On Mar 11, 2013, at 11:49 AM, Joe Niederberger <niederberger@comcast.net> wrote:

At the same time I knew that the final step had to involve 3 coins or less

Except that's not true.

The balanced strategy gives

1. AAAA BBBB CCCC <- 3 groups of 4 coins.

2. ABBB CCCB <- This is the next weighing if in step 1 AAAA != BBBB (otherwise it is trivial)

3. AB or BBB <- this can be resolved in one weighing AND also knowing the result of step 2.

You cannot end up with a group of 4 coins in step 3 and in one more weighing know which single coin is counterfeit, even if you know which way it leans.

Bob Hansen