House challenges your brain

In a house with two floors, on the ground are three power switches that are all off. On the first floor, there is a light, which can be activated by one of the three switches. If either or both of the wrong switches are left on, the light won't work. You can switch the power on/off as much as you like, but you can only check the light upstairs once.

In the living room, there are three boxes that each contain two balls. In the first box, there are two white balls, in the next one two black balls, and in the last box, there is one of each colour. On each box, labels indicate the contents, but all boxes were labelled incorrectly. If you open a box, you can only remove one ball. You cannot see the other one.

You go to the kitchen to find nine coins. All the coins seem identical, but one of them is counterfeit. You know that the counterfeit coin weighs slightly less than the other coins. In front of you, there is an old-fashioned balance weight, which can tell if the coins or coin that you place on one scale weigh(s) more or less than the coins on the other scale.

You are standing in front of two closed doors, and there is a guard in front of each door. One of the doors leads to freedom, the other one leads to a dungeon. One of the guards can only tell the truth, the other one can only tell lies – but you do not know who. You are only allowed to ask one guard one question.