A bookworm eats a straight way through a encyclopedia consisting of ten parts. Each part has 1000 pages. The bookworm starts on the front cover of the first part and ends on the back cover of the last part. From how many pages did the bookworm eat?

Suppose you have ten slow matches (also called match cord) and a lighter. If a slow match is lighted, it will burn for exactly one hour. The slow matches do not burn at constant speed, in other words it can happen that the first half of the slow match is burned in 15 minutes, while the remaining part will take three quarters. How can you measure exactly 45 minutes using these slow matches, and what is the minimum of slow matches you need for this?

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?