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        <title>Recreational Mathematics Magazine Feed</title>
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            <title>Recreational Mathematics Magazine Feed</title>
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        <copyright>All rights reserved 2026, Ludus Association</copyright>
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            <title><![CDATA[The Seven Dice Shuffle]]></title>
            <link>https://reference-global.com/article/10.2478/rmm-2026-0006</link>
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            <pubDate>Wed, 27 May 2026 00:00:00 GMT</pubDate>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[Some Mathematics in the Game Polygon]]></title>
            <link>https://reference-global.com/article/10.2478/rmm-2026-0005</link>
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            <pubDate>Wed, 27 May 2026 00:00:00 GMT</pubDate>
            <category>ARTICLE</category>
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        <item>
            <title><![CDATA[Card Games Unveiled: Exploring the Underlying Linear Algebra]]></title>
            <link>https://reference-global.com/article/10.2478/rmm-2026-0001</link>
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            <pubDate>Wed, 27 May 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[We discuss four famous card games that can help learn linear algebra. The games are: SET, Socks, Spot it!, and EvenQuads. We describe the game in the language of vector, affine, and projective spaces. We also show how these games are connected to each other. A separate section is devoted to playing Socks with the EvenQuads deck and vice versa.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[How many mutually non-attacking, non-knight pieces can we place on an m × n chessboard?]]></title>
            <link>https://reference-global.com/article/10.2478/rmm-2026-0002</link>
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            <pubDate>Wed, 27 May 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[How many black and white chess pieces – excluding knights – can we place on the squares of an m × n chess board so that none of those pieces attack any other piece? We answer this question for all rectangular boards. If n &gt; 1, the answer is 



⌊ 2m3 ⌋
\left\lfloor {{{2m} \over 3}} \right\rfloor


 plus either 0, 1, or 2.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[Metric spaces in chess and international chess pieces graph diameters]]></title>
            <link>https://reference-global.com/article/10.2478/rmm-2026-0003</link>
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            <pubDate>Wed, 27 May 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[This paper aims to study the graph radii and diameters induced by the k-dimensional versions of the well-known six international chess pieces on every finite {n×n×· · ·×n} ⊆ ℤk lattice since they originate as many interesting metric spaces for every proper pair (n, k). For this purpose, we finally discuss a mathematically consistent generalization of all the planar FIDE chess pieces to an appropriate k-dimensional environment, finding (for all k ∈ ℤ+) the exact values of the graph radii and diameters of the k-rook, k-king, k-bishop, and the corresponding values for the 3-queen, 3-knight, and 3-pawn. We also provide tight bounds for the graph radii and diameters of the k-queen, k-knight, and k-pawn, holding for every k ⩾ 4.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[Louis Gros’s Theory of the Chinese Rings]]></title>
            <link>https://reference-global.com/article/10.2478/rmm-2026-0004</link>
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            <pubDate>Wed, 27 May 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[After Pacioli and Cardano in the 16th, Wallis in the 17th, and Lichtenberg in the 18th century, it was the French legal professional Louis Gros who published in 1872 a Théorie du Baguenodier. The small book was based on the revolutionary new idea to marry the mechanical puzzle which is now known as the Chinese Rings with the binary number system. An unpublished, much broader manuscript, discovered recently by Lisa Rougetet, offers new insight into Gros’s biography and the circumstances of his scientific achievements. Although the mathematical results were mainly empirical, we will demonstrate that they are all well-founded in modern interpretation.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[Some mathematical and geometrical interpretations of the Sator Square]]></title>
            <link>https://reference-global.com/article/10.2478/rmm-2025-0009</link>
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            <pubDate>Fri, 28 Nov 2025 00:00:00 GMT</pubDate>
            <description><![CDATA[In 1738, the King of Naples and future King of Spain, Carlos III, commissioned the Spanish military engineer Roque Joaquín de Alcubierre to begin the excavations of the ruins of the ancient Roman city of Pompeii and its surroundings, buried by the terrible explosion of Vesuvius in AD 79. Since that time, archaeologists have brought to light wonderful treasures found in the among ruins. Among them, the Sator Square is one of the most peculiar, apparently simple but mysterious. Supernatural and medicinal powers have been attributed to this object and its use was widespread during the Middle Age. Studies to explain its origin and meaning have been varied. There are theories that relate it to religion, the occult, medicine and music. However, no explanation has been convincing beyond pseudo-scientific sensationalism. In this study, the author intends to eliminate the mystical character of the Sator Square and suggests considering it as a simple palindrome or a game of words with certain symmetrical properties. However, these properties are not exclusive to the Sator Suare but are present in various mathematical and geometric objects.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[Reverse Divisors and Magic Numbers]]></title>
            <link>https://reference-global.com/article/10.2478/rmm-2025-0012</link>
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            <pubDate>Fri, 28 Nov 2025 00:00:00 GMT</pubDate>
            <description><![CDATA[The study examines the relationship between Ball’s magic numbers and reverse divisors. These numbers are the source of beautiful and curious properties. Activities related to numbers can be a fun way to motivate mathematics students, while also enabling surprising analysis and connections.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[Beyond chance: Predicting the unpredictable]]></title>
            <link>https://reference-global.com/article/10.2478/rmm-2025-0008</link>
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            <pubDate>Fri, 28 Nov 2025 00:00:00 GMT</pubDate>
            <description><![CDATA[The outcome of a randomly tossed fair coin is generally considered unpredictable in the sense that the probability of a successful prediction is always 1/2. But there are scenarios, highly contrived, where successful predictions are expected more often than not. Two such scenarios are presented, raising questions as to their real-world relevance.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[The Odd Hummer Principle]]></title>
            <link>https://reference-global.com/article/10.2478/rmm-2025-0011</link>
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            <pubDate>Fri, 28 Nov 2025 00:00:00 GMT</pubDate>
            <description><![CDATA[The Hummer Principle was born from the mind of Bob Hummer in 1946, which consists of performing card shuffles with an even number of cards while leaving some properties of the deck intact. In this document, we will present a generalization of this principle for an odd number of cards, along with ideas for applying and adapting magic tricks that use the Hummer Principle to a more general setting. Finally, we will discuss future work in this area.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[Magic Venn Diagrams]]></title>
            <link>https://reference-global.com/article/10.2478/rmm-2025-0010</link>
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            <pubDate>Fri, 28 Nov 2025 00:00:00 GMT</pubDate>
            <description><![CDATA[A magic Venn diagram (MVD) of order n, size r, degree d and magic sum m is a Venn diagram of n sets A1, A2, . . . , An, in which r of the 2n non-overlapping Venn regions are weighted 1-1 by the numbers 1, 2, . . . , r in such a way that each set Ai contains d weights adding up to the constant m. After demonstrating how MVDs arise and how they encompass a broad array of magic figures, we give results on the frequencies of different MVD’s of orders 3 and 4, by combinatorial type and magic sum. Illustrations and explanations are given for several of the smaller types.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[Connecting parking functions to another classic car-related puzzle]]></title>
            <link>https://reference-global.com/article/10.2478/rmm-2025-0004</link>
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            <pubDate>Thu, 26 Jun 2025 00:00:00 GMT</pubDate>
            <description><![CDATA[Parking functions are a well-studied area of combinatorics that have connections to Cayley’s tree formula, Catalan numbers, Dyck paths, and much more. We connect parking functions to another classic car-related puzzle called the gas stations puzzle. Looking at it through this lens, we give two new proofs of results in this area that are natural extensions of the original connection.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[A Mathematical Analysis of Tilt]]></title>
            <link>https://reference-global.com/article/10.2478/rmm-2025-0007</link>
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            <pubDate>Thu, 26 Jun 2025 00:00:00 GMT</pubDate>
            <description><![CDATA[The logic game Tilt has 40 challenge cards labeled beginner, intermediate, advanced, and expert. In this article, we use mathematics to analyze the game and use various techniques to measure its difficulty. We create a digraph for each game’s possible configurations and use the graph’s properties to determine its difficulty. We also imagine random gameplay and use the theory of absorbing Markov chains to analyze the difficulty of the game.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[Coins that Change Their Weights]]></title>
            <link>https://reference-global.com/article/10.2478/rmm-2025-0005</link>
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            <pubDate>Thu, 26 Jun 2025 00:00:00 GMT</pubDate>
            <description><![CDATA[As in many coin puzzles, we have several identical-looking coins, with one of them fake and the rest real. The real coins weigh the same. Our fake coin is special in that it can change its weight. The coin can pretend to be a real coin, a fake coin that is lighter than a real one, and a fake coin that is heavier than a real one. In addition, each time the coin is on the scale, it changes its weight in a predetermined fashion.In this paper, we seek to find our fake coin using a balance scale and the smallest number of weighings.We consider different possibilities for the fake coin. We discuss coins that change weight between two states or between three states. The 2-state coin that changes weight from lighter to real and back has been studied before, so we concentrate on the 2-state coin that changes weight from lighter to heavier and back. We also study the 3-state coin, which changes its weight from lighter to heavier to real and back to lighter.Given the total number of coins and the starting state of the fake coin, we calculate the smallest number of weighings needed to identify the fake coin. We provide an oblivious optimal strategy for this number of weighings. We also discuss what happens if the starting state is unknown or mixed. In such cases, adaptive strategies are often more powerful than oblivious ones.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[Generalized Triangular Numbers and Combinatorial Explanations]]></title>
            <link>https://reference-global.com/article/10.2478/rmm-2025-0006</link>
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            <pubDate>Thu, 26 Jun 2025 00:00:00 GMT</pubDate>
            <description><![CDATA[The formula for the sums of the first integers, which are known as triangular numbers, is well known and there are many proofs for it: by induction, graphical, by combinatorics, etc. The sum of the first triangular numbers is known as tetrahedral numbers. In this article1, we discuss a generalization of triangular and tetrahedral numbers where the number of summation symbols is variable. We repeat results from the literature that state that these so-called generalized triangular numbers can be represented via multicombinations, i.e. combinations with repetitions, and give an illustrative explanation for this formula, which is based on combinatorics. Via high-dimensional illustrations, we show that these generalized triangular numbers are figurate numbers, namely hyper-tetrahedral numbers, see Figure 1. Additionally, we demonstrate that there is a relation between the height and the dimension of these hypertetrahedra, i.e. a series of generalized triangular numbers with fixed dimension and varying height can be represented as such a series with fixed height and varying dimension, and vice versa.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[Maximum arrangements of nonattacking kings on the 2n × 2n chessboard]]></title>
            <link>https://reference-global.com/article/10.2478/rmm-2025-0003</link>
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            <pubDate>Thu, 26 Jun 2025 00:00:00 GMT</pubDate>
            <description><![CDATA[To count the number of maximum independent arrangements of n2 kings on a 2n × 2n chessboard, we build a 2n × (n + 1) matrix whose entries are independent arrangements of n kings on 2 × 2n rectangles. Utilizing upper and lower bound functions dependent of the entries of the matrix, we recursively construct independent solutions, and provide an equation and algorithm.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[Star Anagram Detection and Classification]]></title>
            <link>https://reference-global.com/article/10.2478/rmm-2025-0002</link>
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            <pubDate>Thu, 26 Jun 2025 00:00:00 GMT</pubDate>
            <description><![CDATA[A star anagram is a rearrangement of the letters of one word to produce another word where no letter retains its original neighbors. These maximally shuffled anagrams are rare, comprising only about 5.7% of anagrams in English. They can also be depicted as unicursal polygons with varying forms, including the eponymous stars. We develop automated methods for detecting stars among other anagrams and for classifying them based on their polygon’s degree of both rotational and reflective symmetry. Next, we explore several properties of star anagrams including proofs for two results about the edge lengths of perfect, i.e., maximally symmetric, stars leveraging perhaps surprising connections to modular arithmetic and the celebrated Chinese Remainder Theorem. Finally, we conduct an exhaustive search of English for star anagrams and provide numerical results about their clustering into common shapes along with examples of geometrically noteworthy stars.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[Two eggs any style generalizing egg-drop experiments]]></title>
            <link>https://reference-global.com/article/10.2478/rmm-2025-0001</link>
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            <pubDate>Thu, 26 Jun 2025 00:00:00 GMT</pubDate>
            <description><![CDATA[The egg-drop experiment introduced by Konhauser, Velleman, and Wagon, later generalized by Boardman, is further generalized to two additional types. The three separate types of egg-drop experiment under consideration are examined in the context of binary decision trees. It is shown that all three types of egg-drop experiment are binary decision problems that can be solved efficiently using a non-redundant algorithm—a class of algorithms introduced here. The preceding theoretical results are applied to the three types of egg-drop experiment to compute, for each, the maximum height of a building that can be dealt with using a given number of egg-droppings.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[No π for you!]]></title>
            <link>https://reference-global.com/article/10.2478/rmm-2024-0011</link>
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            <pubDate>Fri, 20 Sep 2024 00:00:00 GMT</pubDate>
            <description><![CDATA[In which we serve up several helpings of not- π.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[Stern, Gamow, and the Shabbat Elevator Effect]]></title>
            <link>https://reference-global.com/article/10.2478/rmm-2024-0009</link>
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            <pubDate>Fri, 20 Sep 2024 00:00:00 GMT</pubDate>
            <description><![CDATA[In addition to being known for their other work, physicists George Gamow and Marvin Stern also published an analysis of an intriguing problem regarding their perception that although both worked on different floors, it seemed that the first elevator to arrive on their respective floors was traveling in the opposite direction of their destination. In this manuscript, a fictitious conversation occurs between the two in regards to the probability of the elevator stopping on every floor (which they term the Shabbat Effect). One claims that it is the number of elevator occupants that predominates whereas the other claims it is the number of floors in the building that predominates in giving rise to this effect. Equations for estimating the probability of the Shabbat Effect are developed and analyzed. The resulting equations show that the relationship between the number of elevator occupants and floors is surprisingly complicated. Consequently, no general rule can be given for whether the probability of the Shabbat Effect increases or decreases for an arbitrary change in the number of occupants and floors. However, it discovered that for similar changes in the number of occupants and floors, it is the number of floors that predominates in determining the probability of the elevator stopping on every floor.]]></description>
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