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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Smallest rectangle that fits the first 10 rectangles [closed]

What is the area of the smallest rectangle that can fit 10 rectangles with areas 1 to 10, inclusive? Rectangles must have integer sides and cannot overlap.
Dmitry Kamenetsky's user avatar
2 votes
2 answers
167 views

Orchard planting problem of 5 points per circle [closed]

In General orchard planting problem for circles , the problem of 4 points per circle has been studied. The problem here is that what is the maximum number of 5-point circles for a configuration of n ...
Zhaohui Du's user avatar
-4 votes
3 answers
257 views

Right angle triangle with an area of 41 [closed]

Can you find a right angle triangle with the shortest sides and whose area is equal to 41? All sides have to be rational numbers. HINT: The length of the hypotenuse is $44.05/3$ I hope this will help ...
Vassilis Parassidis's user avatar
13 votes
1 answer
342 views

Ernie and the disappointing drill bits

I was driving to Ernie's place a couple of days ago, with Ernie in the passenger seat, when we drove past an old building with a faded sign reading Lar's Tool's. Beneath it, scrawled on the front wall ...
Penguino's user avatar
  • 13.9k
6 votes
5 answers
3k views

Four equidistant points on Earth

Are there four points on Earth such that the distance between any pair of them is always the same? Distance is measured as shortest distance on Earth "as the crow flies" so without requiring ...
quarague's user avatar
  • 1,823
11 votes
3 answers
3k views

Five equidistant cities

Is it possible to have 5 cities connected with roads, such that the shortest path between any pair of cities has the same length?
Dmitry Kamenetsky's user avatar
15 votes
1 answer
2k views

Add 3 matches to make 6 squares

This puzzle appeared at the UQ Mobile store at Shibuya Scramble Square: マッチ棒でできた六角形にマッチ棒を 3本追加して正方形を6つ作りなさい Add 3 matches to this (a regular hexagon made out of 6 matches) to produce 6 squares. No ...
Parcly Taxel's user avatar
  • 7,678
9 votes
3 answers
452 views

PSE Advent Calendar 2022 (Day 17) Priority polar problem

This puzzle is part of the Puzzling Stack Exchange Advent Calendar 2022. The accepted answer to this question will be awarded a bounty worth 50 reputation.< Previous Door Next Door > Dear ...
Retudin's user avatar
  • 8,601
3 votes
1 answer
195 views

A dissection puzzle where you're allowed to use dilation

You may be familiar with Dudeney's famous dissection of the equilateral triangle into a square. (A nice physical version is demonstrated here.) His dissection uses four pieces. I believe this to be ...
Akiva Weinberger's user avatar
7 votes
1 answer
523 views

Two arcs equal three arcs

(Gonna answer my own question, as is encouraged.) To set the stage: an arc (or a Jordan arc) is a non-self-intersecting curve with two distinct endpoints. (For those who are familiar with topology, it'...
Akiva Weinberger's user avatar
14 votes
5 answers
3k views

Dividing a square field into 5 equal regions

A farmer has a 10m x 10m field that has fences around the perimeter. What is the least number of 1m fences he needs to add to divide the field into 5 regions of equal area?
Dmitry Kamenetsky's user avatar
10 votes
2 answers
2k views

Can you eat a 4-dimensional Rubik's Cube?

If you follow the traditional Rubik's cube eating conventions, Start by eating any piece except the central one Next, eat a piece orthogonally adjacent to the previously eaten piece (repeat) The last ...
Bass's user avatar
  • 77.4k
-4 votes
1 answer
178 views

Attempting to make an interesting puzzle

Hmmm, what could it mean? (it's pretty easy)
beanmanofbeans's user avatar
7 votes
1 answer
765 views

Infected squares warmup: infect a 7x7 board with 21 squares

You can consider this a "warmup" to my other question about infected squares. On a $7\times7$ square, some cells are infected; if a cell shares an edge with $3$ infected squares, it becomes ...
Akiva Weinberger's user avatar
9 votes
2 answers
450 views

Infected cubes puzzle in 3D with threshold 4

(This question was previously posted on Math SE, but received no answers.) 3D infected cubes puzzle with threshold $4$: On an $n\times n\times n$ cube, some cells are infected; if a cell shares a ...
Akiva Weinberger's user avatar
7 votes
0 answers
190 views

Can you construct a nonagon with 47 rods?

Stiv's Diabolical Instruments now offers a bundle of exactly 47 equal-length rods that can be joined by hinges at their ends – and only the ends – to form planar linkages (i.e. all hinge axes are ...
Parcly Taxel's user avatar
  • 7,678
1 vote
2 answers
795 views

Flow3rs fDr Charlie

Clues: [4 contextual images] Instructions: Name that serial killer _ a _ _ _ _ _ _ _ _ _ _ _ _
Tyler's user avatar
  • 1,093
3 votes
1 answer
330 views

Seven octahedral nets to cover an octahedron

After solving Cover a single cube with FIVE identical cube nets I had the idea for this puzzle, which may be regarded as a natural generalisation to triangular grids. Find two different nets, A and B, ...
Parcly Taxel's user avatar
  • 7,678
16 votes
1 answer
504 views

Cover a single cube with FIVE identical cube nets

Start with five identical cubes: Your challenge: Cut and unwrap all five cubes into five identical cube nets. Show how to re-fold these five cube nets to form the surface of a single larger cube, ...
plasticinsect's user avatar
3 votes
0 answers
198 views

Perfect 9-sided die [closed]

I am working on a fair 9-sided die and I settled on a design where you select three edges of a cube where the two sides that one edge touches don't overlap with any of the other sides touched by the ...
Gabe White's user avatar
10 votes
3 answers
832 views

Catching the "L" train

This is a more difficult version of an earlier puzzle. Hit the "C" ball at such an angle that it creates a chain reaction which ultimately dislodges the "L" ball. Whenever the ...
SlowMagic's user avatar
  • 13.8k
46 votes
12 answers
5k views

What percentage is grey?

The evenly spaced lines are drawn parallel to the base of triangle. What percentage of the triangle is grey?
Simd's user avatar
  • 7,845
46 votes
1 answer
3k views

Release the "Q" ball

Hit the "I" ball at such an angle that it creates a chain reaction which ultimately dislodges the "Q" ball. Whenever the ball in motion hits a stationary ball, the ball in motion ...
SlowMagic's user avatar
  • 13.8k
7 votes
3 answers
1k views

Beyond earth and countries fighting for land

Consider 2 countries, A,B that have discovered a new planet, the size of Earth. They have decided to split the planet into regions of minimum area $10^3 m^2$ and maximum area $10^5 m^2$, with borders ...
Cris's user avatar
  • 189
4 votes
1 answer
179 views

Can you Avoid the Spear-Wielding Gladiator?

You are trapped in a circular coliseum, and a gladiator with a spear is chasing you. You can't defend yourself, but you can run faster than the gladiator. You run at 11 feet per second, and the ...
jjj's user avatar
  • 41
5 votes
0 answers
258 views

What is a Good Pasta Number™?

This puzzle is inspired by JLee's What is a Word/Phrase™ series and the subsequent "Number" variants. (Actually, I'd originally tried to create a more original puzzle using the same idea, ...
Auride's user avatar
  • 624
7 votes
3 answers
1k views

Double chess stalemate with 60 units

Inspired by Symmetrical Chess Position With No Legal Moves Can you arrange on a chessboard 18 kings, 6 rooks and 6 bishops of each colour (i.e. 60 units, leaving 4 empty squares) so that neither side ...
Laska's user avatar
  • 1,919
23 votes
3 answers
2k views

A pentagon that can measure the first 7 integer distances

A pentagon can be used to measure 10 distances - one distance between each pair of its 5 vertices. Can you find a pentagon that can measure every integer distance from 1 to 7, inclusive?
Dmitry Kamenetsky's user avatar
2 votes
2 answers
738 views

Cut a square piece of paper

You are given a square piece of paper shown below: Can you cut this paper in a way that: The shortest distance from A to B is double the shortest distance from A to C; and The shortest distance from ...
Dmitry Kamenetsky's user avatar
8 votes
1 answer
245 views

Six loops of threads

The puzzle: Put six loops of threads together, in such a way that they cannot be separated from each other, but if any one of the loops is cut, then all threads can be separated from each other. As ...
WhatsUp's user avatar
  • 7,387
0 votes
2 answers
161 views

What is the measure of $\angle{BAE}$ and the length of $BE$ and $ED$ in a square?

The puzzle is as follows: Suppose that you have a square whose sides measure 1 inch. Let each vertex be $A$, $B$, $C$ and $D$. Now, pick a point $E$ on the interior of this square so that $\angle{EDA}...
Chris Steinbeck Bell's user avatar
14 votes
1 answer
2k views

Turn two cubes into one!

Here are two identical cubes: Your challenge: Start with two cubes of exactly the same size. Cut the surface of each of these two cubes along its edges and unfold the surface into a 2D shape. (So ...
plasticinsect's user avatar
8 votes
1 answer
220 views

Tetromino in a Pentomino Lair

Inspired by this question: Can you fit twelve pentominoes (not necessarily distinct) and one tetromino inside a 10 x 10 grid such that they do not overlap or touch each other orthogonally (...
hexomino's user avatar
  • 136k
2 votes
1 answer
166 views

Flipping through the faces of a cube?

Let's place a cube on a table and flip it around a bit. In fact, flip it according to the following instructions: Flip forward twice. Flip left twice. Flip backward twice. Flip right twice. Assuming ...
Hazel へいぜる's user avatar
13 votes
1 answer
251 views

Flipping Platonic solids

A cube is flipping on a table along its edges without sliding. If the cube flips two steps forward, two steps to the left, two steps backward, two steps to the right, then the cube is back to its ...
WhatsUp's user avatar
  • 7,387
11 votes
3 answers
1k views

Fitting pentominoes inside a 10x10 grid

What is the most number of pentominoes that you can fit inside a 10x10 grid, such that they do not overlap or touch each other orthogonally (horizontally or vertically)? Bonus: what is the most number ...
Dmitry Kamenetsky's user avatar
10 votes
3 answers
1k views

Ten tetrominoes inside an 8x8 grid

Can you place ten tetrominoes inside an 8x8 grid, such that they do not overlap or touch each other orthogonally (horizontally or vertically) ?
Dmitry Kamenetsky's user avatar
6 votes
2 answers
267 views

Ernie and the Menacing Monopoles

While driving home from a fishing trip Ernie and I saw a road-side sign pointing down a gravel track that announced ‘MYSTERIOUS SOUTH SLOPING TREES’. It was getting well on into the afternoon, and I ...
Penguino's user avatar
  • 13.9k
25 votes
3 answers
3k views

Twenty-four trees in eighteen rows of four

A very old puzzle, #146 from American Agriculturist, April 1865: How may twenty-four trees be planted in exactly eighteen rows, with four trees in each row? A row consists of a number of trees in a ...
Will Octagon Gibson's user avatar
40 votes
2 answers
2k views

Can you refold a hyper plus sign into a cube?

If you take a cube, and grow a new cube out from each of its six faces, you will get a "hyper plus sign": This 3D solid has an interesting property. It can be sliced along its edges and ...
plasticinsect's user avatar
3 votes
2 answers
207 views

How high does the ladder reach up the wall?

A ladder of length $l$ rests against a vertical wall. Suppose that there is a rung on the ladder which has the same distance $d$ from both the wall and the (horizontal) ground. Find explicitly, in ...
Simd's user avatar
  • 7,845
4 votes
3 answers
448 views

8x8 Grid with no parallels

In the 8x8 grid graph shown below; you can put points to the edge of grid as shown below (blue dots). The example above has 4 points and you construct a line between two points as shown below; so ...
Oray's user avatar
  • 30.3k
1 vote
2 answers
242 views

Two triangles in a circle

This puzzle is inspired by this great puzzle. You are given a circle. You can draw two non-overlapping triangles of any size and shape inside that circle. What is the highest percentage of the circle ...
Dmitry Kamenetsky's user avatar
3 votes
1 answer
354 views

A donut, a piece of string and a pair of spectacles

This is a simplified version of this physical puzzle. I believe it captures the essence at much reduced complexity. Please, forgive my poor drawing skills. The goal is disentangling the orange torus ...
loopy walt's user avatar
  • 21.2k
2 votes
1 answer
247 views

Complete sets of pictures by replacing blanks

I made a couple of new ones. I liked making the first one the most. The first one seems to be the easiest for me but I can see someone getting stuck on it if they don't figure out the idea. The second ...
Nikita M. Grimm's user avatar
-1 votes
2 answers
368 views

Fill the blank with an image that fits into the given set

I tried to make them not too boring. The intended solution is very hard so I tried to slightly hint at it by implementing multiple solutions that lead to the same answer. I also tried to make more ...
Nikita M. Grimm's user avatar
13 votes
2 answers
515 views

Put three pieces of cake into a round box

You're about to cut three pieces from a large cake to put in a round box of radius 1. If the pieces must be congruent triangles, and cannot overlap, what shape gives you the maximum amount of cake?
Eric's user avatar
  • 6,498
4 votes
1 answer
232 views

Each snowflake is beautiful but some are "pretty"

Let's define "snowflakey" pattern as Regular polygon surrounded by other regular polygons number of surrounding polygons equals to a number of angles of polygon in the middle Here are two ...
ScalewingedAcidicorn's user avatar
2 votes
1 answer
202 views

How to fill up the numbers in a set of empty discs drawing a pentagon? The target sum is 10 [duplicate]

Can anyone explain to me the math behind the problem? I want to convert the mathematical solution into an efficient algorithm. The target sum can be any given number. For reference please check the ...
Shashwata Shastri's user avatar
1 vote
1 answer
322 views

Can you escape from two lions?

You're at the center of a circular arena. A pair of lions are at the border, planning to catch you. One of them moves as fast as you, but the other moves slower than you. The three of you are confined ...
Eric's user avatar
  • 6,498

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