This examines the workings of the trick Penn & Teller concluded with in episode 1 of season 3 of "Fool Me". And how/why it works - it's clever use of simple mathematics - absolutely beautiful, and masterfully presented. There's a TL;DR at the bottom if you don't want to read the full explanation and just want less illusion to the process.
|Fold, tear, stack||ABCDabcd|
|top card to bottom||BCDabcdA|
|top 2 cards to bottom||DabcdABC|
|top 3 cards somewhere in the middle||cDabdABC cdDabABC cdADabBC cdBADabC
|Note: This is the crucial setup that is required and that everyone performs identically.|
|top card near your heart = c||xxxxxxC|
The Illusion Of Choice
|1 2 or 3 cards off the top somewhere in the middle||xxxxxxC|
|Note: It matters not how many, or where, as the top and middle can change, as only the bottom card is important.|
|exchange top card with random other person, and put somewhere in the middle||xxxxxxC|
|Note: Again, top and middle can change, as only the bottom card is important.|
|1, 2, or 3 cards and throw them away||xxxxxC xxxxC xxxC|
|monday card to the bottom||xxxxCx xxxCx xxCx|
|tuesday card to the bottom||xxxCxx xxCxx xCxx|
|wednesday card to the bottom||xxCxxx xCxxx Cxxx|
|thursday card to the bottom||xCxxxx Cxxxx xxxC|
|friday card to the bottom||Cxxxxx xxxxC xxCx|
|saturday day card to the bottom||xxxxxC xxxCc xCxx|
|sunday day card to the bottom||xxxxCx xxCxx Cxxx|
|Note: "All got a different number of cards, all in a different order" - not so, the position of the desired card is a function of the number of cards which are left|
The Josephus Count
The final sequence can be thought of in terms of the Josephus problem from Knuth et al.'s Concrete Mathematics. OK, there's also a Josephus Count wiki page. Anyway - the card which will remain is mathematically determined.
J2(6 = 1102) = 1012 = 5; J2(5 = 1012) = 0112 = 3; J2(4 = 1002) = 0012 = 1;
And sure enough, those with 6 cards have C in position 5, those with 5 cards have it in position 3, and those with 4 cards have it in position 1. Genius!
|Loves me card to the bottom||xxxCxx xCxxx xxxC|
|Loves me not card thrown||xxCxx Cxxx xxC|
|Loves me card to the bottom||xCxxx xxxC xCx|
|Loves me not card thrown||Cxxx xxC Cx|
|Card chewing and "Minnesota 1978" - beautiful patter. humoristic engagement with the audience! This is what makes Penn and Teller brilliant showmen.|
|Loves me card to the bottom||xxxC xCx xC|
|Loves me not card thrown||xxC Cx C|
|Loves me card to the bottom||xCx xC C|
|Loves me not card thrown||Cx C C|
|Loves me card to the bottom||xC C C|
|Loves me not card thrown||C C C|
Simply follow the instructions with 3 pieces of white paper, and one piece of coloured paper in the order: white, white, black, white. You'll see that all the "shuffling" operations where you apparently have some choice about the order of the cards are irrelevant.
Another hastily constructed page by Phil Carmody
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