BALTIC-WAY 1999 Problem 8
We are given 1999 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 1000 -th by weight can be determined using no more than 1000000 operations and that this is the only coin whose position by weight can be determined using this machine.
Dataset text NuminaMath olympiads. Quoted with source.
Solutions
No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.