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

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Modern Puzzles by Henry Ernest Dudeney: $197$

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.


Sources

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