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.

1. Mr. Robinson lives in Detroit and the brakeman's nearest neighbor earns exactly 3 times as much as the brakeman. Therefore, neither Mr. Robinson nor Mr. Jones are the brakeman's nearest neighbor, so it must be Mr. Smith.

2. Smith beats the fireman at billiards and the passenger whose name is the same as the brakeman's lives in Chicago. Mr. Robinson lives in Detroit and Mr. Smith lives between Chicago and Detroit. Therefore, it must be Mr. Jones who lives in Chicago and Jones is the brakeman.

3. Smith is not the brakeman and he is not the fireman. He must be the engineer.