Henry Ernest Dudeney/Puzzles and Curious Problems/314 - Card Shuffling
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Puzzles and Curious Problems by Henry Ernest Dudeney: $314$
- Card Shuffling
- The rudimentary method of shuffling a pack of cards is to take the pack face downwards in the left hand and then transfer them one by one to the right hand,
- putting the second on top of the third, the third under, the fourth above, and so on until all are transferred.
- If you do this with any even number of cards and keep on repeating the shuffle in the same way,
- the cards will in due time return to their original order.
- Try with $4$ cards, and you will find the order is restored in $3$ shuffles.
- In fact, where the number of cards is $2$, $4$, $8$, $16$, $32$, $64$,
- the number of shuffles to get them back to the original arrangement is $2$, $3$, $4$, $5$, $6$, $7$ respectively.
- Now, how many shuffles are necessary in the case of $14$ cards?
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Sources
- 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Crossing River Problem, and Problems Concerning Games and Puzzle Games: $314$. -- Card Shuffling
- 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Unclassified Puzzles: $512$. Card Shuffling