Card Tricks and Information

TL;DR

This paper explores the mathematical and theoretical foundations of card tricks involving face-down and multi-orientation cards, proposing a new 3-card trick and analyzing its limits and variations.

Contribution

It introduces a novel 3-card trick allowing face-down and multi-orientation cards, and provides theoretical analysis of deck size limits and variations with multiple or duplicate cards.

Findings

Maximum deck size estimates based on the number of chosen cards.

Feasibility of hiding multiple cards and handling duplicate cards.

Theoretical framework for card trick complexity and design.

Abstract

Fitch Cheney's 5-card trick was introduced in 1950. In 2013, Mulcahy invented a 4-card trick in which the cards are allowed to be displayed face down. We suggest our own invention: a 3-card trick in which the cards can be face down and also allowed to be placed both vertically and horizontally. We discuss the theory behind all the tricks and estimate the maximum deck size given the number of chosen cards. We also discuss the cases of hiding several cards and the deck that has duplicates.