Perfect In-Shuffles

Probability Level 2

A magician is so good at shuffling that his shuffles are always perfect in-shuffles. That means his shuffles are done in the following two steps:

  1. Split the pile of cards exactly in half.
  2. Interleave the top half with the bottom half such that every second card is from the top half.

If he started with six cards and shuffled thrice, he would get the original arrangement back.

If he started with a deck of 52 cards, how many shuffles would he need to get the original arrangement back?


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