Counting Counterfeit Coins: A New Coin Weighing Problem

TL;DR

This paper introduces a new variant of the counterfeit coin problem, providing theoretical bounds and a flexible weighing strategy to determine counterfeit coins efficiently.

Contribution

It presents a novel formulation of the counterfeit coin problem, deriving lower bounds and proposing a versatile weighing procedure adaptable to various parameters.

Findings

Derived lower bounds for optimal weighings

Developed a new adaptable weighing strategy

Extended the traditional problem framework

Abstract

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.