Recreational Mathematics Magazine
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Latest Articles from Recreational Mathematics Magazinehttp://rmm.ludus-opuscula.org/Home/ArticleDetails/1214
http://rmm.ludus-opuscula.org/Home/ArticleDetails/1214
The 5-Way Scale<div style="text-align: justify;">In this paper, we discuss coin-weighing problems that use a 5-way scale which has five different possible outcomes: MUCH LESS, LESS, EQUAL, MORE, and MUCH MORE. The 5-way scale provides more information than the regular 3-way scale. We study the problem of finding two fake coins from a pile of identically looking coins in a minimal number of weighings using a 5-way scale. We discuss similarities and differences between the 5-way and 3-way scale. We introduce a strategy for a 5-way scale that can find both counterfeit coins among 2<sup>k</sup> coins in k+1 weighings, which is better than any strategy for a 3-way scale.</div>http://rmm.ludus-opuscula.org/Home/ArticleDetails/1215
http://rmm.ludus-opuscula.org/Home/ArticleDetails/1215
Exploring mod 2 n-queens games<div style="text-align: justify;">We introduce a two player game on an n×n chessboard where queens are placed by alternating turns on a chessboard square whose availability is determined by the parity of the number of queens already on the board which can attack that square. The game is explored as well as its variations and complexity.</div>http://rmm.ludus-opuscula.org/Home/ArticleDetails/1216
http://rmm.ludus-opuscula.org/Home/ArticleDetails/1216
New Year Mathematical Card or V Points Mathematical Constant<div style="text-align: justify;">The article describes an attempt to define a new mathematical constant - the probability of obtaining a hyperbola or an ellipse when throwing five random points on a plane.</div>http://rmm.ludus-opuscula.org/Home/ArticleDetails/1217
http://rmm.ludus-opuscula.org/Home/ArticleDetails/1217
Xor-Magic Graphs<div style="text-align: justify;">A connected graph on 2<sup>n</sup> vertices is defined to be <em>xor-magic</em> if the vertices can be labeled with distinct n-bit binary numbers in such a way that the label at each vertex is equal to the bitwise xor of the labels on the adjacent vertices. We show that there is at least one 3-regular xor-magic graph on 2<sup>n</sup> vertices for every n≥2. We classify the 3-regular xor-magic graphs on 8 and 16 vertices, and give multiple examples of 3-regular xor-magic graphs on 32 vertices, including the well-known Dyck graph.</div>