Mathematical_Recreations-Kraitchik-2e

Games 3~3
of the cuts, we find that it occupies the 29th position, that
is, it lies in the third row and third column.
Suppose we wish to determine which card is the second in
the fourth row. Its final position is then 3 ·13 + 2 = 41.
Before cutting, its position was 41 + 3 = 44. Before the
third shuffling its position was 2·44 - 52 - 1 = 35; behre
the second shuffling, 2·35 - 52 - 1 = 1 7, before the first
shuffling, 52 - 2 ·17 + 2 = 20. Hence it was the 7 of clubs.
15. Offer a pack of n cards to a person and ask him to note
the position x of one of the first m of them. Deal out the
first m cards and pick them up so as to invert their order.
Cut the deck so as to bring y cards from the bottom to the
top. The position of the selected card is now y + m - x + 1.
Now deal off the cards, telling the victim to start counting
to himself at the (x + l)th card and to stop you at the (y +
m + l)th card. The card dealt out at that moment is the
chosen card.