The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » Math Topics » geometry.puzzles

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
John Conway

Posts: 2,238
Registered: 12/3/04
Re: Solution!!
Posted: Jan 27, 1999 9:46 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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
and then performs the weighings indicated by


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

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.