``` wu :: forums (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi) riddles >> hard >> 5 Card Magic Trick (Message started by: GnomeSain on May 21st, 2011, 6:07pm) ``` Title: 5 Card Magic Trick Post by GnomeSain on May 21st, 2011, 6:07pm By the pigeon-hole 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 3rd, 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 13th, 2012, 8:23pm That is a really cool trick!Thanks,Keith Gilabert Title: Re: 5 Card Magic Trick Post by RandyMagic on Nov 13th, 2014, 2:37am Easy and cool trick! I tried myself and did not know it would be so much fun! Powered by YaBB 1 Gold - SP 1.4! Forum software copyright © 2000-2004 Yet another Bulletin Board