Fun math puzzle: two mathematicians and a coin…
The king is very angry at his two best mathematicians, but rather than executing them immediately institutes the following process:
They are banished to opposite ends of the kingdom, kept under 24 hour guard. Every day in both Westerville and Eastgate where the mathematicians are being kept one of the guards flips a coin and records the result. Each mathematician must then guess the result of the flip at the other end of the kingdom. A messenger is then dispatched from each location to the royal palace to share the results of the flip and their mathematician’s guess. As long as one of the two mathematicians guesses right, the lives of both mathematicians are spared until the next day. The first day that both mathematicians are wrong, they are both executed.
The king imagined this game would not last more than a week or so. The mathematicians, however, hatched a clever plan as they were being ushered out the door of the castle.
What do the mathematicians do to live as long a life as they can, and on average how long should the king have to wait to execute them?