>>15575596Far off, in Fantasyland, there is a secluded town called
Dottown. Every resident of Dottown has a colored dot upon his
or her forehead. This dot is always either red or blue, and
everyone in town knows this. In fact, this is proclaimed as a
point of pride at the daily noon gathering of the entire
populace.
Every day at noon, the entire town gathers together, and each
person sees every other person and every other person's forehead
dot. No one ever misses this gathering.
No one dies in Dottown for any reason, with one exception.
If anyone knows the color of his or her own dot, that person
will die that night. Everyone else will notice this at the
gathering at noon the next day (and not before).
For fear of death, there are no mirrors in Dottown, and no one
ever says anything about the dots, except for the formal
proclamation at noon each day.
Everyone in town is extremely intelligent, so if it is possible
to figure out the color of one's own dot, one will do so
immediately. Unfortunately, there is no way to avoid this.
One day, after many years of peace in the town, a stranger
arrives in Dottown. At the noon meeting on that day, the
stranger announces to all, ``There is at least one person in
this town with a red dot.'' All believe this mysterious
stranger. The stranger then leaves town, without saying
anything further.
What happens to Dottown?
This is a mathematical puzzle. That is, there is no trick
buried in my narrative above. No one is colorblind, or any such
thing.
