# ClassS04CS141/ChallengeProblem1

ClassS04CS141 | ClassS04CS141 | recent changes | Preferences

### Challenge problem 1:

On an island there are 5 blue-eyed people and 5 brown-eyed people.

On the island the following things are common knowledge:

• Their are no reflective surfaces.
• No-one discusses eye color.
• If an islander deduces that his or her eyes are blue, then he or she will jump to their death into the sea the following midnight.
• The islanders are smart -- if, from the facts known to an islander, it follows logically from those facts that the islander has blue eyes, then the islander will indeed figure this out within a matter of minutes.
• Each day at noon the islanders meet in the town square.

Days go by and no-one jumps, because, although each person can see everyone else's eye color, nobody knows their own. Then one day, a trusted visitor comes to the noon meeting and announces

"There are people on this island with blue eyes."

1. What happens?
2. When?
3. Why?
4. What precisely is wrong with the following line of reasoning:
"What the visitor announced, everyone already knew. That is, everyone already knew that there were blue-eyed people on the island. Therefore, no new deductions are possible. Therefore, nothing different happens."

It suffices to answer (1-3) above, but if you get 1-3, I encourage you to try 4 also!

Submissions for this problem are due by Friday, April 9 at 5pm.

ClassS04CS141 | ClassS04CS141 | recent changes | Preferences