'The brakeman-fireman-engineer' is an old logic puzzle, somewhat along the lines of Einstein's famous puzzle. This version of the puzzle appeared in O. Jacoby and W.H. Benson's Mathematics for Pleasure (1962).

The names, not necessarily respectively, of the brakeman, fireman, and engineer of a certain train were Smith, Jones, and Robinson. Three passengers on the train happened to have the same names and, in order to distinguish them from the railway employees, will be referred to hereafter as Mr. Smith, Mr. Jones, and Mr. Robinson. Mr. Robinson lived in Detroit; the brakeman lived halfway between Chicago and Detroit; Mr. Jones earned exactly $2,000 per year; Smith beat the fireman at billiards; the brakeman's next-door neighbor, one of the passengers, earned exactly three times as much as the brakeman; and the passenger who lived in Chicago had the same name as the brakeman. What was the name of the engineer?

Stumped? Here's the answer to the brakeman, the fireman, and the engineer.

One method of solving puzzles like this involves setting up a grid representing all possible relations between the variables in the problem, and filling it in with X's for impossible relations or O's for certain ones (or ?'s for unknown relations in this example, though you'd ordinarily use blank cells), and using it to assist in solving by process of elimination.

The grid for this problem might look like this:

         b f e
   Smith ? ? ?
   Jones ? ? ?
Robinson ? ? ?

Note that some other information, like the passengers, incomes, and homes are not included. These are merely window dressing, though this puzzle has more than most.

Full Solution

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