  In 2007, a new variety of the well-known problem of identifying a counterfeit
coin using a balance scale was introduced in the sixth International Kolmogorov
Math Tournament. This paper offers a comprehensive overview of this new problem
by presenting it in the context of the traditional coin weighing puzzle and
then explaining what makes the new problem mathematically unique. Two weighing
strategies described previously are used to derive lower bounds for the optimal
number of admissible situations for given parameters. Additionally, a new
weighing procedure is described that can be adapted to provide a solution for a
broad spectrum of initial parameters by representing the number of counterfeit
coins as a linear combination of positive integers. In closing, we offer a new
form of the traditional counterfeit coin problem and provide a lower bound for
the number of weighings necessary to solve it.
