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On a certain passenger train three
passengers and the conductor engaged in a conversation. The following
facts were given:

- The names of the passengers were Smith, Jones and Robinson.
- The conductor said that these were the names of his crew, which
consisted of an engineer, a fireman, and a brakeman.
- Mr. Robinson (the passenger) said that he lived in Detroit.
- The conductor said that his engineer lived halfway between Chicago
and Detroit.
- Mr. Jones (passenger) said he earned exactly $20,000 a year.
- The conductor said that his fireman always lost at billiards to
Smith, one of the crewmembers.
- One of the passengers lived next to the engineer and received
exactly 3 times as much salary as the brakeman.
- The engineer had the same name as the passenger living in Chicago.
What are the names of the brakeman, the fireman, and the engineer?
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