John has a deck of 52 cards, stacked in a pile with their backs facing up. He separates the small pile consisting of the seven cards on the top of the deck, turns it upside down, and places it at the bottom of the deck. All cards are again in one pile, but not all of them face down; the seven cards at the bottom do, in fact, face up. He repeats this move until all cards have their backs facing up again. In total, how many moves did John make?

(In reply to re(3): computer verification -- simulation by Charlie)

BTW, doing the same shuffling to numbers 1 to 52 shows that after those 112 iterations, each card is in its own position, so the whole deck is completely the same as at the beginning--location and orientation.

Posted by Charlie on 2020-11-30 20:08:28