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        riddles >> general problem-solving / chatting / whatever >> Card Trick (video)
        
(Message started by: BenVitale on Feb 19^th, 2011, 7:56pm)

Title: Card Trick (video)
Post by BenVitale on Feb 19^th, 2011, 7:56pm

I tried to embed this youtube video, but couldn't.

Could you explain this trick?

http://www.youtube.com/watch?v=GS9AN3XwghA

Title: Re: Card Trick (video)
Post by towr on Feb 20^th, 2011, 11:12am

Well, for a start cutting the deck just shifts the cycle of cards, but doesn't change the order of the cards in the cycle.

Title: Re: Card Trick (video)
Post by sherperr on Sep 5^th, 2011, 3:35am

cool trick, no idea why it works but i know there are hundreds of great card tricks that are worked out by mathematics.

Title: Re: Card Trick (video)
Post by Jesse on Feb 2^nd, 2012, 3:12pm

I'm gonna go Blonde on this one. I haven't a clue. But would love ton see more... Fun Fun.

Title: Re: Card Trick (video)
Post by SMQ on Feb 3^rd, 2012, 5:56am

Ignore the cuts (since, as both the video and towr point out, they only change where in the sequence you're starting, and the final intentional cut to an ace removes their effect), and ignore the suits, since they're irrelevant to the trick.

Give each card a value from 0 through 12: ace = 0, two = 1, three = 2, ..., jack = 10, queen = 11, king = 12 (one less than their traditional values). The starting, sorted deck, then looks like [0, 1, 2, ..., 12, 0, 1, 2, ..., 12, 0, 1, 2, ..., 12, 0, 1, 2, ..., 12].

The effect of the three-shuffle he shows is to multiply the value in each position by 3 (mod 13). I.e. after the first pre-trick three-shuffle, the deck looks like [0, 3, 6, 9, 12, 2, 5, 8, 11, 1, 4, 7, 10, 0, 3, 6, ...].

The combined effect of the three three-shuffles (one before the trick, and two during), then, is to multiply the value at each position by 3³ = 27. But 27 == 1 (mod 13), so that's an identity transform! It leaves the suits scrambled (we don't care about that), but the values in their original order.

--SMQ