```Date: Sat, 26 Oct 1996 21:21:27 -0700
Subject: Problem Solving
Rafayel
```

On a train, Smith, Rodriguez, Jones are the fireman, brakeman, and engineer, but not in that order. Also aboard the train are three businessman who have the same names, a Mr. Smith, a Mr. Rodriguez, and a Mr. Jones.

Clues:

1. Mr. Rodriguez lives in Detroit.
2. The brakeman lives exactly halfway between Chicago and Detroit.
3. Mr Jones earns \$20,000 a year.
4. The brakeman's nearest neighbor, one of the passengers earns exactly 3 times as much as the brakeman.
5. Smith beats the fireman at billiards.
6. The passenger whose name is the same as the brakeman's lives in Chicago.
Who is the engineer? Why?
Hi Rafayel:

In this type of problem you have to analyze the clues one at a time. Sometimes using a table helps keep track of what you are doing. In the table below I have a column for the occupations of the workers on the train and a column for the businessmen. The statement of the problem makes a distinction, using the label Mr., between the train workers and the businessmen. I have labeled my conclusiions (a), (b), ... to keep track of the order.

 Fireman (e) Not Smith (g) Must be Rodriguez Mr. Smith Brakeman (b) Lives half way between Detroit and Chicago (d) Nearest Neighbour is Mr. Smith (f) Name is Jones Mr. Rodriguez (a) Lives in Detroit Engineer (h) Must be Smith Mr. Jones (c) \$20,000 per year

(a)
Clue 1.
(b)
Clue 2.
(c)
Clue 3.
(d)
Since Mr. Rodriguez lives in Detroit he is not the brakeman's nearest neighbor.
Since 20,000 is not a multiple of 3 Mr Jones is not the brakeman's nearest neighbor.
The brakeman's nearest neighbor must be Mr. Smith.
(e)
Since Smith beats the fireman at billiards, the fireman is not Smith.
(f)
The passenger whose name is the same as the brademan's cannot be Mr. Rodriguez since Mr. Rodriguez lives in Detriot.
The passenger whose name is the same as the brademan's cannot be Mr. Smith since Mr. Smith lives half way between Detriot and Chicago.
The passenger whose name is the same as the brademan's must be Mr. Jones.
(g)
Since the brakeman is Jones and the fireman is not Smith he must be Rodriguez.
(h)
The engineer is Smith.

Cheers
Penny

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