

Title: 5 Card Magic Trick Post by GnomeSain on May 21^{st}, 2011, 6:07pm By the pigeonhole principle, you're going to have least a pair of the same suit. Call these cards A and B. For simplicity suppose the ranks are just from 1 to 13. We define the distance d(A,B) to be how many steps it to go from A forward mod 13 to B. So for example, d(3,5) = 2 and d(9,3) = 7. Then, for any A and B , we are guarenteed either d(A,B) is less than or equal to 6 or d(B,A) is less than or equal to 6. If d(A,B) is less than or equal to 6, we will guess B and flip A on the fourth. If d(B,A) is less than or equal to 6, we will guess A and flip B on the fourth. That means, the first three cards X,Y and Z will have to convey what d(A,B) or d(B,A) is. We use the usual card ordering on them and note the total arrangement of orderings is 3! = 6. So we have just enough to convey the distance from A to B. 

Title: Re: 5 Card Magic Trick Post by arun gupta on Apr 3^{rd}, 2012, 10:13pm I thought this is one of the best and easy trick. I tried and do it many times in a day. Thanks! 

Title: Keith Gilabert. 5 Card Magic Trick Post by keithgilabert on May 13^{th}, 2012, 8:23pm That is a really cool trick! Thanks, Keith Gilabert 

Title: Re: 5 Card Magic Trick Post by RandyMagic on Nov 13^{th}, 2014, 2:37am Easy and cool trick! I tried myself and did not know it would be so much fun! 

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