Problem: A Sunday evening, a king has imprisoned two of the finest logicians in a tower. Each logician sees his half of the kingdom from the window of the tower. They are in separate rooms, and cannot hear or see each other. The king, playful, visits the logicians separately and offers them a way to escape:
« There are 10 or 13 villages in my kingdom. You have to guess which of the two. Every day, a guard will come to your cell to ask you for the answer. If you answer correctly, both of you will immediately be set free; if you answer falsely, both of you will be killed that day; if you don’t answer, you’ll just stay in your cell. » The logicians both accept the deal.
Neither answers on Monday, Tuesday, Wednesday or Thursday. On Friday, they both answer correctly, and are set free.
How many villages were there? How were they distributed on the landscape?
