The nine card problem is a magic trick performed by shuffling nine playing cards according to a set of rules. The magic is that a particular card will always reappear. The success of this trick can be easily explained by considering the lengths of the words in the names of playing cards, which define the shuffling rules. In this paper, we use permutations to prove that the trick will always work. We then use this methodology to generalize the trick to any number of cards with shuffles according to different rules.
Mathematics Magazine presents articles and notes on undergraduate mathematical topics in a lively expository style that appeals to students and faculty throughout the undergraduate years. The journal originally began in 1926 as a series of pamphlets to encourage membership in the Louisiana-Mississipi Section of the Mathematical Association of America, and soon evolved into the regional publication Mathematics News Letter. Beginning in 1935, the journal was published with the help of Louisiana State University and, as it began addressing larger issues in teaching math, was renamed National Mathematics Magazine. In 1947, the journal's title was shortened to Mathematics Magazine, and in 1960 it became an official publication of the Mathematical Association of America. Mathematics Magazine is published five times per year.
The Mathematical Association of America (MAA) is the largest professional society that focuses on undergraduate mathematics education. Our members include university, college, and high school teachers; graduate and undergraduate students; pure and applied mathematicians; computer scientists; statisticians; and many others in academia, government, business, and industry. We welcome all who are interested in the mathematical sciences. The mission of the MAA is "to advance the mathematical sciences, especially at the collegiate level." This mission guides our core interests: Education: We support learning in the mathematical sciences by encouraging effective curriculum, teaching, and assessment at all levels. Research: We support research, scholarship, and its exposition at all appropriate levels and venues, including research by undergraduates. Professional Development: We provide resources and activities that foster scholarship, professional growth, and cooperation among teachers, other professionals, and students. Public Policy: We influence institutional and public policy through advocacy for the importance, uses, and needs of the mathematical sciences. Public Appreciation: We promote the general understanding and appreciation of mathematics. We encourage students of all ages, particularly those from underrepresented groups, to pursue activities and careers in the mathematical sciences.