The Mad Scientists - Challenge Problem

The Mad Scientists

       There was once a village of 50 very smart and very crazy scientists. Each day these mad scientists studied advanced calculus and biomedical research and plotted devious evils upon the world. Realizing that the scientists must be stopped, a neighboring town of wise men sent their leader to place a curse on the scientists. The curse was: On each scientist’s back was placed a bomb, either white or black, and any scientist who discovered the color of his own bomb would explode that day at midnight. Unknown to the scientists, the leader of the wise men placed 10 black bombs and 40 white bombs.

        Of course, the scientists thought they could outsmart this curse. They removed all mirrors and reflective objects from the village and vowed never to tell another scientist the color of his bomb – for they saw each other every day and each could see the color of everyone’s bomb except their own.

        Five years passed and the scientists believed they had outsmarted the wise men. There had been no explosions and life progressed as usual. Then came a turning point. The leader of the wise men returned to the village and called for all the scientists to gather around him. Thinking that he might remove the curse, each of the 50 mad scientists listened carefully to what the wise man had to say. And it was this: “I will tell no one the color of his own bomb, but I will tell you all this. There is at least one black bomb.” And then he left the village.

        Thinking nothing of the incident, the mad scientists continued their evil plots. Then, some number of days later, they exploded. Why?


1.     Why did the scientists explode?

2.     It seems paradoxical that the scientists blew up since they already knew there was at least one black bomb. After all, the scientists with black bombs saw 9 other black bombs each day and the 40 scientists with white bombs saw 10 black bombs each day. Yet if the wise man never calls them to the meeting, no one will ever explode! Why does it make a difference when the wise man tells them something they seem to already know? Better yet, what does he indirectly tell them that they didn’t know before?