I hope this 5th and last logic puzzle exceeds all your expectations:
Two wise men were captured by a tyrant king. They were locked up in two separate cells in a tower in solitary confinement.
One of the cells pointed Eastwards and from there you could see half of the kingdom. The other pointed Westwards and you could see the other half. So, from their cells, the two wise men could see all the cities of the kingdom, but none of them was visible to both of them.
To prove their intelligence the tyrant told them the cities in his Kingdom were either 10 or 13. If any of them was able to guess correctly how many there were he would free them. A wrong answer would mean instant execution. Every evening a jailer would visit them, provide them with food and they could tell him the answer.
On the fifth evening both men were freed.
What logic reasoning did they follow to solve the problem? How many cities are there and how many did each man see?