The 21 Card Trick and its Generalization

TL;DR

This paper explores the mathematical principles behind the 21 card trick and presents a complete generalization, demonstrating that the trick can be performed with any number of cards.

Contribution

It provides a comprehensive mathematical analysis and generalization of the classic 21 card trick, extending its applicability to any number of cards.

Findings

The trick's success relies on specific mathematical properties.

A generalized method allows performing the trick with any number of cards.

The paper formalizes the underlying mathematics of the trick.

Abstract

The 21 card trick is well known. It was recently shown in an episode of the popular YouTube channel Numberphile. In that trick, the audience is asked to remember a card, and through a series of steps, the magician is able to find the card. In this article, we look into the mathematics behind the trick, and look at a complete generalization of the trick. We show that this trick can be performed with any number of cards.