Using a two pan balance to determine a fake coin
Source: Iberoamerican Olympiad 2014, Problem 4
September 24, 2014
inductionmodular arithmeticcombinatorics proposedcombinatorics
Problem Statement
coins are placed on a table, are genuine and have the same weight, and one is fake, with a different weight. Using a two pan balance, the goal is to determine with certainty the fake coin, and whether it is lighter or heavier than a genuine coin. Whenever one can deduce that one or more coins are genuine, they will be inmediately discarded and may no longer be used in subsequent weighings. Determine all for which the goal is achievable. (There are no limits regarding how many times one may use the balance).Note: the only difference between genuine and fake coins is their weight; otherwise, they are identical.