<abstract xmlns="http://www.w3.org/1999/xhtml">We investigate a type of a Sudoku variant called Sudo-Kurve, which allows bent rows and columns, and develop a new, yet equivalent, variant we call a Sudo-Cube. We examine the total number of distinct solution grids for this type with or without symmetry. We study other mathematical aspects of this puzzle along with the minimum number of clues needed and the number of ways to place individual symbols.</abstract>

Mathematics of a Sudo-Kurve

<abstract xmlns="http://www.w3.org/1999/xhtml">This article presents a simple analysis of cones which are used to generate a given conic curve by section by a plane. It was found that if the given curve is an ellipse, then the locus of vertices of the cones is a hyperbola. The hyperbola has foci which coincidence with the ellipse vertices. Similarly, if the given curve is the hyperbola, the locus of vertex of the cones is the ellipse. In the second case, the foci of the ellipse are located in the hyperbola’s vertices. These two relationships create a kind of conjunction between the ellipse and the hyperbola which originate from the cones used for generation of these curves. The presented conjunction of the ellipse and hyperbola is a perfect example of mathematical beauty which may be shown by the use of very simple geometry. As in the past the conic curves appear to be very interesting and fruitful mathematical beings.</abstract>

Ellipse, hyperbola and their conjunction

<abstract xmlns="http://www.w3.org/1999/xhtml">A <italic>dragon king</italic> is a shogi piece that moves any number of squares vertically or horizontally or one square diagonally but does not move through or jump over other pieces. We construct infinite families of solutions to the <italic>n + k dragon kings problem</italic> of placing <italic>k</italic> pawns and <italic>n + k</italic> mutually nonattacking dragon kings on an <italic>n</italic>×<italic>n</italic> board, including solutions symmetric with respect to quarter-turn or half-turn rotations, solutions symmetric with respect to one or two diagonal reections, and solutions not symmetric with respect to any nontrivial rotation or reection. We show that an <italic>n + k</italic> dragon kings solution exists whenever <italic>n</italic> > <italic>k + 5</italic> and that, given some extra conditions, symmetric solutions exist for <italic>n</italic> > <italic>2k + 5</italic>.</abstract>

Reflections on the <italic>n</italic> +<italic>k</italic> dragon kings problem

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Recreational Mathematics Magazine

The Recreational Mathematics Magazine is published by the Ludus Association with the support of the　Interuniversity Centre for the History of Science and Technology. The journal is electronic and semiannual, and focuses on results that provide amusing, witty but nonetheless original and scientifically profound mathematical nuggets. The issues are published in the exact moments of the equinox. It's a magazine for mathematicians, and other mathematics lovers, who enjoy imaginative ideas, non-standard approaches, and surprising procedures. Occasionally, some papers that do not require any mathematical background will be published.  Examples of topics to be adressed include: games and puzzles, problems, mathmagic, mathematics and arts, math and fun with algorithms, reviews and news.  Recreational mathematics focuses on insight, imagination and beauty. Historically, we know that some areas of mathematics are strongly linked to recreational mathematics - probability, graph theory, number theory, etc. Thus, recreational mathematics can also be very serious. Many professional mathematicians confessed that their love for math was gained when reading the articles by Martin Gardner in Scientific American.  While there are conferences related to the subject as the amazing Gathering for Gardner, and high-quality magazines that accept recreational papers as the American Mathematical Monthly, the number of initiatives related to this important subject is not large.  This context led us to launch this magazine. We will seek to provide a quality publication. We shall endeavor to be read with pleasure. In mathematics, the most important are the underlying ideas and nothing is as exciting as an amazing idea. So, we seek sophistication, imagination and awe.  Rejection Rate   50%   Recreational Mathematics Magazine is a journal for mathematicians who enjoy imaginative ideas, non-standard approaches, and surprising procedures. The journal addresses such topics as: games and puzzles, problems, mathmagic, mathematics and arts, math and fun with algorithms.  Archiving  Sciendo archives the contents of this journal in Portico - digital long-term preservation service of scholarly books, journals and collections.  Plagiarism Policy  The editorial board is participating in a growing community of Similarity Check System's users in order to ensure that the content published is original and trustworthy. Similarity Check is a medium that allows for comprehensive manuscripts screening, aimed to eliminate plagiarism and provide a high standard and quality peer-review process.  Target group:   researchers in the fields of games and puzzles, problems, mathmagic, mathematics and arts, math and fun with algorithms  Financed by Fundação para a Ciência e a Tecnologia, I.P./MCTES through national funds (PIDDAC) – PTDC/HAR-HIS/28627/2017, UIDB/00286/2020 and UIDB/00678/2020. 

Recreational Mathematics Magazine

Volume 5 (2018): Issue 10 (December 2018)

Mathematics of a Sudo-Kurve

Ellipse, hyperbola and their conjunction

Reflections on the n +k dragon kings problem

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