There is a village where everyone has a blue or red dot on their forehead. Every day at noon they all gather in the central square and look at each other. No one says anything, and after a couple of minutes they disperse, and if anyone can figure out their own dot color, they kill themselves.
That happens at midnight. One day, during the meeting at noon, a stranger comes by and announces to everyone “I see at least one blue dot.” Now, it turns out that there are 15 blue dots and 20 red dots. What happens?
Bonus: Once you’ve come up with the answer, what information did the guest impart? Clearly everyone already knew that he saw at least one blue dot. So how did saying something everyone already knew change anything?