A number has 6 different digits. If the last digit is moved to the front, then a new number is formed which is exaclty 5 times the old number. With which number did we start?

To enter the house of the professor, you first have to walk up a stairs which consists out of twenty steps. The professor thinks his stairs are boring so he decides to paint them. He buys two colors, yellow and green. Every step will be either painted yellow or green and moreover the professor does not want to have two yellow steps directly after each other. In how many ways can the professor paint his stairs? And what is the name of the professor?

Recently, somebody told: "My grandfather was born on the first sunday of the year. His seventh birthday was also on a sunday!" In which year was this grandfather born?