Recreational Mathematics Magazine
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Latest Articles from Recreational Mathematics Magazinehttp://rmm.ludus-opuscula.org/Home/ArticleDetails/1202
http://rmm.ludus-opuscula.org/Home/ArticleDetails/1202
Mathematics of a Sudo-Kurve<div style="text-align: justify;">We investigate a type of a Sudoku variant called Sudo-Kurve, which allows bent rows and columns, and develop a new, yet equivalent, variant we call a Sudo-Cube. We examine the total number of distinct solution grids for this type with or without symmetry. We study other mathematical aspects of this puzzle along with the minimum number of clues needed and the number of ways to place individual symbols.</div>http://rmm.ludus-opuscula.org/Home/ArticleDetails/1203
http://rmm.ludus-opuscula.org/Home/ArticleDetails/1203
Ellipse, hyperbola and their conjunction<div style="text-align: justify;">This article presents a simple analysis of cones which are used to generate a given conic curve by section by a plane. It was found that if the given curve is an ellipse, then the locus of vertices of the cones is a hyperbola. The hyperbola has foci which coincidence with the ellipse vertices. Similarly, if the given curve is the hyperbola, the locus of vertex of the cones is the ellipse. In the second case, the foci of the ellipse are located in the hyperbola's vertices. These two relationships create a kind of conjunction between the ellipse and the hyperbola which originate from the cones used for generation of these curves. The presented conjunction of the ellipse and hyperbola is a perfect example of mathematical beauty which may be shown by the use of very simple geometry. As in the past the conic curves appear to be very interesting and fruitful mathematical beings.</div>http://rmm.ludus-opuscula.org/Home/ArticleDetails/1204
http://rmm.ludus-opuscula.org/Home/ArticleDetails/1204
Reflections on the n+k dragon kings problem<div style="text-align: justify;">A <em>dragon king</em> is a shogi piece that moves any number of squares vertically or horizontally or one square diagonally but does not move through or jump over other pieces. We construct infinite families of solutions to the <em>n+k dragon kings problem</em> of placing <em>k</em> pawns and <em>n</em>+<em>k</em> mutually nonattacking dragon kings on an <em>n</em>×<em>n</em> board, including solutions symmetric with respect to quarter-turn or half-turn rotations, solutions symmetric with respect to one or two diagonal reflections, and solutions not symmetric with respect to any nontrivial rotation or reflection. We show that an <em>n</em>+<em>k</em> dragon kings solution exists whenever <em>n</em>≥<em>k</em>+5 and that, given some extra conditions, symmetric solutions exist for <em>n</em>≥2<em>k</em>+5.</div>