Questions tagged [graph-theory]

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

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14
votes
1answer
306 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
143 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 ...
11
votes
2answers
473 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 ...
13
votes
2answers
266 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
138 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
166 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
144 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
103 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
64 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
496 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
549 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: ...
10
votes
2answers
547 views

National Graph Lottery

In UK's National Lottery players choose 6 different whole numbers in the range 1 to 59, and win a large prize if all six match with the day's draw. Each choice of six numbers by a player gives rise ...
12
votes
1answer
401 views

The arrow of time flies in reverse

Here is the puzzle: (Click on the image to see a larger image.) Overview: This is a word graph. The nodes are short words, the edges are long words. Whenever an edge (i.e., a long word) connects ...
10
votes
2answers
587 views

A Magic Flying Saucer

Place 19 different positive integers on the vertices of this graph so that the 13 products of three numbers in a straight line are all equal. Do so in such a way that the product is as small as ...
5
votes
1answer
210 views

Uncover Lenny Fingers' street hustle

Lenny Fingers is out on the street again, hustling people with his shell games. This time, he's using words. As you walk by, Lenny grabs you with an enthusiastic smile and shows you two words side-...
15
votes
1answer
335 views

Newton's cradles

I went to one of those discovery stores and picked up a few Newton's cradles, except these have hanging words instead of hanging spheres. Check it out: This one has a starter pendulum with two ...
7
votes
1answer
192 views

Stars of the Celestial Bagua

Check this out: Okay, it might be more impressive if I show you what is moving along the arrows: At every vertex in a long word. Flowing in to every vertex are two short words ("inputs"). ...
13
votes
1answer
1k views

Primes in a Diamond

Label the vertices of this graph with numbers 1 to 16 in such a way that the edges between any two vertices whose sum and absolute difference are both primes are precisely the edges of a hamiltonian ...
10
votes
4answers
329 views

Choo-choo! Word trains

All aboard the Word Train Express! Engineering a word train is simple: I'll give you the locomotive (the first word) and the caboose (the last word), and I'll specify the number of boxcars (...
4
votes
1answer
226 views

London Underground puzzle

This is something I have thought about during my commute through the London Underground. Is it possible to make a trip through the London underground in such a way that: You have to use all ...
24
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5answers
2k views

Superhero words!

Quietly walking among us are words which are actually superheroes in disguise! Just as Diana Prince spins around to become Wonder Woman, some seemingly ordinary words can spin around to reveal their ...
12
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2answers
2k views

My Graph Theory Students

I have 18 students in my graph theory course this semester: Anne, Bernard, Clare, David,..., and Rachel. At the start of the course I asked them to draw the graph below, in which each of them is ...
-1
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2answers
118 views

Can this be drawn in one line without going over the line?

Can this image be drawn in one line and without going over any lines?
17
votes
2answers
521 views

Maximum Height of a Hotel with Strange Elevators

I encountered this puzzle many years ago, and I think back on it often as it is unique and thought provoking. As far as I know nobody has proved the given solution as optimum, so it may still be ...
6
votes
7answers
323 views

Find minimum number of meeting periods to reach 2 degrees of separation for a group [closed]

I am running a training course and I want to arrange a set of 1:1 meeting periods between the participants such that at the end of the day there is a maximum of 2 degrees of separation between any of ...
10
votes
1answer
1k views

How many colors does it take?

This question is from a popular monthly science magazine in my country: You have an 8x8 square where any 3 squares forming a tromino (including reflections and rotations) must consist of three ...
4
votes
2answers
154 views

Identify this type of graph puzzle

There are $V-1$ pieces, each with an identifying symbol. The board is a graph with $V$ vertices and some number of edges $E$. The idea is to move around the pieces so that each piece's symbol matches ...
0
votes
1answer
119 views

A Colorful Honeycomb

What strategy can you use to color using only 6 colors the lines in an infinite hexagonal tiling such that no two sides of the same hexagon have the same color?
11
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6answers
734 views

I Have To Be With Them!

It's almost time for another year of school! But before school starts, Principal Little needs to form classes. Because there are so many people in a class, the parents are always complaining, asking ...
3
votes
1answer
213 views

Create a map of a game's portals

Given a set of rooms, each with a N, a S, an E, and a W exit/entrance to another of the rooms, create as simple a map as possible that graphically represents their connections. The rooms in question ...
-4
votes
1answer
365 views

A party of jealous guys

I was really happy for the fact that I won the inter-galactic best magician award. So I decided to throw a party of $n$ people (excluding me). The people who came to that party was jealous, really ...
22
votes
1answer
757 views

A Tour Around a Triangle

Place the 18 even integers between 2 and 36 in the empty nodes of this triangular graph in such a way that if a path is drawn by coloring in red all the edges joining any two nodes whose numbers add ...
17
votes
1answer
503 views

A partition of 1000 into nine parts

The sum of nine whole numbers is 1000. If those numbers are placed on the vertices of this graph, two of them will be joined by an edge if and only if they have a common divisor greater than 1 (i.e. ...
14
votes
3answers
381 views

Fearful asymmetry

An asymmetric graph (or identity graph) has every vertex unique: no different relabeling of the vertices leaves the edges unchanged. The trivial graph on one vertex is (trivially) asymmetric. All ...
11
votes
1answer
483 views

Any hope for Humpty Dumpty?

It was inevitable, really... Each fragment of shell has exactly three sharp points, joined by smooth curves. While the King's horses can count reasonably well, his men have been known to confuse ...
4
votes
2answers
258 views

How many nodes in the network?

I don't actually have a solution in mind for these, but it seemed puzzly enough to bring to the table. Seems as though someone must have come up with this before, but if so, I couldn't find it when I ...
5
votes
3answers
563 views

Magic-preserving Permutations on a 4x4 Magic Square

Messing around with some magic-square puzzles, I faced the problem of deciding whether some two magical squares are, in fact, the one and same square wearing a different hat. It seemed to me, that for ...
7
votes
2answers
213 views

A partition of 1000 into six parts with least and greatest product possible

Find six positive natural numbers, not necessarily distinct, whose sum is 1000 and which, if placed appropriately on the vertices of the following graph, two of them will be joined by an edge if and ...
16
votes
3answers
2k views

A partition of 100 into nine parts

The sum of $9$ positive natural numbers, not necessarily distinct, is $100$. If placed appropriately on the vertices of the following graph, two of them will be joined by an edge if and only if they ...
24
votes
7answers
6k views

Hacking an electronic keypad

You are a spy trying to break into an enemy facility. The back door is protected by an electronic keypad lock. You know that this particular lock is opened by a four digit code. Any stream of button ...
1
vote
1answer
269 views

Scheduling Meetings

I came across this problem in real life and thought it could be made into an interesting puzzle. I will enjoy seeing how my eventual solution could be improved! Here's the situation. There ...
5
votes
2answers
188 views

Triangle of Safety

Saitama: "The Hero Association called me for a low-level mission, can you meet them as my representative?" Genos: "No." Saitama: "Aww, man.. That's not fun." Then Saitama decided to meet Hero ...
7
votes
1answer
187 views

Trip Routes that Visit 9 of 10 Cities

There are 10 cities on this island. For each pair of cities, they may have a bidirectional path. A trip route is defined as a route which start on a city e.g. $A$, goes to 8 of 9 other cities exactly ...
4
votes
1answer
312 views

A certain partition of 130

Given a multiset of positive integers, its P-graph is the loopless graph whose vertex set consists of those integers, any two of which are joined by an edge if they have a common divisor greater than ...
7
votes
2answers
283 views

Teacup geometry

Inspired by the three utilities puzzle from prog_SAHIL I'm now posting a similar puzzle that makes use of the topology of a cup with a handle: The question is: How many distinct points can you ...
5
votes
1answer
190 views

A minor rearrangement of the one sided hexominoes in 12 simultaneous shapes

Here are the one sided hexominoes arranged into 12 congruent shapes. But there are one or two flaws: The dark blue hexominoes, which are the symmetric ones, may not occur more than once each in a ...
14
votes
2answers
368 views

Hexominoes into 7 simultaneous congruent shapes

I came up with this puzzle 16 years ago, it was on Ed Pegg's Mathpuzzle site but nobody solved it AFAIK. The 35 hexominoes (which look like this): are to be arranged, in groups of five, into seven ...
12
votes
5answers
1k views

Soccer balls in the stadium

The coach asks you take as many soccer balls as possible and put those balls onto the field with the condition that For any arbitrary set of three balls, at least two of those balls are exactly 10 ...
12
votes
1answer
302 views

Multibranched tree

The Furca Fractalis tree grows in a very special way. Starting with the trunk there are three possibilities to continue growing: It can split in two branches. It can grow one branch and one leaf. ...
12
votes
1answer
365 views

Jigsaw Logic: ?s galore

I am working on a 256 piece jigsaw puzzle, but I am having a lot of trouble. Instead of the picture being a landscape or painting, the final image is just a sixteen by sixteen grid of identical ...