Given a deck of 2^n cards and shuffled as follows: Take the bottom and top cards of the deck and place them on the table to start a new deck. Then take the remaining bottom and top cards and place them on the newly started pile. Continue this process until all cards are gone from the original pack. Prove that after n+1 shuffles, the deck of 2^n cards will return to their original position. (Question was from the book, Number Theory by George Andrews) Eg: for a deck of 8 cards (1,2,3,4,5,6,7,8) -> (4,5,3,6,2,7,1,8) -> (6,2,3,7,5,1,4,8) -> (7,5,3,1,2,4,6,8) -> (1,2,3,4,5,6,7,8)
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