Far 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?
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.
Let's call the day of the pronouncement Day 0. So, what happens on Day 1, Day 2, and so forth? If you want to use variables, call the numeric population P, the number of persons with red dots R, and the number of persons with blue dots B. Thus, P = R + B.
I've never seen this puzzle in written form before, but I've heard it several times.
Good luck. Give yourself a chance to solve the puzzle before checking the hints and answers.
Hints
Answer
Let's call the day of the pronouncement Day 0. So, what happens on Day 1, Day 2, and so forth? If you want to use variables, call the numeric population P, the number of persons with red dots R, and the number of persons with blue dots B. Thus, P = R + B.
I've never seen this puzzle in written form before, but I've heard it several times.
Good luck. Give yourself a chance to solve the puzzle before checking the hints and answers.
Hints
Answer
Puzzle for printing
Thanks for playing!
Thanks for playing!
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