Questions tagged [graph-theory]

A puzzle built around graphs: sets of nodes joined together by paths.

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7
votes
1answer
157 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
votes
1answer
77 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
votes
1answer
358 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
406 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
votes
1answer
227 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
votes
2answers
342 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
votes
1answer
93 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
vote
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 ...
6
votes
2answers
192 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
169 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
793 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
304 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
56 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
173 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
386 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
votes
2answers
207 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
votes
3answers
282 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
votes
1answer
107 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
209 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
99 views

What's the graph relation? #1

What is the relation that connects the nodes of this digraph?
3
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1answer
78 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
76 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
votes
2answers
116 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 ...
1
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1answer
64 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
105 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
242 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
189 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
votes
1answer
430 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
votes
1answer
529 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
votes
2answers
348 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
votes
1answer
111 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
votes
1answer
162 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
629 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
votes
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
votes
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
votes
1answer
141 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
votes
2answers
399 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
169 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 ...
12
votes
2answers
495 views

Heavens to Megatron!

See if you can fill in all the blank letter tiles in this graph using the clues sets below. Each set of clues yields a name or word. The name or word is guaranteed to follow some connected path ...
14
votes
2answers
295 views

Happy birthday Ramanujan!

On December 22 2019, Ramanujan would have been 132 years old. In his memory here are two puzzles around 132. In the six vertices of each of these graphs place six positive integers that add up to ...
5
votes
1answer
146 views

The grandest zoo in Appelhaken

In the magnificent country of Appelhaken there is a zoo. Not just any zoo, but a grand zoo, a magnificent zoo, called Appelhaken Grand Magnificent Magnificent Grand Grand Zoo. In this zoo there are ...
8
votes
1answer
174 views

The grandest bridge in Appelhaken [duplicate]

In the capital of the grand country of Appelhaken there is a plane garden containing four magnificent monuments. So magnificent are they that the country has a Law requiring that there must be a ...
2
votes
3answers
164 views

Problems on Graphs

I want to test if someone with no experience in Graph Theory can solve my Problems involving Graphs. If you do know some Graph Theory I'd appreciate if you let me know in your answer. They do not ...
0
votes
2answers
119 views

Painting edges of a 3x3 grid with 4 colours

Can you paint the edges of a 3x3 grid with 4 colours, such that: The colours of edges of every 1x1 square are different. The colours of edges adjacent to every vertex are different. Here is a ...
0
votes
1answer
77 views

Painting edges of a 2x2 grid with 4 colours

Can you paint the edges of a 2x2 grid with 4 colours, such that: The colours of edges of every 1x1 square are different. The colours of edges adjacent to every vertex are different. Good luck!
9
votes
1answer
522 views

Connect the wires without setting off the bomb

You just saw a planted time bomb! Just 5 minutes are remaining until it explodes and as you are in currently in a rural area (no bomb disposal squad) and you know how bombs usually work it is up to ...
8
votes
1answer
582 views

Winning the Lottery

Bob: I hear you won the lottery. Alice: So I did! Bob: What six numbers did you win it with? Alice: Can't remember. All I recall is that they were all different, and none greater than 28. Bob: ...