# 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.
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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?
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### 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 ...
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### 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 ...
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### 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 ...
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'...
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?
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### 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 ...
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### Attempting to make an interesting puzzle

Hmmm, what could it mean? (it's pretty easy)
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### 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 ...
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 ...
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 ...
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### Flow3rs fDr Charlie

Clues: [4 contextual images] Instructions: Name that serial killer _ a _ _ _ _ _ _ _ _ _ _ _ _
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### 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, ...
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### 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, ...
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### 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 ...
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### 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 ...
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### What percentage is grey?

The evenly spaced lines are drawn parallel to the base of triangle. What percentage of the triangle is grey?
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### 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 ...
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### 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 ...
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### 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 ...
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### 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, ...
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### 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 ...
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### 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?
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### 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 ...
245 views

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 ...
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### 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 ...
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1 vote
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### 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 ...
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 ...
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### 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 ...
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 ...
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?
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### 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 ...