KZ-MO 1999 Problem 4
Seven dwarfs live in one house and each has its own hat. One morning one day, two dwarfs inadvertently exchanged hats. At any time, any three gnomes can sit down at the round table and exchange hats clockwise. Is it possible that by evening all the gnomes will be with their hats.
Dataset text AI-MO AoPS. 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.