# 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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### 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? ...
288 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 ...
166 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
153 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?
555 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 ...
331 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 ...
364 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 ...
211 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 scale ...
201 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 ...
283 views

### Dissect a square into 3:2 non-congruent integer-sided rectangles

(Similar to the recent 3:1 rectangle question) Tile a square completely with rectangles which have aspect ratio 3:2, integral side lengths and all different sizes. In other words selected from 2x3, ...
398 views

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### Polygon neighbors

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 ...
6k 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 ...
682 views

### Radar towers in a military field

The military field has rectangle shape with the dimension of 16 km to 12 km and recently there are some drone activities around the area and drones are not welcome to the military region! Your ...
188 views

### Arrange six cigarettes in such a way that each cigarette touches every other cigarette [duplicate]

What are some ways to arrange six cigarettes in such a way that each cigarette touches every other cigarette?
3k views

### A hungry ant on a matchbox

A hungry ant is standing on the top of an empty matchbox cover (without its drawer) and has detected the smell of a drop of honey on the floor of the cover as shown in the figure below. What is the ...
203 views

### 15 pawns on a chessboard

15 pawns are placed on the centers of distinct squares of a chessboard. Prove that there are three pawns which form a right triangle. In the example board below, a couple of right triangles are ...
1k views

### Wooden Snake Puzzle

I have a wooden snake puzzle in my collection that has been unsolved for years. I wondered if any of you might be interested. I have fiddled with it, but think it might need dynamic programming or ...
602 views

### Help! I lost my marble(s)!

Tomorrow is the annual meetup for the Northwest Region Marble Lovers Association. The days festivities will include various marble games, admiring collections of marbles, a guest speaker who will talk ...