<abstract xmlns="http://www.w3.org/1999/xhtml"> We consider special cases of a modified version of the Tower of Hanoi puzzle and demonstrate how to find upper bounds on the minimum number of moves that it takes to complete these cases.</abstract>

Several Bounds for the K-Tower of Hanoi Puzzle

<abstract xmlns="http://www.w3.org/1999/xhtml"> Picaria is a traditional board game, played by the Zuni tribe of the American Southwest and other parts of the world, such as a rural Southwest region in Sweden. It is related to the popular children’s game of Tic-tac-toe, but the 2 players have only 3 stones each, and in the second phase of the game, pieces are slided, along specified move edges, in attempts to create the three-in-a-row. We provide a rigorous solution, and prove that the game is a draw; moreover our solution gives insights to strategies that players can use.</abstract>

Eternal Picaria

<abstract xmlns="http://www.w3.org/1999/xhtml"> By using two different invariants for the Rubik’s Magic puzzle, one of metric type, the other of topological type, we can dramatically reduce the universe of constructible configurations of the puzzle. Finding the set of actually constructible shapes remains however a challenging task, that we tackle by first reducing the target shapes to specific configurations: the octominoid 3D shapes, with all tiles parallel to one coordinate plane; and the planar “face-up” shapes, with all tiles (considered of infinitesimal width) lying in a common plane and without superposed consecutive tiles. There are still plenty of interesting configurations that do not belong to either of these two collections. The set of constructible configurations (those that can be obtained by manipulation of the undecorated puzzle from the starting situation) is a subset of the set of configurations with vanishing invariants. We were able to actually construct all octominoid shapes with vanishing invariants and most of the planar “face-up” configurations. Particularly important is the topological invariant, of which we recently found mention in [7] by Tom Verhoeff. </abstract>

Exploring the “Rubik's Magic” Universe

<abstract xmlns="http://www.w3.org/1999/xhtml"> Peg solitaire is an old puzzle with a 300 year history. We consider two ways a computer can be utilized to find interesting peg solitaire puzzles. It is common for a peg solitaire puzzle to begin from a symmetric board position, we have computed solvable symmetric board positions for four board shapes. A new idea is to search for board positions which have a unique starting jump leading to a solution. We show many challenging puzzles uncovered by this search technique. Clever solvers can take advantage of the uniqueness property to help solve these puzzles.</abstract>

Designing Peg Solitaire Puzzles

<abstract xmlns="http://www.w3.org/1999/xhtml"> In this article, we reveal how Benjamin Franklin constructed his second 8 × 8 magic square. We also construct two new 8 × 8 Franklin squares</abstract>

Demystifying Benjamin Franklin’s Other 8-Square

<abstract xmlns="http://www.w3.org/1999/xhtml"> The three-pile trick is a well-known card trick performed with a deck of 27 cards which dates back to the early seventeenth century at least and its objective is to uncover the card chosen by a volunteer. The main purpose of this research is to give a mathematical generalization of the three-pile trick for any deck of ab cards with a, b ≥ 2 any integers by means of a finite family of simple discrete functions. Then, it is proved each of these functions has just one or two stable fixed points. Based on this findings a list of 222 (three-pile trick)-type brand new card tricks was generated for either a package of 52 playing cards or any appropriate portion of it with a number of piles between 3 and 7. It is worth noting that all the card tricks on the list share the three main properties that have characterized the three-pile trick: simplicity, self-performing and infallibility. Finally, a general performing protocol, useful for magicians, is given for all the cases. All the employed math techniques involve naive theory of discrete functions, basic properties of the quotient and remainder of the division of integers and modular arithmetic.</abstract>

On a Mathematical Model for an Old Card Trick

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. 

Recreational Mathematics Magazine

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

Games and Puzzles

Several Bounds for the K-Tower of Hanoi Puzzle

Eternal Picaria

Exploring the “Rubik's Magic” Universe

Designing Peg Solitaire Puzzles

Articles

Demystifying Benjamin Franklin’s Other 8-Square

Mathmagic

On a Mathematical Model for an Old Card Trick

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