# 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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### Tiling rectangles with N 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 T pentomino plus rectangles ...
571 views

### Tiling rectangles with F pentomino plus rectangles

Inspired by Polyomino Z pentomino and rectangle packing into rectangle Also in this series: Tiling rectangles with N pentomino plus rectangles Tiling rectangles with T pentomino plus rectangles ...
553 views

### Tiling rectangles with W 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 ...
283 views

### Random chord to a circle around a triangle

This puzzle is literally a math textbook question. Its only redeeming feature is that it also happens to be too broad in a surprisingly interesting way. The problem Given the circle $\mathbf O$ ...
612 views

### For n nodes that are connected to at most m and at least 2 other nodes, what values of n and m always allow the connections to not intersect?

I am trying to develop a puzzle game where $n$ nodes are generated and placed randomly on the screen. Each node is connected to at most $m$ and at least 2 other nodes by straight lines. This is an ...
6k views

### Is there only one solution to the “Ten Penny Puzzle” or more?

Not knowing the dimensions of the square in the Ten Penny Puzzle I ask if there is more than one unique solution that isn't a reflection/mirror of the one shown in the video, if you know the ...
2k views

### Four points with only two distances

Your task is this: Find all arrangements of four distinct points in the plane such that only two distances occur between them. When you have $4$ distinct points, you can measure the distance ...
839 views

### Slashes, Dashes, and Boxes: Oh My!

These riddles are really hard until you figure out how to look at them at the right angle. Sometimes it's hard to connect the dots at first. This riddle might contain a hint to my other riddle. Or ...
2k views

### Draw a hexagon that can’t be divided into two quadrilaterals by a single straight line.

I’m kind of stumped. Logically if a hexagon has 6 sides and you split it and add one (the line) it will always result in two quadrilaterals. I may be off.
232 views

### Two puzzles about encompassing convex sets

Prove that any convex set of area $1$ is contained in a rectangle of area $2$. Prove that any convex set of area $1$ is contained in a triangle of area $4$. Notes: (1) is from "The Art of ...
458 views

### How many possible different shapes are there on a 4x4 dot grid?

Alright. This math required to do this is way beyond me, so please be patient. I edited this a lot to make the question more solvable and easier to understand, without making the answer less useful ...
98 views

### Ways to cut and reassemble a solid object [closed]

I have been puzzling over this for a few years and still have no answer. How many ways can a solid object like a cube or a ball be cut into pieces such that it is possible to take apart and put ...
3k views

### What is the shape of the object?

There is a 3D object, so that when you look at it from 3 different angles, you can see the shape of a triangle, rectangle, or circle. What does it look like in 3D?
250 views

### Make lots of squares with only 6 squares

You are going to draw $6$ congruent squares to make as many squares as you can! What is the maximum amount of squares (except the original squares) you can create by drawing 6 congruent squares? ...
3k views

### What's the perimeter of the hexagon?

Consider a hexagon which is equiangular but not equilateral: all angles equal to 120 degrees but four consecutive sides of length $a,b,c,d$ not necessarily equal. What is the perimeter of the hexagon? ...
284 views

### Wooden Snake Puzzle - logic behind solution

I refer to the wooden snake puzzle in this post: Wooden Snake Puzzle I notice that there are 6 solutions to the 4x4x4 snake, which start respectively as follows: FRB… (↗→↙…, which is also the ...
163 views

### Ugh! The extra SQUARE! [duplicate]

Can you split this figure into two congruent pieces with a line? The line need not be straight. :D
151 views

### Finding the equation among shapes

There is a relation between the shapes in the top equation on the left side. If we apply such an equation to the bottom shapes, which one from the right choices can fill the question mark? Source: ...
134 views

### Combining parts to make an square

In the following picture, if one puts some of the shapes A, B, C, D, and E together, they can make a square. Then which shapes would be redundant? Only A Only D Only E A and D Can you construct the ...
1k views

### Putting the pips on a d6

Using a blank cube and a bunch of circular stickers, an average person constructs a d6. A d6 is also known as a six-sided die, or sometimes, a dice. For the purpose of this puzzle, the average person ...
5k views

### Odd-looking circle

A man is told to make a circle He makes this: Where is the man?
497 views

### Laser Beams in Helsinki Skies

(The first two chapters are just for flavour, you can safely skip to the TL;DR near the end.) This puzzle in situated Helsinki for a reason: for the city's "200 years as capital" celebration, the ...
328 views

### Minimal-length curve guaranteed to intersect all secants of circle [duplicate]

Consider a unit circle C. The goal is to find a curve L such that: all secant lines of C intersect L; the length of L is minimal among those with property 1 above. Any closed curve containing C (for ...
2k views

### Old 6-piece wooden cross puzzle

I found this old puzzle and have no idea how to get it together. I have been trying to complete it for several hours now but to no avail. The pieces of the puzzle are as follows: Also sorry if it has ...
363 views

### Minimize the intersection area

You are given two identical pieces of paper of size $a \times \sqrt{2} a$, like the standard DIN A4 paper. Put one paper on top of the other, such that none of the corners is under or above the other ...
210 views

### 2018 January Challenge: Geometry [closed]

Considering it's the beginning of a new year, I have created the following challenge. I hope to make one every month until December 2018! Here goes: Show that $AD-AB>AC^3$. Do not use ...
200 views

### Two similar hand tiling puzzles

Make a square from each of these lists of aspect ratio $1:2$ rectangles 1, 4, 5, 6, 7, 9, 11, 12, 13, 14, 15, 17 ...