Patience rewarded

Extract

When I was younger, and had nothing better to do with my spare time, I sometimes used to play my own game of ‘patience’. I would take a pack of 52 playing cards and arrange them in order, ace to king of each suit and then the four suits one on top of the other. I would begin my game by taking the card at the top of the pack and putting it at the bottom; then taking the second card and placing it face upwards on the table; then the third card was transferred to the bottom of the pack; then the fourth card was placed on top of the second on the table; and so on, until all the cards had been placed in a new pile on the table. I would then turn the pack on the table face downwards and perform the whole operation again with the cards arranged in this new order. My aim was to see if, by repeating the whole operation enough times, I could get the cards back into their original order. If I had known that I would need to perform the operation 840 times, I probably would not have bothered to continue with my game.