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Topic: coins problem
Replies: 7   Last Post: Jun 16, 2009 10:34 PM

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John Conway

Posts: 2,238
Registered: 12/3/04
Re: Solution!!
Posted: Jan 27, 1999 9:46 PM
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I was intending to give the most-memorable solution I know to
the 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 coin
was posed to Felix by his mother. He labels the coins with the
letters of
F. AM NOT LICKED
and 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) all
give different answers. This solution is due to C.A.B.Smith, writing
under a pseudonym I've forgotten.

In the general case n weighings suffice to locate a fake coin
out of (3^n - 3)/2, and it's impossible to do better even though
the "information count" would allow (3^n - 1)/2. Just the other
day 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 anyone
would like to see it. [It's distinctly more elegant than anyone
could reasonably expect to find in a week.]

John Conway





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