```Date: Jan 27, 1999 9:46 PM
Author: John Conway
Subject: Re: Solution!!

I was intending to give the most-memorable solution I know tothe 12 coins problem.  It was published in a poem in "Eureka",the Cambridge University undergraduate mathematical journal,many years ago.  I the poem, the problem of finding the fake coinwas posed to Felix by his mother.  He labels the coins with theletters of               F. AM NOT LICKEDand then performs the weighings indicated by                MA DO  LIKE                ME TO  FIND                 FAKE  COIN.   It's easy to check that the 25 different cases (whether there is a fake coin, and if so which it is, and whether it's heavy or light) allgive different answers.  This solution is due to C.A.B.Smith, writingunder a pseudonym I've forgotten.   In the general case n weighings suffice to locate a fake coinout of  (3^n - 3)/2, and it's impossible to do better even thoughthe "information count" would allow  (3^n - 1)/2.  Just the otherday I read a very neat solution in a popular book by Dan Pedoe,which is in my office so I could retail it tomorrow if anyonewould like to see it.  [It's distinctly more elegant than anyonecould reasonably expect to find in a week.]     John  Conway
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