# 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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### 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, ...
852 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 ...
781 views

### Need some help with my math homework (pretty please?)

Can someone help with a problem from my math textbook? This is the problem I'm stuck on: I don't really get how these kinds of problems work. I think they want me to find the width of the rectangle? ...
537 views

### 3³+4³+5³=6³ Puzzle

A classic puzzle asks us to break a 6x6x6 cube into the smallest number of pieces which can be reassembled into 3 physically separate cubes of sizes 3, 4, & 5. 3³+4³+5³ =27+64+125 =216 =6³ An 8-...
2k views

### What is the maximum number of fish possible in your tank?

You want to put some fish in a square tank. But these fish fight whenever they are in the same tank. Sadly, you have only 1 tank, but you can put glass panes inside the tank to divide it, not ...
37k views

### Find 10 triangles in a five pointed star using two straight lines

This puzzle consists of counting ten triangles (check three sides for each one, remember that there don't exist triangles with more than three sides :P) using two straight lines that cross the figure ...
260 views

### Make a Venn diagram with five triangles

A Venn diagram consists of a set of partially overlapping shapes on a plane, arranged in a particular way: for any particular labelling of each of the shapes as "inside" or "outside&...
200 views

### Tile dominoes in a 3x10 space [closed]

How many ways are there to tile 1x2 (unmarked) dominoes in a 3x10 space? This is a harder version of Tile dominoes in a 2x10 space, since that was too easy.
3k views

### Make exactly 101 squares using as few lines as possible

With how few straight lines can you make exactly 101 squares? The squares don’t necessarily have be the same size. Clarification 1: By lines, I mean you can use mathematical line segments and/or ...
254 views

### 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 ...
228 views

### Tile a square with five rectangles with 10 distinct edges

The baby brother of: Cutting a square into seven rectangles Tile a square with five rectangles. Select the lengths of the edges of the rectangles from the set $1$ through $10$, with no length ...
138 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. ...
559 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), ...
2k views

### What's the missing pattern? 3x3 grid, dot pattern

What is the missing piece to this pattern? Got it as a quiz at work - no one here knows what it is!
283 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 ...
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 ...
390 views

### Two digits in one

Here is a digit: However, it is, at the same time, another digit. How can it be?
1 vote
183 views

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 ...
539 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 ...
4k 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 ...
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 ...
188 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 - ...
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.
999 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 ...
332 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:
505 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 ...
1k views

### The Challenge Square

Q: Can you divide this shape into 4 equal parts, and then form a square? This puzzle was published by Henry Dudeney who received the puzzle from Edward B. Escott.
690 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 ...
288 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. ...
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 ...
1 vote
180 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 ...
536 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 ...
515 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 ...
149 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 ...
268 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 ...
172 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 ...
512 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.
521 views

### One vs many. Can white force a draw?

On an infinite chessboard there's a single white king and N black kings. The nearest black king must be K moves away from the white king. Given N, white dictates the value of (finite) K, then black ...
320 views

### Tiling rectangles with U pentomino plus rectangles

Inspired by Polyomino Z pentomino and rectangle packing into rectangle Also in this series: Tiling rectangles with F pentomino plus rectangles Tiling rectangles with N pentomino plus rectangles ...
339 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/...
295 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 ...
950 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 ...
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 ...
639 views

### Ernie and the Chocolate Bomb

Last week when I visited Ernie he complained that his trousers had shrunk in the wash. I suggested an alternate possibility – he was putting on weight. So he decided to go on a diet and to support him,...
833 views

### Help! I lost my marble(s)!

Tomorrow is the annual meetup for the Northwest Region Marble Lovers Association. The day's festivities will include various marble games, admiring collections of marbles, a guest speaker who will ...
716 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 ...
1k views

### Pentominoes On the Edge

Archived Source Introducing Pentominoes! It's the same concept as tetrominoes except they use 5 tiles instead of 4. Discounting rotations and reflections, there are 12 different free pentominoes. (If ...
2k views

### 5 points on a ball, divide the ball into 2 halves so that one half as exactly 4 points

Suppose that you take a pen and mark five points on a ball. I claim that no matter where you draw those points, I can always slice the ball into two equal halves (two equal and closed hemispheres) ...