Skip to main content

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]

Filter by
Sorted by
Tagged with
2 votes
1 answer
111 views

ORIGAMI: Above and beyond

It's been a long time since I've posted an origami puzzle! An origami puzzle is solved with some thickness $x$ iff it can be folded into a rectangle (possibly a square) with thickness $x$ everywhere. ...
Sny's user avatar
  • 3,157
3 votes
0 answers
144 views
+100

origami SNY t28

It's been a long time since I've posted an origami puzzle! Fold the shape into a rectangle such that the rectangle is 28 layers thick everywhere. The purple part is the puzzle. Although solutions are ...
Sny's user avatar
  • 3,157
26 votes
3 answers
1k views

Try Triling ("Triangular-Tiling")

You are given a grid. Some of the cells in the grid are labelled with positive numbers. You must partition the grid into triangles. There must be a triangle for each labelled cell Each cell must be ...
user23087's user avatar
  • 770
1 vote
0 answers
172 views

Deadlock possible in Minefield?

A deadlock is a position in which neither player has won and neither player has a legal placement available. My question is, "Can you find a deadlock position in Minefield?" And, if you ...
Mark Steere's user avatar
-4 votes
2 answers
366 views

Two digits in one

Here is a digit: However, it is, at the same time, another digit. How can it be?
web adventurer's user avatar
4 votes
2 answers
277 views

origami J-SHAPED t2

It's been a long time since I've posted an origami puzzle! Fold the shape into a rectangle such that the rectangle is 2 layers thick everywhere. The red part is not included in the puzzle; the purple ...
Sny's user avatar
  • 3,157
7 votes
3 answers
472 views

Geometry Puzzle: Tangent Circles with Integer Radii

Take as a semi-related example a series of circles with radii 10, 9, 8, ..., 2, 1. Place the first (largest) circle in the center and subsequent circles around it, keeping tangency between subsequent ...
Brandan's user avatar
  • 85
9 votes
3 answers
522 views

ORIGAMI PUZZLES completed version

You may have seen some posts by Sunny Lu here on my origami puzzles. Now, the full version is out! The goal is to fold the paper into a rectangle (or square) with constant thickness (see examples), ...
Omega_3301's user avatar
9 votes
3 answers
1k views

Tiling a 16x16 square with 1x4 rectangles

Consider a 16x16 square subdivided by grid lines into unit squares. It is easy to completely tile (no overlaps, no gaps) this square with 64 1x4 rectangles. Each 1x4 rectangle in the tiling (no ...
Will Octagon Gibson's user avatar
9 votes
2 answers
1k views

Can you tile a 15x16 rectangle using eight rectangles whose sizes are 1x2, 2x3, 3x4, ... 8x9?

Can you tile a 15x16 rectangle using eight rectangles whose sizes are 1x2, 2x3, 3x4, ... 8x9? No two rectangles can be the same size.
Will Octagon Gibson's user avatar
2 votes
0 answers
185 views

Ernie and the conduits of constant cross-section

It all started last week, when Acme Engineering loaned him a prototype version of their 3D Home Printer (this was as a reward for Ernie providing them, patent-free, with a suitable building material - ...
Penguino's user avatar
  • 14k
26 votes
5 answers
3k views

Can you tile a 25 x 25 square with a mixture of 2 x 2 squares and 3 x 3 squares?

Can you tile a $25 \times 25$ square (no overlaps, no gaps) with a mixture of $2 \times 2$ squares and $3 \times 3$ squares? This puzzle is by David A. Klarner. Clarification: The number of $2 \times ...
Will Octagon Gibson's user avatar
3 votes
1 answer
329 views

Build a slanted pyramid with ten L-shaped blocks

Consider the following L-shaped 3-dimensional object made up of three unit cubes joined at their faces: Use 10 of the above L-shaped pieces to make the following shape:
Will Octagon Gibson's user avatar
11 votes
4 answers
991 views

Make a square table top with the minimal needed amount of straight cuts

inspired by : Make a square table top with six (or fewer) pieces A carpenter has three pieces of beautiful wood, measuring 12 inches, 15 inches, and 16 inches square, respectively. They want to use ...
Retudin's user avatar
  • 9,208
10 votes
2 answers
499 views

Make a square table top with six (or fewer) pieces

A man had three pieces of beautiful wood, measuring 12 inches, 15 inches, and 16 inches square respectively. He wanted to cut these into the fewest pieces possible that would fit together and form a ...
Will Octagon Gibson's user avatar
6 votes
5 answers
679 views

Circles crossing every cell of an NxN grid

What is the least number of circles you need to draw, such that every cell of an NxN grid is crossed? A circle crosses a grid cell if one of the points on its circumference lies completely inside the ...
Dmitry Kamenetsky's user avatar
1 vote
1 answer
173 views

Recursive rhombic dodecahedron tiling

Say you have a single rhombic dodecahedron, call it "layer p0". If you then tile identical dodecahedrons around it so that it gets completely covered, the number of dodecahedrons on the ...
TheMasterOfCubes's user avatar
2 votes
1 answer
531 views

Is it possible to fill an arbitrarily large hex grid completely given these rules? #2

Based off of this. Lets say you have two players, Red and Blue, that alternate filling an arbitrarily large hexagonal grid of tessellated hexagons with pieces of their color. Hexagons can either be ...
Sny's user avatar
  • 3,157
4 votes
1 answer
506 views

Is it possible to fill an arbitrarily large hex grid completely given these rules?

Lets say you have two players, Red and Blue, that alternate filling an arbitrarily large hexagonal grid of tessellated hexagons with pieces of their color. Hexagons can either be filled or empty. A ...
Alek Erickson's user avatar
13 votes
3 answers
2k views

Circles crossing every cell of an 8x8 grid

What is the least number of circles you need to draw, such that every cell of an 8x8 grid is crossed? A circle crosses a grid cell if one of the points on its circumference lies completely inside the ...
Dmitry Kamenetsky's user avatar
6 votes
1 answer
283 views

April Fools Origami Update

Me (Sunny Lu) and Ωmega_3301 have made a special April Fools edition of origami puzzles. The objective is to fold a shape into a rectangle with uniform thickness. The thickness will be given to you. ...
Sny's user avatar
  • 3,157
7 votes
1 answer
536 views

origami WAVE t2

Fold the shape into a rectangle such that the rectangle is 2 layers thick everywhere. The grey part is not included in the puzzle; the purple part is the puzzle. Although solutions are not required ...
Sny's user avatar
  • 3,157
-4 votes
1 answer
146 views

Logic and Geometry Problem #6

Is it possible for a deadlock to occur in Necklace? Can there be a square on which neither Red nor Blue can place a stone? If it is possible, I need to see an example of that. If a deadlock is not ...
Mark Steere's user avatar
4 votes
1 answer
168 views

origami USHAPE t3

Fold the shape into a rectangle such that the rectangle is 3 layers thick everywhere. Although solutions are not required to be applicable in real life, using an actual sheet of paper is a great ...
Sny's user avatar
  • 3,157
4 votes
1 answer
265 views

ORTHOGONAL origami FISH t8

Since the last puzzle got cheesed, we're adding a new restriction (in italics) Fold the shape into a rectangle such that the rectangle is 8 layers thick everywhere. All folds must be orthogonal ...
Sny's user avatar
  • 3,157
12 votes
1 answer
504 views

origami FISH thickness 8

Fold the shape into a rectangle such that the rectangle is 8 layers thick everywhere. A puzzle for this type of orgami puzzle game made by Ωmega_3301, similar to this question.
Sny's user avatar
  • 3,157
7 votes
1 answer
333 views

Can 42 1x2x4 cuboids be packed into a 7x7x7 cube?

Can 42 1x2x4 cuboids be packed into a 7x7x7 cube without cutting any of them? Assume that all cuboids have their axes parallel to the axes of the big cube. I tried using https://www.jaapsch.net/...
mathlander's user avatar
  • 1,251
12 votes
1 answer
930 views

Anna tries to make triangles from broken sticks

Anna and Boris play a game with a red stick, a white stick and a blue stick, each of which is 1 meter long. Anna starts by breaking the red stick into three pieces. Then Boris breaks the white stick ...
Will Octagon Gibson's user avatar
9 votes
2 answers
289 views

How do I constrain a puzzle and keep a singular solution?

I am tinkering with a puzzle framework that has the following rules: In a 6x6 grid of squares, arrange 8 strips of connected squares such that there exists exactly one strip of every length (i.e. a ...
Brandan's user avatar
  • 85
24 votes
2 answers
4k views

A pizza dilemma

You are a waiter at a restaurant. The restaurant is known for its signature dish: the Donut Pizza. The Donut Pizza is a 5-inch square pizza with a 1-inch square hole in the middle. After several ...
mathlander's user avatar
  • 1,251
13 votes
4 answers
707 views

Pleasant Cuboids

A rectangular prism (or cuboid) made up of xyz identical unit cubes (x along its width, y along its length, and z along its height). Some of those cubes are internal, while the rest are external. Such ...
Bernardo Recamán Santos's user avatar
8 votes
2 answers
420 views

The shady puzzle that will keep you in the dark

The image below is the horizontal cross section of a room. The bulb shows the position of the single light source. When the light is switched on, one wall (marked in brown) remains completely in ...
Will Octagon Gibson's user avatar
14 votes
7 answers
3k views

Join six cities with roads

Warmup question: Each of five cities is connected to the others by four roads. Show that it is possible for the roads to intersect only once with exactly two roads crossing over at that single ...
Will Octagon Gibson's user avatar
8 votes
3 answers
1k views

Walking in a random direction

I walk $\pi$ km in one direction followed by $\pi$ km in another direction. In expectation how far am I now from my starting location? Both directions are chosen uniformly at random between $0^{\circ}$...
Dmitry Kamenetsky's user avatar
17 votes
3 answers
3k views

What is the total area of the two quarter circles?

Puzzle by Catriona Agg. The yellow circle has radius 4. What’s the total area of the two quarter circles?
Simd's user avatar
  • 7,845
-1 votes
1 answer
167 views

icosahedral net [closed]

The net of $20$ triangles shown to the right can be folded to form a regular icosahedron. Inside each of the triangular faces, write a number from $1$ to $20$ with each number used exactly once. Any ...
godlification's user avatar
3 votes
2 answers
333 views

Find maximum circular array sum [closed]

Take this 10 by 10 grid of numbers. ...
Simd's user avatar
  • 7,845
1 vote
0 answers
229 views

Covering a Square Floor with Square Rugs [closed]

You are given a finite collection of axis-aligned square rugs. (You do not choose the collection of rugs that you receive and the rugs are not necessarily all the same size.) Your objective is to move ...
Basset Hound Video's user avatar
3 votes
1 answer
371 views

Longest cycle on a cube

What is the length of the longest straight path on the surface of a unit cube, such that it starts and ends at the same point? The path can cross itself and must be straight on every edge and face ...
Dmitry Kamenetsky's user avatar
5 votes
1 answer
184 views

Find the optimal partition in this matrix

Given a particular matrix of integers, the challenge is to draw a boundary line through the cells so that the sum of the numbers on the boundary line or above is as large as possible. In this case &...
Simd's user avatar
  • 7,845
6 votes
3 answers
536 views

Find the optimal dividing line

Consider the following grid of numbers: In machine readable form: ...
Simd's user avatar
  • 7,845
-2 votes
1 answer
188 views

Deciding whether a set of points on a 2D plane has axial symmetry [closed]

The problem to solve: Let's say we have a set of $n$ points on the 2D plane. Determine whether it has axial symmetry. My attempt so far: For n=2 the answer is trivially "yes". For n=3 ...
Nick's user avatar
  • 1,695
10 votes
3 answers
1k views

A Sierpiński Carpet ratio

This math problem popped into my head and I wanted to share it with you: We have the Sierpiński carpet, which is a fractal built like this: Draw a square. Divide it into 9 equal subsquares arranged ...
Francesco Sollazzi's user avatar
2 votes
1 answer
275 views

Nimber mnemonic combinatorial puzzle

Please see my previous question for more background. The following represents an unfolded version of PG(3,2) with 1 as the center point: Given that each number must be an end point of a line which ...
stargirl's user avatar
21 votes
5 answers
3k views

Mishustin's circle problem

This problem was given to high school students by the Russian prime minister Mishustin. We have a circle. We are given some point on the circle and its diameter, as shown below. We are given a ...
Dmitry Kamenetsky's user avatar
2 votes
1 answer
239 views

Nimber Mnemonics

Note I originally tried to ask a variation of this question on math.stack; however 1 commenter pointed out that math.stack is not a puzzle site, which made me think maybe the fine folks of puzzling ...
stargirl's user avatar
9 votes
3 answers
1k views

Rearrange words to make a sentence

The following puzzle is from the October 1961 issue of the Eureka journal (published by The Cambridge University Mathematical Society): Rearrange the order of the following so as to make a true ...
Will Octagon Gibson's user avatar
6 votes
4 answers
2k views

A Prime Ant's Excursion in the Cartesian Plane

An ant resides at the origin of the Cartesian plane. One morning she sets out on a long excursion of its first quadrant and pledges to walk a different prime number of units every day starting with 2, ...
Bernardo Recamán Santos's user avatar
17 votes
3 answers
1k views

Put infinitely many equilateral triangles of equal size on the plane

...such that There's no overlapping No more such triangles can be added without overlapping. Let $r$ be, on average, the ratio of the area covered by triangles with respect to the area which is not. ...
Eric's user avatar
  • 6,536
0 votes
1 answer
63 views

Construction of non-rhombus but still paralellogram non-square-non-rectangle non-kite via Pythagorean triplet

Is it possible to construct a non-rhombus but parallelogram and quadrilateral non-square, Non-rectangle by putting four 3-4-5 (Pythagorean triplet) triangles together and making the 90 degree angle ...
user avatar

1
2 3 4 5
23