# Volume 6 (2019): Edition 11 (September 2019)

Détails du magazine
Format
Magazine
eISSN
2182-1976
Première publication
16 Apr 2016
Période de publication
2 fois par an
Langues
Anglais

4 Articles
Accès libre

#### The 5-Way Scale

Publié en ligne: 11 Oct 2019
Pages: 5 - 14

#### Résumé

In this paper, we discuss coin-weighing problems that use a 5-way scale which has five different possible outcomes: MUCH LESS, LESS, EQUAL, MORE, and MUCH MORE. The 5-way scale provides more information than the regular 3-way scale. We study the problem of finding two fake coins from a pile of identically looking coins in a minimal number of weighings using a 5-way scale. We discuss similarities and differences between the 5-way and 3-way scale. We introduce a strategy for a 5-way scale that can find both counterfeit coins among 2k coins in k + 1 weighings, which is better than any strategy for a 3-way scale.

#### Mots clés

• coin weighings
Accès libre

#### Exploring mod 2 n-queens games

Publié en ligne: 11 Oct 2019
Pages: 15 - 25

#### Résumé

We introduce a two player game on an n × n chessboard where queens are placed by alternating turns on a chessboard square whose availability is determined by the parity of the number of queens already on the board which can attack that square. The game is explored as well as its variations and complexity.

• Chess
• independence
• -queens
Accès libre

#### New Year Mathematical Card or V Points Mathematical Constant

Publié en ligne: 11 Oct 2019
Pages: 27 - 33

#### Résumé

The article describes an attempt to define a new mathematical constant - the probability of obtaining a hyperbola or an ellipse when throwing five random points on a plane.

#### Mots clés

• second-order plane curve
• hyperbola
• ellipse
• pseudo-random number
Accès libre

#### Xor-Magic Graphs

Publié en ligne: 11 Oct 2019
Pages: 35 - 44

#### Résumé

A connected graph on 2n vertices is defined to be xor-magic if the vertices can be labeled with distinct n-bit binary numbers in such a way that the label at each vertex is equal to the bitwise xor of the labels on the adjacent vertices. We show that there is at least one 3-regular xor-magic graph on 2n vertices for every n ⩾ 2. We classify the 3-regular xor-magic graphs on 8 and 16 vertices, and give multiple examples of 3-regular xor-magic graphs on 32 vertices, including the well-known Dyck graph.

#### Mots clés

• cubic graph
• regular graph
• graph theory
• combinatorics
• linear algebra
• binary
• xor