52! (Fifty-Two Factorial)
EFFECT, PRESENTATION WITH PATTER:
“Magic can be pretty astonishing,” you begin.
“But sometimes reality is even more amazing.” You place a plaque on the table. It’s an 8” by 10” card folded in half and kept closed by a large paper clip or bulldog clip. There’s writing and diagrams on both sides of the card that you refer to in the following.
“The number you see here is called ‘Fifty-two Factorial.’ It represents mathematically the number of ways the 52 cards in a shuffled deck can be positioned. And it’s an unbelievable number.” You place a deck of cards on the table.
“Cut off about half of these cards and give them a good shuffle like this.” You take the bottom half and give them a good overhand shuffle. After your helper shuffles their half, you switch packets with them.
“You can give these a good mix too.” Finally, you reassemble the deck.
“Believe it or not, these cards are now organized in a manner that has never been known in human history. That’s what fifty-two factorial means: 52 times 51 times 50 … and so on down to 1. That number is 8.63 with 64 zeros after it! That number is greater than the number of stars in the universe! It’s 2 times greater than the droplets of water that fill every ocean on earth, 5 times greater than the grains of sand in every desert on the planet. This is all true, mind-blowing stuff! And you are about to make it even more amazing! Ready?”
Marilyn nods yes.
“From the top of the deck, deal off any small number of cards. Less than10.” She deals 6 cards.
“Give those a good shuffle and pull out any one of them.” She extracts one card and turns it face up. It is the 4 of hearts.
“This is a very important card – the ‘starter card’ – as it sets off a series of statistically disconnected events. Are you OK with this card? You can exchange it for any other card on the table. But I’ll only let you have one switch-out.” Marilyn decides to exchange it for another face-down card. She selects one, turns it face up and you place it on top of the 4H. This card is the 7 of spades.
“OK. So, we start with a random card with a value of 7. Please pick up the rest of the deck and on top of the 7, deal 7 cards face-down and turn that 7th card face up.” Your volunteer deals six cards face down on top the 7 of spades and then places the 7th card face up. This time, it’s the King of hearts.
“I’ll give you one more chance to add a few more zeroes to that already ridiculously impossible number. You can swap out the King for another of your unused cards on the table thus rearranging the number yet again. Or we can just keep the King and carry on.” Marilyn decides to keep the King. She deals down 13 more cards and turns the 13th face up. This process continues until eventually, she turns up a 7 of hearts. At this point, she cannot continue, as there are less than the correct number (7) of cards remaining in her hand.
“So, we must stop at this point as you cannot deal down any further.” You turn the few remaining cards face up to show all the cards Marilyn could have stopped at.
“As we now know, we could have wound up with any of the 52 cards in the deck as predicated by fifty-two factorial and the immutable laws of mathematics. But you ended up with this specific card – the seven of hearts. Oh … there is one more interesting fact about 52-Factorial...” With that, you unclip and snap open the info card. On the inside is an 8 x 10-inch reproduction of the seven of hearts.
Supply your own deck of cards. We will supply the rest.