Start with a deck of cards, in order, by suit and number;
Ace of clubs, 2C, 3C, ..., KC, AD, 2D, ..., KD, AH, 2H, .., KH, AS, 2S, ... KS.
Deal the deck into four hands of 13 cards each, so the first hand consists of AC, 5C, 9C etc, the last card the ten of spades.
* does any hand have a pair of cards of the same number?
Stack the four hands as a pile, first hand on top, then 2nd, 3rd, and 4th, and deal out again for four new hands.
* how many times do you need to repeat this to end up with a deck where the cards are in the original order, AC, 2C, ... KS ?