Four little gnomes are on one side of a scary wood. They have to travel through the wood to the other side. They can only do this safely if they have some light. Together they carry only one small candle. Unfortunately this candle only gives enough light for two gnomes. Some of the gnomes can walk faster than others. One of them can at fastest walk to the other side in 1 minute, one in 2 minutes, one in 5 minutes and the slow one in 10 minutes. If two gnomes are on the other side of the wood, one of course has to go back to bring the candle. If the gnomes go to the other side as quickly as possible, how much time does it take them in total?

On a train, Smith, Robinson, and Jones are the fireman, brakeman, and the engineer, but NOT respectively. Also aboard the train are three businessmen who have the same names: a Mr. Smith, a Mr. Robinson, and a Mr. Jones. Using the clues below, can you determine the identity of the Engineer?

1. Mr. Robinson lives in Detroit.
2. The brakeman lives exactly halfway between Chicago and Detroit.
3. Mr. Jones earns exactly $20,000 per year.
4. The brakeman's nearest neighbor, one of the passengers, earns exactly three times as much as the brakeman.
5. Smith beats the fireman in billiards.
6. The passenger whose name is the same as the brakeman's lives in Chicago.

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?