by **Smythe Dakota** » Thu Sep 27, 2012 5:35 am

How about a generalization?

For any positive integer N, what is the smallest number W of weighings that is guaranteed to find the false coin?

Apparently, for N=12, W=3.

And, what is the smallest number X of weighings that is guaranteed not only to find the false coin, but also to determine whether it is lighter or heavier than the others?

Obviously, for each N, X is greater than or equal to W. Does X ever equal W, or is X always greater?

Are these functions monotone? Or are there cases where, if N is increased, W decreases?

Bill Smythe