

Magic Tricks based on deep Mathematics - _giu
http://mathoverflow.net/questions/9754/magic-trick-based-on-deep-mathematics

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nkurz
The card trick mentioned is fun to ponder. Here's a link that gives the full
article: <http://courses.csail.mit.edu/6.042/fall09/cardTrick.pdf>

"You, my friend, are about to witness the best card trick there is. Here, take
this ordinary deck of cards, and draw a hand of five cards from it. Choose
them deliberately or randomly, whichever you prefer -- but do not show them to
me! Show them instead to my lovely assistant, who will now give me four of
them, one at a time: the 7 of Spades, then the Queen of Hearts, the 8 of
Clubs, the 3 of Diamonds. There is one card left in your hand, known only to
you and my assistant. And the hidden card, my friend, is the King of Spades."

~~~
btilly
That is more involved than I thought. I was looking for a covert information
channel. For instance the assistant could hold the cards in 2 different ways,
4 cards represents 16 bits of information, plus 2 more bits for which card is
the high card.

Here is a simpler one that impresses many people. Deal out 3 cards across,
return to the top, 3 more cards, and so on until you've dealt out 27 cards in
3 columns. Have the other person pick a card but don't indicate what it is.
Ask them to indicate which column has the card. Stack the 3 columns with that
in the middle. Now redeal go through the same procedure. Repeat one more time.
Now count the cards out. Card #14 is the picked card.

Why does it work? Well the first time you deal it could have been anywhere,
the second time it is down to the 3 middle rows, the third time it is in the
middle row, then you stacked it in the middle of the deck.

~~~
rimantas
Actually you may let the one you are showing the trick to to choose the order,
you need just to notice where did the column with the card go. 2 if it is on
the bottom, 1 if in the middle, 0 if on the top. When you got your three
digits, reverse them and convert from ternary to decimal—that will be the
number of cards _above_ yours. In the case you are putting column with a card
to the middle you'd get 111, that is 1 _3^2+1_ 3^1+1*3^0=9+3+1=13. Hence your
card is #14.

I think this was in one of the books by M. Gardner.

~~~
rimantas
Corrections: bottom-2, middle-1, top-0. 1×3^2+1×3^1+1×3^0=9+3+1=13

