<abstract xmlns="http://www.w3.org/1999/xhtml">

We present placements of mutually non-attacking chess pieces of mixed type that occupy more than half of the squares of an <italic>m</italic> × <italic>n</italic> board. If both white and black pawns are allowed as separate types, there are arrangements, which we also present, that occupy at least two-thirds of the board squares.
</abstract>

Arrangements of mutually non-attacking chess pieces of mixed type

<abstract xmlns="http://www.w3.org/1999/xhtml">

This paper shows our discovery of the fiboquadratic numbers, quadratic Fibonacci numbers in rithmomachia. This board game consists in performing mathematical operations to attack an opponent through geometric numbered pieces. We will show that the numbers on the board pieces are the first terms of six sequences that we will define through a recursive pattern of superpartients. We then prove that this extension is the solution of a recurrence relation with initial conditions, and therefore, is unique. The fiboquadratic numbers we introduce in this work are not limited to the context of this board. In general, we can generate any fiboquadratic sequence with arbitrary initial conditions.
</abstract>

Universidad Nacional Experimental Politécnica “Antonio José de Sucre”, Vice-rectory of Barquisimeto

Fiboquadratic numbers and Rithmomachia

<abstract xmlns="http://www.w3.org/1999/xhtml">

The game <italic>Spot It!</italic> is played with a deck of cards in which every pair of cards has exactly one matching symbol and the aim is to be the fastest at finding the match. It is known that finite projective planes correspond to decks in which every card contains <italic>n</italic> symbols and every symbol appears on <italic>n</italic> cards. In this paper we relax the hypothesis on the number of cards on which a symbol appears: we study symmetric decks in which every symbol appears the same number of times and we introduce the concept of <italic>maximal</italic> deck, providing a sufficient condition for a deck to have this property. We also produce various examples of interesting decks which do not correspond to projective planes.
</abstract>

On the existence of <italic>Spot It!</italic> decks that are not projective planes

<abstract xmlns="http://www.w3.org/1999/xhtml">

A standard deck of 52 playing cards has 4 suits: clubs (♣), spades (♠), hearts (♥) and diamonds (♦). Each suit has 13 denominations, or ranks, 2, 3, 4, 5, 6, 7, 8, 9, 10, J (Jack), Q (Queen), K (King) and A (Ace). But sometimes, a card goes missing – lost between the couch cushions, clothes-pinned in the bike spokes, filched by the cat, eaten by the dog (see Figure 1), or maybe misplaced in a matching deck. You may find yourself not playing with a full deck. Building a house of cards? No problem. Playing poker? Problem. Or is it? Ask yourself the following question:
What is the probability of being dealt a Two-Pair hand of five cards from a well-shuffled deck when the Ace of Spades is missing from the deck? Specifically, how does it compare to the probability of being dealt a Two-Pair hand from a standard 52-card deck?
What does your ‘probability intuition’ tell you? On the one hand, with a missing Ace of Spades there are fewer Two-Pair hands. On the other hand, there are also fewer total five-card hands. The ratio of these two numbers defines the probability; which way it goes seems unclear. Let’s do the calculation – first for the standard 52-card deck and then for the 51-card deck missing the Ace of Spades.
</abstract>

Not Playing With a Full Deck?

<abstract xmlns="http://www.w3.org/1999/xhtml">

This is a fairy tale taking place in Chessland, located in the Bermuda triangle. The chess pieces survey their land and trap enemy pieces. Behind the story, there is fascinating mathematics on how to optimize surveying and trapping. The tale is written by the students in the PRIMES STEP junior group, who were in grades 6 through 9. The paper has a conclusion, written by the group’s mentor, Tanya Khovanova, explaining the students’ results in terms of graph theory.
</abstract>

The Struggles of Chessland

<abstract xmlns="http://www.w3.org/1999/xhtml">

The one-cushion escape from snooker in a circular table can be viewed as a ge-ometric problem involving the reflection of a light ray in a circular mirror. There are at most four escapes in any given configuration. We will obtain specific configurations in which there are exactly 0, 1, 2, 3 or 4 escapes. The details consist in determining the number of real solutions in the interval (−1; 1) of certain polynomial equations, of degrees two, three or four.
</abstract>

The One-Cushion Escape from Snooker in a Circular Table

<abstract xmlns="http://www.w3.org/1999/xhtml">

The Game of Cycles is an impartial game on a planar graph that was introduced by Francis Su. In this short note we address some questions that have been raised on the game, and raise some further questions. We assume that the reader is familiar with basic notions from combinatorial game theory.
</abstract>

Some remarks on the Game of Cycles

AHEAD OF PRINT

Volume 11 (2024): Issue 18 (March 2024)

Volume 10 (2023): Issue 17 (January 2023)

Volume 9 (2022): Issue 16 (June 2022)

Volume 8 (2021): Issue 15 (November 2021)

Volume 8 (2021): Issue 14 (October 2021)

Volume 7 (2020): Issue 13 (November 2020)

Volume 6 (2019): Issue 12 (December 2019)

Volume 6 (2019): Issue 11 (September 2019)

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

Volume 5 (2018): Issue 9 (September 2018)

Volume 4 (2017): Issue 8 (December 2017)

Volume 4 (2017): Issue 7 (May 2017)

Volume 3 (2016): Issue 6 (December 2016)

Volume 3 (2016): Issue 5 (March 2016)

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. 