Lee WA visitor tells an island something everyone there already knows, and it changes everything.
On an island live 100 people with blue eyes. Nobody knows their own eye colour, there are no mirrors, and nobody ever talks about eyes. Anyone who works out their own eye colour must leave the island at the next dawn. Everyone can see everyone else, and everyone is perfectly logical. One day a visitor announces, “At least one of you has blue eyes.” What happens?
Work it out for one blue-eyed islander, then for two.
With one, he would see no blue eyes, know it was him and leave at the first dawn. With two, each would wait for the other to go, and when nobody did, both would leave on the second. The same logic climbs all the way to 100.
The visitor tells nobody anything they couldn’t already see. What changes is that now everyone knows that everyone else knows.
Source: Traditional induction puzzle