Cyber Sue: Kid Carson's Little Sister
Cyber Sue, like her mentor Kid Carson, can perform a perfect shuffle (cutting the deck precisely in two and laying down the cards, one from each hand, in alternation), but unlike the Kid who can perfectly shuffle an entire 52 card deck, Cyber Sue can only guarantee a perfect shuffle for decks of 4, 6, 8, or 10 cards.
The original order of the deck is labeled with the counting numbers. Each time you click Shuffle, Cyber Sue will perform a perfect shuffle. How many perfect shuffles will restore the deck to its original order?