I think you guys will enjoy this one! Have fun!
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Question
You have a deck of 52 cards, numbered 1 through 52 (for convenience), in numerical order that you cut in perfect halves and shuffle. Also, you're the world's greatest shuffler (i.e. you did not have a fun childhood) and can perfectly shuffle cards via "in-shuffling" (e.g. with the first shuffle resulting in 1, 27, 2, 28, 3, 29,..., 26, 52) each time you shuffle. If you repeat the process of "in-shuffling" over and over again, will you eventually reorder the cards so they'll be back in numerical order? If so, how many iterations does it take? Lastly, what if you had N cards instead of 52?
Additionally, you're a pro at "out-shuffling" (e.g. with the first shuffle resulting in 27, 1, 28, 2,..., 52, 26). If you repeat the process of "out-shuffling" over and over again, will you eventually reorder the cards so they'll be back in numerical order? If so, how many iterations does it take? Lastly, what if you had N cards instead of 52?
Good Luck!
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