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 Faulty Card Shuffler (Posted on 2013-07-24)
This card shuffler, instead of randomizing the positions of cards in the deck, always rearranges any given set of cards into the same new order.

If for example one puts all the hearts into the shuffler, in the order A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, and runs that through the shuffler first once, and then, without rearranging the cards, runs it through again, the resulting sequence after the second shuffle is always:

10, 9, Q, 8, K, 3, 4, A, 5, J, 6, 2, 7

The question is:

What was the order of the cards after the first run through this non-randomizing shuffler?

From the Skeptics' Guide to the Universe podcast episode of June 22, 2013 (episode 414).

 See The Solution Submitted by Charlie Rating: 4.0000 (2 votes)

 Subject Author Date re(3): ? Solution for any set of subcycles? Steve Herman 2013-07-29 23:37:59 re(2): ? Solution for any set of subcycles? Larry 2013-07-29 21:42:52 re: ? Solution for any set of subcycles? Charlie 2013-07-29 10:05:25 ? Solution for any set of subcycles? Larry 2013-07-28 15:03:18 Cycle length determined Steve Herman 2013-07-25 09:13:57 Brians solution broll 2013-07-25 03:09:11 Cycle length is not obvious Steve Herman 2013-07-25 00:38:57 re: Solution Ady TZIDON 2013-07-24 17:00:42 Solution Brian Smith 2013-07-24 16:28:59 The Hard Way? (spoiler) Steve Herman 2013-07-24 14:37:37

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