What's going on with the math?
|
Lets look first at the what happen if we use a prime number (a number with no factors) as
the modulo. We have already discovered that with 12 cards (modulo 13) the cards rotate through every spot forming only one color group. But this does not happen every time that a prime number is used as a modulo. Sometimes the cards return to their original configuration more quickly. For example when 30 cards are used (modulo 31) the cards return to their original configuration after only 5 perfect shuffles, giving 6 color groups each with five stripes. This table shows the size and number of color groups given by perfect shuffles of decks of cards one less than a prime. Notice that for some primes only one color group is formed while for others 2 or more of the same size are formed. Currently there is no known way to predict how a prime modulo will divide into color groups. It depends on whether 2 is a primitive root of the prime, a problem not known to have a solution other than checking. |
 |
Page 1 2 3 4 5
Home
What is a perfect shuffle anyway?
See more perfect shuffle scarves
Knit your own perfect shuffle scarf.
Who came up with this brilliant idea?
Find out more