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Questions tagged [graph-theory]

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A puzzle built around graphs: sets of nodes joined together by paths. General graph theory questions are off-topic but can be asked on Mathematics Stack Exchange using the [graph-theory] tag.

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2
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1answer
127 views

My sixteen graph theory students

I will have sixteen students in my graph theory course this semester. In our first session I asked each of them with which of the other 15 students in the class they were already acquainted before the ...
2
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0answers
81 views

Infected Cylinder and Torus

A variant of the well known Infected Checkerboard problem. If we've a 𝑛x𝑛 square, then we fold it along top and bottom row to form a cylinder. A cell in this cylinder becomes infected if at least ...
1
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1answer
78 views

Painting a plane!

Paint the points on a plane with three colors, so that the points on each line are a maximum of 2 colors, and all three colors are used. (Math Festival 1990)
4
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1answer
154 views

Visiting streets, not houses

The section points are houses and lines are streets, all with one unit length. What is the fewest number of units you must travel to visit every street at least once?
22
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1answer
571 views

New Year Graph Puzzle

In the graph below, each node is coloured either red or yellow, except for the white node in the bottom left, which I've marked with an X. Can you tell me what the white node marked with X represents?...
0
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2answers
71 views

Show that no lines need cross [closed]

There are n red points and n blue points in the plane. Show that you can always join all the red and blue points with straight lines so that no two lines cross. Each point can have exactly one line ...
14
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1answer
394 views

Currency connections

Two Forex traders are trying to communicate about their trades. They send each other images with a hidden meaning like this one: Can you work out which currencies they are trading? Hint:
7
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2answers
818 views

Frog game on a dandelion graph

There is some noise in the local pond. A group of frogs wants to host a birthday party! There is a total of 22 lily pads in the pond, each housing a single frog. They are labelled as numbers from 0 to ...
9
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2answers
459 views

Dragon summoning spell

The parchment shown below got stained with something. See if you can determine the obscured parts.
7
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1answer
163 views

Four color a map - but go light on the fourth color!

Here's a map, which I found here: Your challenge is to four-color this map while minimizing your use of the fourth color. More specifically, color the map with four colors so each region is a ...
3
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1answer
82 views

How many different ways can you color the diagram?

This question is a continuation of this one. Here are nine squares, connected by lines. Each square must be colored, and two squares connected by a line must be colored differently. Question 1. What ...
12
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1answer
363 views

Infection (Information Dissemination) Puzzle

There are 2020 people in a room. One person has COVID. After each minute, each person $\mathrm{P}$ is paired with some other person $\mathrm{Q}$ who was never paired with $\mathrm{P}$ before, and they ...
2
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0answers
407 views

A robot moving on a grid. Part 2

This is an extension of the discussion A robot is placed on a grid point. At each move the robot must take three steps along the edge of the grid. After each step the robot must turn right. Lengths of ...
2
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1answer
234 views

A robot moving on a grid

In the spirit the question I propose the puzzle: A robot is placed on a vertex of a grid. At each move the robot must take three steps along the edge of the grid. After each step the robot must turn ...
5
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2answers
345 views

Seventeen positive integers

Find 17 positive integers such that no four of them have, pairwise, a common divisor greater than 1, but, likewise, no four of them are, pairwise, relatively prime. Do so in such a way that the ...
5
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1answer
96 views

The sandpiles on the beach

We call a convex polyhedron a sandpile if one of the faces, called base, has a common edge with all the other faces. Furthermore, each vertex is linked with three edges. We consider the sandpiles by ...
1
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2answers
163 views

LGBT+ SpeedDating

Congratulations! You are now the lucky franchise owner of 'SpeedDating Inc'. We are the number one organiser of speed-dating events in WhereverYouAre. We would love for you to start organizing new ...
7
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2answers
214 views

Phone pattern security

My phone is unlocked using a security pattern. This is a path drawn through a 3x3 grid of dots with the following rules: The path can start at any dot The path visits neighbouring dots: horizontally,...
8
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2answers
171 views

Intersecting shapes on a flat surface

What is the maximum number of enclosed regions that you can create by drawing two circles and two triangles on a flat surface? Try answering with mathematical arguments.
10
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4answers
799 views

Draw this planar graph

The playing board for this puzzle is a short list of digits; there is one rule governing possible moves: The 1 may swap with a digit one place to the right; the <...
11
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1answer
308 views

Gaby´s Puzzle (Primes Around a Circle)

To keep them busy during lockdown, Gaby asked her children to find a way to place the first sixteen primes (2 to 53) around a circle so that either the sum or difference (or both) of any two of them ...
2
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1answer
91 views

What's the graph relation? #4

What's the relation that joins the nodes? Previous What's the graph relation? #1 What's the graph relation? #2 What's the graph relation? #3
4
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1answer
229 views

What's the graph relation? #3

What's the relation that joins the nodes? Previous What's the graph relation? #1 What's the graph relation? #2
6
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2answers
388 views

Primes in a Line

Place the first 20 primes (2 to 71) in a line so that the sum or difference (or both) of any two primes that find themselves next to each other is always a perfect square. For which other values of N ...
3
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2answers
258 views

How many ways to draw the figure without lifting pencil? [duplicate]

The rules are very simple ... Star at A, end at A. From one point you can to go to the other point by only one line (no turning at cross roads). No going over any line more than once. find the ...
7
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3answers
292 views

What is the minimum count of steps required to complete this dominoes maze?

Here's a map: How to play Legend: (◾) = Start point ★ = Objective ⚑ = End point Mission: ...
3
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1answer
153 views

Sing me the song of days gone by, sing me the song that made me cry

Sing me the song of days gone by, sing me the song that made me cry. The remorse, regret, and pain I'm in, reflects the memories of what has been. Hint 1
6
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1answer
254 views

What's the graph relation? #2

What's the relation that joins the nodes? Open the image in a new tab if you'd like to see the diagram with better resolution. Previous What's the graph relation? #1 Hint 1
4
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1answer
161 views

What's the graph relation? #1

What is the relation that connects the nodes of this digraph?
3
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1answer
120 views

Name that node #2

What is the value of the unknown node? Previous Name that node #1 (Beginner's Level Puzzle)
5
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1answer
119 views

Name that node #1 (Beginner's Level Puzzle)

While Puzzling.SE has some extremely clever and difficult puzzles that are being solved by people whose intellect amazes me, I wanted to make some graph puzzles that were specifically meant for ...
2
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2answers
159 views

A complex matter of relations (What am I?)

There is many-a-kind of number, which sometimes makes me feel dumber. Let's say that we start from zero to four, and see if that leads us to learn some more. Some numbers you might see as a ...
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1answer
109 views

A simple matter of relations (What am I?)

Don't overthink it, just a little fun. Relations are part of graphs, of which I am one. What is my relation? Hint 1
4
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1answer
157 views

Which node(s) does 0 connect with in this simple graph?

If we add 0 as a node to the graph below, which node(s) will it connect to? Hint 0 Hint 1 Hint 2
0
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1answer
285 views

What's the number in the last node of this directed graph?

Hint 1 Hint 2 Hint 3 Background on puzzle (Spoiler Alert)
3
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1answer
247 views

I'm singing a song, can you follow along?

What song am I singing? I apologize for the resolution. If you open the image itself in a new tab you can magnify to get a better look at the words.
11
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1answer
480 views

Which node(s) does 16 connect with in this simple graph?

If we add 16 as a node to the graph below, which node(s) will it connect to? Hint 1 Hint 2 Hint 3 Hint 4 Hint 5
16
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1answer
1k views

What node does 11 point to?

If we included 11 in the diagram below, which node would it connect to? Hint 1
7
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1answer
224 views

Largest set of independent hexominoes

What is the largest set of hexominoes that can be found in which no two of them are such that one can be converted into the other by cutting out one of its component squares (thus obtaining a ...
5
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1answer
534 views

Find how many colors are needed to color all vertices

In this puzzle you need to identify the minimum number of colors needed to color vertices such that no two adjacent vertices ...
7
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2answers
351 views

Finding the most flexible of all 35 hexominoes

Of all 35 hexominoes, which is (or are) the most flexible of all, that is, the one (or ones) that can be converted into the most other hexominoes just by cutting out one of its component squares (thus ...
2
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1answer
112 views

Happy Birthday, Don!

My friend Johan de Ruiter has made a nice puzzle for Donald Knuth's Birthday. The numbers indicate how many connections that candle has. Can you solve it? Original link: https://www-cs-faculty....
20
votes
1answer
1k views

Four mathematicians and their ages

Four mathematicians, none yet a centenarian, meet for coffee. The graph-theorist among them noticed that the common divisor graph of their ages (that is, the graph whose vertices are their ages, two ...
5
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1answer
167 views

Playing Collatz with graphs

a) Given a set of positive integers, its common divisor graph (CD-graph) is the graph whose vertices are the integers, two of which are joined by an edge if (and only if) they have a common divisor ...
18
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2answers
632 views

Another Rook's Tour

Place numbers 1 to 100 in the cells of this 10 x 10 board in such a way that consecutive numbers, and also numbers 1 and 100, occupy neighboring cells (either vertically or horizontally). Prime ...
9
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1answer
299 views

A Demetri Puzzle

Apparently, yesterday was National Puzzle Day (in the US, I think). As part of the celebration, American comedian Demetri Martin posted a puzzle on Twitter: https://twitter.com/DemetriMartin/status/...
19
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3answers
3k views

A rook's tour of the chessboard

Place numbers 1 to 64 in the cells of this 8 x 8 board in such a way that consecutive numbers, and also numbers 1 and 64, occupy neighboring cells (either vertically or horizontally). Shaded cells ...
4
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1answer
143 views

Another series of fortunate (and sideways) transpositions

Using only a sequence of transpositions, see if you can take this: to this: while maintaining English words on each of the three horizontals. At each step, you may transpose any two neighboring ...
14
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2answers
401 views

A series of fortunate transpositions

Using only a sequence of transpositions, see if you can take this: to this: while maintaining English words on each of the three horizontals. At each step, you may transpose any two neighboring ...
7
votes
1answer
172 views

Given a 7x7 grid, what moves need to be made to get two agents on their respective opposite sides of the grid on the diagonal?

Say I had the following 7x7 grid and two agents on the grid facing one another as shown. The agents can follow the following commands: moveForward, turnRight, turnLeft. The agents have to follow the ...

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