| From the introduction, each child's car is in a line 1st-5th in order going
from the engine to the caboose. By clue 1, the Rock Island car immediately
precedes the log car, which immediately precedes Kelly's Christmas train
car; while by clue 3, the Norfolk & Western car immediately precedes the
barrel car, which immediately precedes Alexis's car. There must be at
least one overlap between these two clues, or six different cars would be
named. By clue 5, the Rock Island car isn't Alexis's; while by clue 7,
the Norfolk & Western car isn't Kelly's. Therefore, clues 1 and 3 can be
arranged in two ways: The Rock Island car immediately precedes the Norfolk
& Western log car, which immediately precedes Kelly's barrel car, which is
coupled at its rear to Alexis's car; or the Norfolk & Western car is followed
by the Rock Island barrel car, which is followed by Alexis's log car,
which is followed by Kelly's car. In either case, by clue 4 where the
cattle car and the Milwaukee Road car are in consecutive order in the train,
the Milwaukee Road car must be the 5th in order after the four named, with
the cattle car then 4th in line and Alexis's in the first case or Kelly's
in the second. Similarly, in either case, by clue 6 where Ben's car is
immediately followed by the Erie-Lackawanna car, Ben's car must be 2nd in
the train (either the Norfolk & Western log car in case one or the Rock Island
barrel car in case two) and the Erie-Lackawanna car must be 3rd. By
elimination, the Burlington Northern car must be 4th in either case. Then
Chad's car must be the 1st one right after the engine (clue 2) and Jamie's car
the 5th one right ahead of the caboose. Chad's is the operating milk car
and Jamie's the coal car (2), Then the second case combination of clues 1 and
3 cannot work, since the Norfolk & Western car isn't the milk car (7). So,
arrangement one completes the Christmas train: the Rock Island car is 1st,
the Norfolk & Western log car is 2nd, Kelly's barrel car is 3rd, and
Alexis's car is 4th. The Lionels' Christmas train runs as follows:
- Engine
- 1st - Chad's Rock Island milk car
- 2nd - Ben's Norfolk & Western log car
- 3rd - Kelly's Erie-Lackawanna barrel car
- 4th - Alexis's Burlington Northern cattle car
- 5th - Jamie's Milwaukee Road coal car
- Caboose
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