# 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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### A blanket for my baby snake

Mama snake wants to knit a blanket for little baby snake. She is not a dissipater and wants to make the blanket of a minimal size (area). But her baby snake is quite a lively baby and it always ...
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### Paint the Rectangle with least number of Circular Stamp Touches

What is the minimum number of touches for painting at least a $100*100$ rectangle if you have one circular stamp tool that paints a circular area of $1$ unit radius in every touch? This question is ...
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1 vote
3k views

### Can you make a Rectangle from an Odd Number of Triangles?

So, the triangles are the same size, they are equilateral triangles. Can you use an odd number of these, to create a rectangle? If so how many, if possible post an image of your answer! Answer with ...
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1 vote
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### How many equal-sized polygons can be used to cover a soccer ball?

It seems that mostly either 26 or 32 equal-size polygons are used to cover a spherical soccer ball. What other configurations are possible?
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### rescue operation - where is your partner?

Your partner's space ship has crashed on an uninhabited planet. Only the radio transmitter and his compass were still in operation. He asks you to rescue him, and tells you how to find him by the ...
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665 views

### Paint the rectangle with least movement

There is a painting brush tool that can paint a circle area of $1$ unit radius. What is the shortest paint track for painting at least a $100*100$ units rectangle area on wall? How much did the brush ...
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### The robotic vacuum cleaner

An engineer has invented a robotic vacuum cleaner to sweep the floor of his house. The floor plan, shown below, is made up of many square tiles, with walls at certain places, represented by black ...
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### The Laziest Surveyor

The new land surveyor and his boss arrived at the work site, a huge and perfectly flat parking lot. His boss said, "Your first assignment is going to be a tough one. You see this parking lot? It ...
• 5,153
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### How to ship the new Slurm 7-pack efficiently

The six-pack is a thing of the past. Beverages of the future will use the seven-pack format. But how will the mighty spacemen of the future manage to ship the Slurm seven-pack efficiently in ...
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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 aren't exist triangles with more than three sides :P ) using two straight lines that cross the ...
11k views

### Chaos and Order: a visual puzzle in stained glass

I created a visual puzzle, which my wife then implemented as part of a stained-glass window. I've no idea if it is (a) obvious, (b) stupid or hopefully (c) extremely clever, and hence would love to ...
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### Santa Claus flies to the South Pole

It is a little known fact that Santa Claus is in fact a vampire. Why else would he spend so much time near the North Pole and travel only at night? Yes, he fears daylight! His problem is that ...
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12k views

### Divide a rectangle with a rectangular hole into two equal parts

Consider any large rectangle from which a smaller rectangular portion has been removed. The removed rectangular portion may have any orientation i.e. the remaining figure is not necessarily symmetric ...
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### A cube puzzle (Multiple of 6)

If you have a cube, say, $3 \times 3 \times 3$, you know that mathematically it's made of $27$ ($3*3*3$) smaller cubes. Now, just remove one full line of smaller cubes (in this case, 3 smaller cubes). ...
2k views

### Find shortest network connecting four points

Given the figure below, find the shortest network of straight line segments (like a Steiner tree, or like parts of a Delaunay triangulation) that connects the four circled points while staying in the ...
440 views

### Make a wide tower of bridge-shapes

In this question, bridge stands for the illustrated convex quadrilateral, constructed from three equilateral triangles. Letters A, B, C, D, E are assigned to each unit length of periphery as shown in ...
3k views

### Probability of three segments forming a triangle

Consider a line segment of length L. This segment is cut in three segments at arbitrary points. What is the probability that these three segments could be rearranged as sides of a triangle?
388 views

### Tower of tiles revisited

An S-tileset is a collection of n oriented tiles, where no two tiles have the same size, each tile is one unit thick, and its non-zero-integer length and width add up to n+1. (So, an S-tileset has n ...
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### Join all circles together only with 6 lines

In the below image, can you draw 6 straight lines that pass all the circles? As soon as you start drawing lines you can't take your pen up until you draw all six lines. hint: you don't have to keep ...
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### How high a tower of tiles can be made?

An $S$-tileset is a collection of $n$ oriented tiles, where no two tiles have the same size, each tile is one unit thick, and its non-zero-integer length and width add up to $n+1$. (So, an $S$-...
2k views

### Folding a hexagon to a rectangle or square, with uniform overlap

A piece of fabric shaped like a regular hexagon with unit-length sides is given, with vertices A...F and center O. Let a fold correspond to folding some fabric along a straight line, without ...
378 views

### Is there a second solution to points and perpendicular bisectors problem?

There is a problem from M.Gardner book ("Wheels, Life, and other Mathematical Amusements", p. 201): [Hallard T. Croft] asked if there existed a finite set of points on the plane such that the ...
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486 views

### Land claim staking

It was traditional during the times of the Oregon Trail and the gold rush that men founding new towns were allowed to stake their claim on land upon arriving to the west coast. Suppose a man is ...
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### Drawing lines on a map

This was a puzzle that appeared in an old math contest as well as an unrelated puzzle book. Suppose we have a two-dimensional map with a lot of cities marked on it. For each city on the map, we ...
887 views

### How long is needed to clear the area of robots?

This question has been written in order to help answer Fastest way to collect an arbitrary army. There is a 1 x 1 square area with corners labelled clockwise A, B, C and D. A finite number of ...
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### When to be sure that we have counted all the squares in such problems

My first question: how would one solve such problems (in general)? What should be the general technique? My second question: When to be sure that we have counted all the squares in such problems?
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653 views

### Does this strategy work?

I'm thinking about the following strategy for Fastest way to collect an arbitrary army: When a soldier decides to go to some house he "reserves" it. Once a soldier is free (has delivered the news to ...
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### Fastest way to collect an arbitrary army

I am looking for solution of this puzzle: There is a kingdom with a square shape with sides of length 1. The castle is located at the center of the square. At the castle the king lives under the ...
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