MathDB
1999 coins with distinct weights

Source: Baltic Way 1999

December 23, 2010
combinatorics proposedcombinatorics

Problem Statement

We are given 19991999 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 10001000th by weight can be determined using no more than 10000001000000 operations and that this is the only coin whose position by weight can be determined using this machine.