Hi, long time lurker here. But since I'm doing a PhD in mathematics, I can't resist chipping in here. So here are two of my favorite logic/probablity puzzles.
First, we once again have a prison with 100 prisoners, who get one chance at freedom. In the courtyard 100 boxes are placed, each labeled with a name of one of the prisoners (all 100 are different). In every box there is a piece of paper. These pieces are also each marked with one of the prisoner's names (again all names are present). These papers have been distributed amongst the boxes completely randomly.
In an hour all prisoners will be called to the yard one at a time. They are allowed to open 50 of the boxes. If one of the boxes opened contains the paper with his name on it , the prisoner passes the test. If all 100 prisoners pass they are all allowed to go free, but if a single one fails they are all stuck inside. The prisoners have an hour to discuss their strategy. What is their best chance of getting out of jail?
To clarify, the prisoners are not allowed to move or otherwise manipulate the boxes and papers besides open 50 of them and see if they found their own name.
The second problem has a more cheerful setting. A princess has reached a marriageable age and no less then 100 suitors have shown up to the kingdom. The princess is now faced with the task of finding the best candidate for marriage. One by one the 100 suitors will present themselves to the princess and ask for her hand. The princess will have to give her answer right away. If the princess rejects a suitor, he will be heart broken and will leave the kingdom immediately.
Fortunately our princess is gifted with a magical ability to judge the suitability of a suitor the second she lays eyes on him. We will assume that the suitability of a suitor can be judged on a linear scale. What strategy should the princess follow to maximize the chance of marrying the best suitor?