec. They are at the corners of a triangle with ...
5
votes
3answers
466 views

Five 5-cent coins touching each other

Is it possible to position five 5-cent coins so that each coin touches the other four coins?
22
votes
1answer
579 views

How can this fractal shape perfectly cover a certain platonic solid?

The following fractal shape has a surprising property: This two-dimensional shape can be folded onto the surface of a regular polyhedron (one of the five platonic solids) in a way that perfectly ...
7
votes
1answer
458 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 ...
15
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 ...
100
votes
1answer
7k 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?
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 ...
6
votes
1answer
225 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 ...
3
votes
2answers
221 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/...
6
votes
5answers
356 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 ...
0
votes
3answers
177 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 ...
8
votes
3answers
341 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 ...
8
votes
1answer
122 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
339 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 ...
2
votes
1answer
102 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)?
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
2answers
206 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 ...
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
85 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
597 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 ...
5
votes
3answers
356 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.
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 ...
2
votes
3answers
177 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
777 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 ...
11
votes
2answers
346 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)...
-1
votes
2answers
112 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
291 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 ...
6
votes
2answers
332 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 ...
5
votes
2answers
164 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 ...
0
votes
2answers
154 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. ...
11
votes
2answers
257 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
266 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.
5
votes
3answers
234 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 ...
3
votes
2answers
250 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 ...
12
votes
2answers
301 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 ...
4
votes
2answers
166 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?
6
votes
3answers
154 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
193 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 ...