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.
652
questions
11
votes
1answer
653 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
285 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
951 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
215 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
154 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
468 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
581 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
459 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 ...
101
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
234 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
103 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
207 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
360 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
252 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
155 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
194 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 ...
