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

by : $314$

 * 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?