Solution to the Counterfeit Coin Problem and its Generalization

TL;DR

This paper presents a method to efficiently identify a counterfeit coin among many using the fewest weighings, and extends the approach to multiple counterfeit coins, providing a systematic and mechanizable solution.

Contribution

It introduces a general, mechanizable method to determine the minimum weighings needed and how to perform them, applicable to any number of coins and counterfeit scenarios.

Findings

Calculates minimum weighings for counterfeit detection

Provides step-by-step weighing procedures

Extends method to multiple counterfeit coins

Abstract

This work deals with a classic problem: "Given a set of coins among which there is a counterfeit coin of a different weight, find this counterfeit coin using ordinary balance scales, with the minimum number of weighings possible, and indicate whether it weighs less or more than the rest". The method proposed here not only calculates the minimum number of weighings necessary, but also indicates how to perform these weighings, it is easily mechanizeable and valid for any number of coins. Instructions are also given as to how to generalize the procedure to include cases where there is more than one counterfeit coin.