Princess Hattius invites several of the court’s Logicians to the forest. She tells them she’ll put a hat on each of their heads. The logicians will be able to see the colours of others’ hats, but not their own. The logicians are used to such puzzles, and so know that they’re not allowed to take off their own hat, or look in a mirror, or lake reflection. They are only allowed to work out their hat’s colour by logic and deduction.
The princess tells them she’ll ring a bell every minute, and that once a logician has worked out his or her own hat’s colour, then they should stand up and leave at the next bell. She also tells them that every colour appears twice, so each logician sees someone else with the same colour hat of their own.
What happens?