In a standard deck, there are 13 cards in each suit,such as hearts. For simplicity we'll number them from 1 to 13. This question is about these 13 cards.
Start with the cards in the usual order. This time you are allowed to divide the deck into three piles, consisting of the top n cards, the next m cards, and the remaining 13-n-m cards. Keeping the order within these piles unchanged, you place one pile at the top, one in the middle, and one on the bottom. You may repeat this as many times as you like, changing m and n if you wish. How many arrangements can you get?
So we can number them from 1 to 13 in the usual order: 1 2 3 4 5 6 7 8 9 10 11 12 13
So as one case I can have firs pile=4 cards, second pile=4 cards and last pile=5 cards. If I do the described permutation, I get:
1 5 9 2 6 10 3 7 11 4 8 12 13
Is this correct? If this is correct, then this question is asking me to consider different values of m and n and consider different arrangements based on these values?