# Herb is tricked by a magician doing card tricks

Ask Marilyn ® by Marilyn vos Savant is a column in Parade Magazine, published by PARADE, 711 Third Avenue, New York, NY 10017, USA. According to Parade, Marilyn vos Savant is listed in the "Guinness Book of World Records Hall of Fame" for "Highest IQ."

In her Parade Magazine column of November 20, 1994, Marilyn reported that eight perfect shuffles will return a deck of cards to its original order.

## I originally wrote

Doing this with an ordinary 52 card deck really would require a magician. However, with a 64 card deck, eight perfect shuffles would in fact return the deck to its original order. If the magician is careful in choosing the extra cards to insert (avoiding kings, queens, jacks, and aces), most people would not notice the extra cards.

It is easy to demonstrate that this is true with two perfect shuffles of a four card deck, three perfect shuffles of an eight card deck, or four perfect shuffles of a 16 card deck.

## Craig Gentry <gentry@law.harvard.edu> replies

I just read your "marilyn is wrong" posting and thought I should inform you that you've made a mistake of your own. Marilyn was absolutely right in stating that eight perfect shuffles will return the cards to their original order.

For the mathematically inclined, here's Craig's Analysis

## I was wrong

As Craig pointed out six perfect shuffles would return a 64 card deck to its original order; eight shuffles would not. Eight perfect shuffles will return a standard 52 card deck to its original order. Here's a C program that demonstrates that Marilyn was in fact correct.
http://www.wiskit.com/marilyn/shuffle.html last updated June 30, 1998 by herbw@wiskit.com