From jgamble@ripco.com Thu Apr 18 00:24:21 CDT 2002 Article: 129244 of sci.math Path: news!husk.cso.niu.edu!vixen.cso.uiuc.edu!uwm.edu!logbridge.uoregon.edu!xmission!news-out.spamkiller.net!propagator2-maxim!propagator-maxim!news-in.spamkiller.net!out.nntp.be!propagator-SanJose!in.nntp.be!gail.ripco.com!jgamble From: jgamble@ripco.com (John M. Gamble) Newsgroups: sci.math Subject: Re: Memory game odds Date: 12 Apr 2002 23:33:12 GMT Organization: Ripco Internet, Chicago Lines: 35 Message-ID: References: NNTP-Posting-Host: lawson.ripco.com X-Trace: gail.ripco.com 1018654392 17572 209.100.227.4 (12 Apr 2002 23:33:12 GMT) X-Complaints-To: usenet@gail.ripco.com NNTP-Posting-Date: 12 Apr 2002 23:33:12 GMT Xref: news sci.math:129244 In article , Jonas wrote: >I'm trying to calculate the odds of completing the memory game in a >certain number of flips. (memory game = you have x pairs of hidden Hmm, weird coincidence. This is not a solution, but i do have a couple of references. I've just been reading old Mathematical Recreations columns, and one by Ian Stewart covers this in the October 1991 Scientific American (subtitle: Concentration: A Winning Strategy). He gives as further reading: The Memory Game (Extended Abstract), Uri Zwick and Michael S. Patterson, Mathematics Institue, University of Warwick, March 22, 1991. I hope this is of some help to you. >cards and you flip 2 over at the time trying to find matches) Assuming >the cards are arranged randomly there's obviously no shortcut here, >you may just as well flip them over in order until you recognize a >card you had before. The number of flips needed for x pairs goes from >x to 2x-1. What i need to know is what are the odds for a certain >number of flips. I can calculate the odds for the extremes: > >x flips - odds 1 on (2x-1)!! >2x-1 flips - odds 1 on 2^x - 2 > >But for everything in between, it's too difficult. Can anyone help? -- -john February 28 1997: Last day libraries could order catalogue cards >from the Library of Congress.