This is a fun card trick

I know, I know... If I tell you all about this card trick, then you'll all know it and you wont be able to fool each other.  Well, I understand that there are still a few people out there who don't read Digital Diner, so this is your chance to fool them.  It is a cute trick.  Watch the video.

Now, for extra credit, can you explain WHY this trick works?  If you understand it, you can make variations on it that will amaze even your friends who have seen this video.


Here's my analysis.

It is all about modular arithmetic.  There are nine cards in your little deck and you rotate through them and reorder them.  Let's start with the initial ordering.  You have three stacks of three cards and the participant picks one.  We will call that card "S" for "selected and all the other cards will be represented by 'X'.  Note that the selected card is on the bottom of one of these stacks (we choose the third one for this example, but it doesn't matter).  In order to fit these on the screen I'll show the stacks of cards in left to right order with the left side being the top and the right side being the bottom..  Here is our initial configuration with the bottom card in the third stack selected.

Stack 1: XXX
Stack 2: XXX
Stack 3: XXS

Now we stack the cards in a very specific way:

XXSXXXXXX

Now we spell out the number of the card first.  Not that all the number have at least three letters.  This means that no matter what number you choose, the selected card will move to the position third from the bottom once you drop all the unused cards on top of it.  Try it for yourself to see how this works.
ACE = 3 characters
TWO = 3 characters
THREE = 5 characters
FOUR = 4 characters
FIVE = 4 characters
SIX = 3 characters
SEVEN = 5 characters
EIGHT = 5 characters
NINE = 4 characters
TEN = 3 characters
JACK = 4 characters
QUEEN = 5 characters
KING = 4 characters

So we end up with:
XXXXXXSXX

Now you spell out 'of' from the top of the deck and drop those cards to the bottom, so the deck looks like this:

OF = 2 characters

XXXXSXXXX

The selected card is exactly in the middle of the deck.  Now we spell out the suit.  This is where it gets fun.  You see all the suits are either 8 or five letters long.

HEARTS = 5 characters
SPADES = 5 characters
CLUBS = 5 characters
DIAMONDS = 8 characters

Lets take a 5 letter suit.  We take five cards off the top, so we get right to the selected card, and then we drop the unused cards on the top.  This has no effect on the position of the selected card!  So we would have:

XXXXSXXXX

Now lets look at what happens with 'diamonds', the 8 character name.

We take eight cards off the top, which means that the selected card is still 5th from the bottom, and then we drop the extras on top.  So even with an 8 character suit, the position of the selected card doesn't change as long as you follow the rule of dropping the extra cards back on the top.  Cool huh?

So now we have:

XXXXSXXXX

and we spell out 'magic'

MAGIC=5 characters

Which brings us to the fifth card... which is our selected card.

Variations

This means that once you get to the point where you have the selected card in the center of the deck, you can spell out any word that you want that is less than nine letters long, like the name of the person who selected the card, or the day of the week, or all of the above.  As long as you place the remaining cards back on the top of the deck, the selected card wont move, and it will be exactly 5 cards deep in your deck.

Make your own variations and amaze your friends.

Via BoingBoing