Henry Ernest Dudeney/Modern Puzzles/197 - A Puzzle with Cards/Solution

by : $197$

 * A Puzzle with Cards
 * Take from the pack the $13$ cards forming the suit of diamonds and arrange them in this order face downwards with the $3$ at the top and $5$ at the bottom:
 * $3$, $8$, $7$, ace, queen, $6$, $4$, $2$, jack, king, $10$, $9$, $5$.
 * Now play them out in a row on the table in this way.
 * As you spell "ace" transfer for each letter a card from the top to the bottom of the pack -- A-C-E -- and play the fourth card on to the table.
 * Then spell T-W-O, while transferring three more cards to the bottom, and place the next card on the table.
 * ''Then spell T-H-R-E-E, while transferring five to the bottom, and so on until all are laid out in a row,
 * and you will find that they will be all in regular order.
 * Of course, you will spell out the knave as J-A-C-K.
 * Can you arrange the whole pack so that they will play out correctly in order,
 * first all the diamonds, then the hearts, then the spades, and lastly the clubs?

Solution
Arrange the pack in the following order face down with $9 \, \clubsuit$ at the top and $5 \, \spadesuit$ at the bottom.

Reading across:


 * $\begin{array}{ccccccccccccc}

9 \, \clubsuit & \mathrm J \, \diamondsuit & 5 \, \clubsuit & \mathrm A \, \diamondsuit & \mathrm K \, \heartsuit & \mathrm K \, \spadesuit & 7 \, \heartsuit & 2 \, \diamondsuit & 6 \, \spadesuit & \mathrm Q \, \diamondsuit & 10 \, \spadesuit & \mathrm A \, \spadesuit & 3 \, \clubsuit \\ 3 \, \diamondsuit & 8 \, \clubsuit & \mathrm K \, \diamondsuit & 8 \, \heartsuit & 7 \, \clubsuit & 4 \, \diamondsuit & 2 \, \spadesuit & \mathrm A \, \heartsuit & \mathrm A \, \clubsuit & 7 \, \spadesuit & 5 \, \diamondsuit & 9 \, \heartsuit & 2 \, \heartsuit\\ \mathrm J \, \spadesuit & 6 \, \diamondsuit & \mathrm Q \, \clubsuit & 6 \, \clubsuit & 10 \, \heartsuit & 3 \, \spadesuit & 3 \, \heartsuit & 7 \, \diamondsuit & 4 \, \clubsuit & 2 \, \clubsuit & 8 \, \spadesuit & \mathrm J \, \heartsuit & 4 \, \heartsuit\\ 8 \, \diamondsuit & \mathrm J \, \clubsuit & 4 \, \spadesuit & \mathrm Q \, \spadesuit & \mathrm K \, \clubsuit & 9 \, \diamondsuit & 5 \, \heartsuit & 10 \, \clubsuit & \mathrm Q  \, \heartsuit & 10 \, \diamondsuit & 9 \, \spadesuit & 6 \, \heartsuit & 5 \, \spadesuit & \end{array}$

Puzzles of this nature are straightforward to solve as follows:

Start with the last card to be spelled, and perform all operations in the reverse order.

You will end up with the complete set of cards in the correct order.