# Volume 10 (2023): Edizione 17 (January 2023)

Dettagli della rivista
Formato
Rivista
eISSN
2182-1976
Pubblicato per la prima volta
16 Apr 2016
Periodo di pubblicazione
2 volte all'anno
Lingue
Inglese

0 Articoli
Accesso libero

#### Economical Dissections

Pubblicato online: 27 Jan 2023
Pagine: 1 - 39

#### Astratto

The Wallace-Bolyai-Gerwien theorem states any polygon can be decomposed into a finite number of polygonal pieces that can be translated and rotated to form any polygon of equal area. The theorem was proved in the early 19th century. The minimum number of pieces necessary to form these common dissections remains an open question. In 1905, Henry Dudney demonstrated a four-piece common dissection between a square and equilateral triangle. We investigate the possible existence of a three-piece common dissection. Specifically, we prove that there does not exist a three-piece common dissection using only convex polygons.

Accesso libero

#### How Unfair is the Unfair Dodgem?

Pubblicato online: 27 Jan 2023
Pagine: 41 - 50

#### Astratto

We study a very simple 2-player board game called Dodgem, curiously the game is difficult to analyze when the number of tokens is not the same for the two players. We provide theoretical and experimental elements which indicate which player benefits from the asymmetry of the game.

Accesso libero

#### Fun with Latin Squares

Pubblicato online: 27 Jan 2023
Pagine: 51 - 74

#### Astratto

Do you want to know what an anti-chiece Latin square is? Or what a non-consecutive toroidal modular Latin square is? We invented a ton of new types of Latin squares, some inspired by existing Sudoku variations. We can’t wait to introduce them to you and answer important questions, such as: do they even exist? If so, under what conditions? What are some of their interesting properties? And how do we generate them?

Accesso libero

#### Go First Dice for Five Players and Beyond.

Pubblicato online: 27 Jan 2023
Pagine: 75 - 87

#### Astratto

Before a game begins, the players need to decide the order of play. This order of play is determined by each player rolling a die. Does there exist a set of dice such that draws are excluded and each order of play is equally likely? For four players the solution involves four 12-sided dice, sold commercially as Go First Dice. However, the solution for five players remained an open question. We present two solutions. The first solution has a particular mathematical structure known as binary dice, and results in a set of five 60-sided dice, where every place is equally likely. The second solution is an inductive construction that results in one one 36-sided die; two 48-sided dice; one 54-sided die; and one 20-sided die, where each permutation is equally likely.

Accesso libero

#### How to Read a Clock

Pubblicato online: 27 Jan 2023
Pagine: 89 - 96

#### Astratto

In this paper we present several binary clocks. Using different geometric figures, we show how one can devise various novel ways of displaying time. We accompany each design with the mathematical background necessary to understand why these designs work.