Recreational Mathematics Magazine
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Latest Articles from Recreational Mathematics Magazinehttp://rmm.ludus-opuscula.org/Home/ArticleDetails/1172
http://rmm.ludus-opuscula.org/Home/ArticleDetails/1172
Designing peg solitaire puzzles<div style="text-align: justify;">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.</div>http://rmm.ludus-opuscula.org/Home/ArticleDetails/1173
http://rmm.ludus-opuscula.org/Home/ArticleDetails/1173
Demystifying Benjamin Franklin's other 8-square<div style="text-align: justify;">In this article, we reveal how Benjamin Franklin constructed his second 8×8 magic square. We also construct two new 8×8 Franklin squares.</div>http://rmm.ludus-opuscula.org/Home/ArticleDetails/1174
http://rmm.ludus-opuscula.org/Home/ArticleDetails/1174
Exploring the "Rubik's magic" universe<div style="text-align: justify;">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 by Tom Verhoeff.</div>http://rmm.ludus-opuscula.org/Home/ArticleDetails/1175
http://rmm.ludus-opuscula.org/Home/ArticleDetails/1175
On a mathematical model for an old card trick<div style="text-align: justify;">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 <em>ab</em> cards with <em>a,b</em>≥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.</div>http://rmm.ludus-opuscula.org/Home/ArticleDetails/1176
http://rmm.ludus-opuscula.org/Home/ArticleDetails/1176
Several bounds for the k-tower of hanoi puzzle<div style="text-align: justify;">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.</div>http://rmm.ludus-opuscula.org/Home/ArticleDetails/1177
http://rmm.ludus-opuscula.org/Home/ArticleDetails/1177
Eternal Picaria<div style="text-align: justify;">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.</div>