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Detalles de la revista
Formato
Revista
eISSN
2182-1976
Publicado por primera vez
16 Apr 2016
Periodo de publicación
2 veces al año
Idiomas
Inglés

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Volumen 6 (2019): Edición 11 (September 2019)

Detalles de la revista
Formato
Revista
eISSN
2182-1976
Publicado por primera vez
16 Apr 2016
Periodo de publicación
2 veces al año
Idiomas
Inglés

Buscar

4 Artículos
Acceso abierto

The 5-Way Scale

Publicado en línea: 11 Oct 2019
Páginas: 5 - 14

Resumen

Abstract

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.

Palabras clave

  • coin weighings
Acceso abierto

Exploring mod 2 n-queens games

Publicado en línea: 11 Oct 2019
Páginas: 15 - 25

Resumen

Abstract

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.

Palabras clave

  • Chess
  • independence
  • -queens
Acceso abierto

New Year Mathematical Card or V Points Mathematical Constant

Publicado en línea: 11 Oct 2019
Páginas: 27 - 33

Resumen

Abstract

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.

Palabras clave

  • second-order plane curve
  • hyperbola
  • ellipse
  • Mathcad
  • pseudo-random number
Acceso abierto

Xor-Magic Graphs

Publicado en línea: 11 Oct 2019
Páginas: 35 - 44

Resumen

Abstract

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.

Palabras clave

  • cubic graph
  • regular graph
  • graph theory
  • combinatorics
  • linear algebra
  • binary
  • xor
4 Artículos
Acceso abierto

The 5-Way Scale

Publicado en línea: 11 Oct 2019
Páginas: 5 - 14

Resumen

Abstract

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.

Palabras clave

  • coin weighings
Acceso abierto

Exploring mod 2 n-queens games

Publicado en línea: 11 Oct 2019
Páginas: 15 - 25

Resumen

Abstract

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.

Palabras clave

  • Chess
  • independence
  • -queens
Acceso abierto

New Year Mathematical Card or V Points Mathematical Constant

Publicado en línea: 11 Oct 2019
Páginas: 27 - 33

Resumen

Abstract

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.

Palabras clave

  • second-order plane curve
  • hyperbola
  • ellipse
  • Mathcad
  • pseudo-random number
Acceso abierto

Xor-Magic Graphs

Publicado en línea: 11 Oct 2019
Páginas: 35 - 44

Resumen

Abstract

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.

Palabras clave

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

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