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Faulty Card Shuffler (Posted on 2013-07-24) Difficulty: 3 of 5
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)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re(3): ? Solution for any set of subcycles?Steve Herman2013-07-29 23:37:59
re(2): ? Solution for any set of subcycles?Larry2013-07-29 21:42:52
re: ? Solution for any set of subcycles?Charlie2013-07-29 10:05:25
? Solution for any set of subcycles?Larry2013-07-28 15:03:18
Some ThoughtsCycle length determinedSteve Herman2013-07-25 09:13:57
Brians solutionbroll2013-07-25 03:09:11
Some ThoughtsCycle length is not obviousSteve Herman2013-07-25 00:38:57
re: SolutionAdy TZIDON2013-07-24 17:00:42
Some ThoughtsSolutionBrian Smith2013-07-24 16:28:59
Some ThoughtsThe Hard Way? (spoiler)Steve Herman2013-07-24 14:37:37
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