Henry Ernest Dudeney/Puzzles and Curious Problems/314 - Card Shuffling

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?

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