# graph-theory's questions - English 1answer

80 graph-theory questions.

### A party of jealous guys

1 answers, 183 views mathematics graph-theory
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 ...

### 17 A partition of 1000 into nine parts

1 answers, 447 views number-theory graph-theory arithmetic
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. ...

### 20 A Tour Around a Triangle

1 answers, 660 views number-theory graph-theory arithmetic
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 ...

### 13 Fearful asymmetry

3 answers, 328 views mathematics graph-theory
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 ...

### 10 Any hope for Humpty Dumpty?

1 answers, 418 views mathematics graph-theory
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 ...

### 3 How many nodes in the network?

2 answers, 217 views mathematics strategy graph-theory 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 Magic-preserving Permutations on a 4x4 Magic Square

3 answers, 191 views combinatorics graph-theory 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 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 ...

### 31 Draw a line through all doors

17 answers, 20.158 views combinatorics graph-theory
I saw the following problem on 4chan and couldn't solve it: It's very likely to be some kind of troll (no solution). I'm hoping to see some rigorous proofs that disprove the existence of such a line....

### 15 A partition of 100 into nine parts

3 answers, 1.909 views mathematics graph-theory arithmetic
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 ...

### 10 Labelling a graph with a partition of 100

Label the vertices of this graph with positive integers (repetitions allowed) whose sum is 100 in such a way that any pair of vertices are joined by an edge if (and only if) they have labels with a ...

### 22 Hacking an electronic keypad

7 answers, 4.170 views combinatorics algorithm graph-theory
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 ...

### 2 Scheduling Meetings

1 answers, 256 views optimization algorithm graph-theory real
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 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 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 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 ...

### 6 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 ...

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

1 answers, 133 views geometry graph-theory tiling polyomino
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 Hexominoes into 7 simultaneous congruent shapes

2 answers, 303 views geometry graph-theory tiling polyomino
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 ...