A jeweller has three boxes: A, B and C. Each box contains three rings, which are either all made of pure gold, or all fake. The fake rings weight 1 gram less then the real ones. It is known that a least one of the boxes contains fake rings. The jeweller has a balance with three weights of exactly 1 gram. Is it possible that the jeweller finds out which box(es) contain the fake rings with weighing only once? And if so, how does she do it? (We define weighing only once that only once a situation is reached in which the balance is in equilibrium.)

At a particular ice cream van two types of ice creams are being sold. The small one costs 1 dollar, the big one 2 dollars. Marsha puts an amount of 2 dollars one the counter and gets without asking the big ice cream. Martha also would like to have an ice cream. She also puts an amount of 2 dollars on the counter. Then the ice cream seller asks her which ice cream she would like to have. Assuming that the persons do not know each other, how can you explain their behavior.

The local weatherman says No Rain, and his record is 2/3 accuracy of prediction. But the Federal Meteorological Service predicts rain, and their record is 3/4.

With no other data available, what is the chance of rain?