# Questions tagged [geometry]

A puzzle related to shapes, geometric objects (polygons, circles, solids, etc.) of any number of dimensions, the relative position of figures, and the properties of space. Use with [mathematics]

1,130 questions
Filter by
Sorted by
Tagged with
1k views

### How long can you survive at the devil's playground?

The devil has trapped you in his playground. The devil knows that you can't cross over the burning boundary of his circle, so he allows you to choose a position within the circle before he starts to ...
• 6,498
206 views

### Rectangles and squares of trominoes filling a grid

Let's have a board 24 squares by 24 squares. This board is to be filled with trominoes of three different colors. There are equal numbers of trominoes of each color. The board is to be filled with ...
• 2,915
840 views

### Cutting off one's nose to spite one's eyes

Disclaimer: to keep graphic depiction of gratuitous violence to a minimum the face to be spited has been deliberately kept abstract. You are required to further reduce any distress this puzzle may ...
• 21.2k
12k views

### Prove that π > 3

It seems that once upon a time some politicians tried to pass a law fixing the value of π to be exactly 3. The idea being to "make math simpler so that our children can get better at math". ...
• 29.8k
1k views

### Reunite the Stars

On an infinite plane, the Prime Star has disintegrated into four constituent stars, the North Star, the South Star, the East Star and the West Star, each traveling at a constant speed of 1 in their ...
• 6,498
200 views

### Going off on multiple tangents

Given two disjoint circles of diameters D1 and D2 draw all shared tangents. Find the intersection points of all pairs of tangents. Discard those collinear with the two circle centre points. Of the ...
• 21.2k
575 views

### Triangles to diamonds

Given a triangle ABC with sides a=|BC|,b=|CA|,c=|AB| a diamond is circumscribed around the triangle's incircle. The diamond and the triangle share the corner C along with (part of) sides a and b. ...
• 5,237
848 views

### Optimal Path between two concentric circle arcs

When travelling along a outer arc between A and B you have two choices, either diverting onto the inner circular arc or carrying on the outer circular arc, as shown below: You start on the outer arc, ...
• 3,040
197 views

### The three door puzzle [closed]

In a long room are three doors. Behind each door one block is hanging from the ceiling. Behind the first door the block is made of concrete; behind the second door the block is made of hardwood; ...
• 2,915
1k views

### Prove why this mechanical linkage for a triangle centroid works

I saw on Twitter this cool mechanical linkage for which the red dot corresponds to the centroid of the triangle defined by the blue dots: Can you prove why this linkage works?
• 338
1k views

### Hidden message in rap text II: "Ya, a ray 'ave july joy!"

This puzzle is inspired by this one by @LukasRotter. Hopefully you don't mind me using similar (well, basically the same) format as yours, Mr. Rotter! ;) The same rapper released another teaser for ...
• 1,746
961 views

### Four non-right angled triangles passing through every dot of a 5x5 grid

This puzzle was suggested by jwezorek in Three triangles passing through every dot of a 5x5 grid 25 dots are drawn as a 5x5 regular square grid. Can you draw 4 non-right angled triangles that pass ...
2k views

### Four triangles passing through every dot of a 7x7 grid

49 dots are drawn as a 7x7 regular square grid. Can you draw 4 triangles that pass through every dot? The corners of the triangles must lie on the dots, ie., they cannot lie outside the grid. The 7x7 ...
3k views

### Three triangles passing through every dot of a 5x5 grid

25 dots are drawn as a 5x5 regular square grid. Can you draw 3 triangles that pass through every dot? The corners of the triangles must lie on the dots, ie., they cannot lie outside the grid.
207 views

### Inscribing a cylinder within a sphere [closed]

Let's have a sphere with R=3. What is the trick to inscribe in this sphere a cylinder almost half its volume? The circumferences of the two bases of the cylinder have to lie on the surface of the ...
• 2,915
597 views

### Largest rectangle from 20 Lego bricks

You have twenty 2x4 Lego bricks, like the one shown below What is the area of the largest rectangle you can make satisfying the following conditions: All bricks must be connected in a single ...
2k views

### Lines and Squares

This 'puzzle' is from the New York Times website, from its puzzles. I decided it was fun and so I would share it with you. Question Here are 10 straight lines and 17 squares. Here are 9 straight ...
• 2,613
5k views

### Can you irrigate your lawn with 23 sprinklers?

You have a perfectly circular lawn with radius exactly 4 metres. Lately the grass has been turning yellow and quite rough, so you go to Stiv's Diabolical Instruments and describe your problem. "...
• 7,678
469 views

### My special animal

The answer to this puzzle is an image not hosted on Imgur. The image host and the ID of the image on that host should become clear when solving the puzzle. (SVG source of the above) Exact coordinates ...
• 7,678
136 views

• 12.2k
1k views

### Folding a piece of paper with numbers in sequence

Divide a rectangular sheet of paper with a side length of 2 × 4 into eight 1 x 1 unit squares and label them as shown in the sketch. Then fold the sheet of paper along the boundaries of the square so ...
• 12.2k