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?
Well, I haven't had my morning coffee yet, but since 7 and 52 are relatively prime, I assume it will take 52 copies of the procedure to get the cards all facing the same way, which will be face up.
So double that to get them all face down again.
I'll say: 104 total moves.
Posted by Larry
on 2020-11-29 07:35:42