2. The two burning ropes problem:

There are two ropes. You have a lighter. One rope burns totally in 1 hour. The ropes burn irregularly, but each of them gets burned totally in exactly one hour. You need to measure fifteen minutes. How to do it? 

3. 100 floors problem:

There is a building with 100 floors. You have two identical balls. You know that there is a floor n, such that if you drop one of the balls you have from this floor it does not break, but if you drop it from any higher floor it breaks. If one ball breaks, you can use another one. What is the minimum amount of drops (trials) you have to make at different floors to be sure to find the floor n? Note that you are supposed to give a general answer (the worst case scenario) for any possible state of the world.

4. The prisoners' problem:

There are 100 prisoners. They are going to be closed in 100 separate cells and will not be able to communicate with each other. Each day, one prisoner will be drawn out of 100, with uniform probability 0.01. If selected, the prisoner will be allowed into one empty room with a lamp inside. The prisoner may switch off the lamp if it is switched on, switch on the lamp if it is switched off or leave it as it is. After he visits the room he goes back to his cell. The prisoners are not allowed to communicate except for using the lamp. However, they can agree, at the beginning, on the strategy such that at some point they will know for sure that all prisoners have already visited the room. What is this strategy?

5. Monty Hall problem:

There are three doors. Behind two of them there is nothing. Behind one of them there is a Ferrari. Suppose you chose one of the doors. Suppose, the host of the game knows where is the car, opens one of the two remaining doors and shows there is nothing there. Should you change your initial choice?