1999 coins with distinct weights
Source: Baltic Way 1999
December 23, 2010
combinatorics proposedcombinatorics
Problem Statement
We are given coins. No two coins have the same weight. A machine is provided which allows us with one operation to determine, for any three coins, which one has the middle weight. Prove that the coin that is the th by weight can be determined using no more than operations and that this is the only coin whose position by weight can be determined using this machine.