This issue does not add private information; it adds something subtler and more powerful: common knowledge. That is why its solution seems slow and, at the same time, relentless.
The island of blue eyes
Riddle statement
On an island live perfectly logical people. Exactly 100 of them have blue eyes. The others have brown eyes, but no one knows the color of their own eyes.
Everyone can see everyone else's eye color. There are no mirrors or reflective surfaces. There is also a strict law: anyone who becomes certain of their own eye color must leave the island at dawn the next day.
One day a visitor arrives and says out loud: "I see at least one person with blue eyes."
What happens next?