An extension of martin Gardner's card trick

Abstract

Martin Gardner’s card trick is a classic mathematical card trick, using number base and ordering to create the magic. This trick lets the inspector memorize a random card and point, after dealing cards into many piles, at the pile that has that card; the process of dealing cards and pointing a pile is repeatly performed; then the chosen card will finally be at the given position. Since Martin Gardner’s card trick and other related card tricks may not be practicable in some situations, it is interesting to find the conditions that make this card trick solvable as well as the ways to perform the trick. This card trick has 3 parameters: the number of piles, the number of cards in each pile and the number of rounds to restack the piles. In this project, we provide an instant program which can tell whether a Gardner’s problem with given parameters is solvable or unsolvable. Moreover, for a solvable problem, all possible ways to perform the Gardner’s trick are provided. Some anticipated conditions on the parameters that make the Gardner’s problem solvable or unsolvable are also given.