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]

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6
votes
2answers
147 views

Fold the plane four times to get the maximum number of cross points

You have a straight line $l$ in an infinite plane. You can fold the plane along any straight line so the line $l$ becomes two rays with a common starting point. In the picture we fold along line $a_1$...
10
votes
3answers
666 views

Tipping a tetrahedron in a plane

A regular tetrahedron with one black and three white faces is positioned with its black face at the bottom of a plane. The tetrahedron is tipped several times over an edge and finally reaches the same ...
9
votes
2answers
433 views

Clash of the Robinsons

"Ridiculous!" you think "What can be the odds? Either I'm hallucinating or the amateur writing this story plunged to new depths of incompetence." Both being equally likely you don'...
8
votes
1answer
374 views

Squares in a quadrant: How big is the pool?

The local council is building a new pool complex. A one hectare ($100\times100$m) block of land has ground suitable for pool-digging, but a local ring road runs through it, leaving only an exact ...
7
votes
1answer
152 views

Ernie and the Cuboidal Crystals

When passing Ernie's letterbox this morning, I found a courier bag about the size of a shoe-box, resting inside (along with a smaller unlabelled bag). I immediately guessed that it was the special ...
48
votes
3answers
13k views

A new way to cut a pizza

Can you cut a pizza (circle) into 12 congruent pieces, such that half of them have crust (circle boundary), while the other half do not? The pieces must have the same shape and area, but can be ...
0
votes
1answer
211 views

When a Cube Loves a Circle [closed]

Align the center of a unit cube to the origin, and one of its long diagonals to the z-axis. In terms of r and h, what proportion of the circle {x^2 + y^2 = r^2, z = h} is inside the cube?
11
votes
2answers
477 views

Match the colors on the edges of the rectangles - is it possible?

In April 1971 (it says so on the back of the cards) I made the following puzzle which requires one to form a square with adjacent colours being the same. Can this puzzle be solved and, if yes, what ...
6
votes
2answers
239 views

Ernie and the Equi-area Tetrahedra

I enjoy spending time with Ernie when he is 'pottering' in his workshop. It is a large open-plan area filled with soldering-stations and oscilloscopes, lathes and milling machines, band-saws and drill-...
6
votes
0answers
180 views

Doubling the cube with rational Meccano strips

In three monographs published in 2006, 2008 and 2014 Gerard 't Hooft considered "Meccano mathematics": how to construct specified distances and regular polygons by a rigid system of ideal ...
8
votes
1answer
292 views

Taping a cardboard square is getting me fired!

I was mucking around in the storeroom today when I should have been working. I had a square $20\times20$ cm piece of cardboard, and a roll of masking tape I'd been using (I can't remember the tape's ...
7
votes
1answer
250 views

Lost Bearings: A Puzzle That I've Designed

I'm Benjamin Curran. I'm a 14 year old puzzle lover and I come to you with this puzzle that I've made up myself. Hopefully you won't find it tricky. Two tourists have gotten themselves lost in the ...
0
votes
1answer
119 views

Catching the Vegetable-Goose [closed]

After an altercation involving giant bees, you have been sentence to some hard labour, specifically harvesting barnacle-lambs: a gourd-like fruit that grows geese in its shell While working, you get ...
-8
votes
1answer
114 views

Puzzling rectangles [closed]

Can you find two unequal rectangles whose areas add to $5\sqrt5$? No computer solutions please.
3
votes
2answers
745 views

Most points on a circle

What is the most number of integer lattice points that lie on the circumference of a single circle whose radius is 80 or less? Please no computer computations.
5
votes
2answers
459 views

Catch the angel in less than 7 units of time

The devil has trapped the angel in a regular hexagram of firewalls. The perimeter of the hexagram is 12. The devil starts at the apex of the hexagram. can move at speed $1$ to leave a trajectory of ...
7
votes
7answers
6k views

Prove that sin(x) ≥ x/2, but without calculus!

Important Note: After when this puzzle was posted, many people pointed out errors and improvements that could be made. I also noticed many flaws, so the post once had gone through drastic changes. ...
4
votes
1answer
641 views

Guess the algorithm

Here you are seeing part of a pattern I created with my computer. Can you either reproduce it or describe the algorithm I used?
11
votes
1answer
460 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 ...
-1
votes
2answers
175 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 ...
6
votes
1answer
803 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 ...
96
votes
2answers
9k 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". ...
16
votes
3answers
900 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 ...
7
votes
1answer
181 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 ...
7
votes
2answers
501 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. ...
11
votes
4answers
797 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, ...
-7
votes
1answer
159 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; ...
12
votes
2answers
966 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?
11
votes
0answers
761 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 ...
11
votes
1answer
892 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 ...
19
votes
1answer
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 ...
15
votes
3answers
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.
-7
votes
2answers
164 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 ...
8
votes
2answers
511 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 ...
10
votes
3answers
781 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 ...
22
votes
7answers
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. "...
4
votes
2answers
431 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 ...
6
votes
2answers
128 views

Vertices of a regular $13$-gon and $14$-gon on a circle with center angle $< 1°$

All vertices of a regular $13$-gon and all vertices of a regular $14$-gon lie on a circle and divide it into $27$ circular arcs. Is there always an arc, which corresponding center angle is less than $...
12
votes
3answers
988 views

A line not intersecting points in the plane

Is it possible to draw a finite or infinite set S of points in the plane, such that any line drawn in this plane neither intersects with exactly one point in S or an infinite number of points in S?
8
votes
1answer
282 views

Survive the infinite zombie attack II

Zombies are back again. Same as last time, You're at the origin, and zombies occupy the points $(100𝑖,100𝑗)$ for all integers $𝑖,𝑗$ except the origin, as shown below: The ratio of your speed to ...
12
votes
2answers
726 views

Paint Eight Squares

Inspired by this question Given a $5 \times 5$ grid of white squares, can you paint $8$ of the squares black so that each white square is orthogonally adjacent to exactly one black square?
1
vote
1answer
276 views

1 lion, with a zebra and a fixed enclosure

Background See the puzzle Variant of lion and 100 zebras from @ghosts-in-the-code which remains unsolved years after it was posted. Several times in the last couple of years I've started to write up ...
-2
votes
2answers
256 views

Filling up squares! ⬜ ⬛ [closed]

You have a white grid of size a) 9x9 b) 10x10 and you are asked to paint some squares black. Your generous friend has given you a challenge: Can you paint them so that each white square has only one ...
-2
votes
1answer
145 views

Trails on a grid filled with skinny tetrominoes

Let's have a 10x10 grid with 12 empty bases. The rest of the grid is filled with skinny tetrominoes. The 5 regular tetrominoes are marked with a red color and the 2 reflections are marked with a green ...
7
votes
6answers
2k views

Dividing a chocolate frosting cake [closed]

Mrs. Betty made a squared cake with chocolate frosting for his neighbors to the afternoon tea. However, first she sliced a middle piece for her two grandchildren and cut it in half: There was no ...
5
votes
1answer
575 views

Flat share share

This is a sequel to Gentrification in Chessshire. Due to the febrile state of the Chesster housing market you and your flat mates are forced to rent out half your place to another group of sharers. ...
1
vote
1answer
225 views

Rearranging the square

You are given a square piece of paper. You can cut it into pieces and rearrange them to form a new shape. You are allowed to rotate and flip pieces, provided that they are all used. Can you cut the ...
-3
votes
1answer
245 views

Open dice Problem

The following figure is folded to form a box. Choose from the alternatives (A), (B), (C) and (D) the boxes that is similar to the box formed. Source: YouTube Video How to answer these type of ...
2
votes
2answers
163 views

A bear of a different colour [duplicate]

Here is a stunning new version of the famous bear problem. IT IS NOT A DUPLICATE, OR LATERAL THINKING. MATHEMATICS REQUIRED. A photographer stepped out of their tent with a camera and walked: 1 km ...
9
votes
2answers
344 views

Gentrification in Chessshire

You can skip the back story and directly jump to the question. Capitalism has arrived in suburban Chesster the community most famed for The Game, and with a vengeance. Rents have trebled in less than ...

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