On an island, 100 people have blue eyes and 100 have brown eyes. No one knows their own eye color. Anyone who deduces their eye color must leave at midnight. One day, a visitor says 'I see someone with blue eyes.' What happens?
Hints
This triggers a chain of inductive reasoning over many days.
Answer
On the 100th night, all blue-eyed people leave simultaneously. Each day with no departures, blue-eyed people gain information. On day 99, each blue-eyed person sees 99 others with blue eyes. When those 99 don't leave, each deduces they must also have blue eyes.