Nine billiard-balls are lying in front of you. Except for one they all have the same weight. The exception is a little bit heavier than the others. What is the minimal number of times you have to use a balance in order to find the wrong billiard ball?

A country far away is called the country of no idea. In this country there live people but no children, they have houses but no cities and villages. The people have cars, but there are no roads. They people are very clean but you won't find a single dustbin in the country of no idea. Why is it called the country of no idea?

Suppose that 1 out of 1000 people of a specific country are infected with the deadly X-virus. An inhabitant of that country goes the hospital and gives some blood for a survey. Her blood is checked on the X-virus by a test which gives a correct outcome in 99% of the cases. The test points out that the woman is infected. After the investigation, a doctor tells the woman that he is 99% sure that she is infected with the X-virus. Can the doctor be right by making this worrying statement?