I found this one at the very good Smart Kit website:
http://www.smart-kit.com/
Two wise men (who really were wise, and knew each other well) were captured by the king of a small kingdom and brought in secret to a lonely tower in the middle of his kingdom, arriving early one morning.
The king told them that as a test of their wisdom they were going to be kept in solitary confinement in the tower, one in a room that looked to the East and one in a room that looked to the West. They would each see half his kingdom (but not necessarily half the number of towns in his kingdom), and be able to count the towns in the half that that they could see. Between them they would be able to see all the towns in his kingdom, but neither would see any of the towns that the other could see.
Every evening a gaoler would visit them in turn, and if either of them could tell the gaoler the total number of towns in the kingdom, they would both be released that same evening. But if either of them gave the wrong answer, they would both be executed.
The last bit of information the king gave them before they were taken to their separate rooms was that there were either 10 or 13 towns in his kingdom.
On the fifth evening after they arrived at the tower, the wise men were freed.
- How did the wise men know how many towns there were in the small kingdom?
- How many towns were there in the small kingdom?
I think you might work the general idea of a solution out quite quickly, but finding a way to rigourously state the solution may be harder. I do now have a way to give the answer in language I hope everyone will be able to follow, although it took me a while. But perhaps I'm slow... and I didn't want to look at the answer given until I'd worked one out myself.
Answers in
as usual please.
Have fun!