| Original Problem: | A freight train passed through a town. Behind the engine was the coal car. The cattle car was between the milk car and the lumber car. The open boxcar was in front of the flat car but directly behind the milk car. Of course, a caboose was at the end. In what order were the cars? |
1. Problem Statement
This problem is called Order The Train. There is a train with many different cars. The problem is to figure out the order of the cars in the train based on clues about which car is in front of which other car.
2. Process
I used the process of Logical Deduction. The first thing I knew was that the engine was at the front of the train. Then the problem told me that the coal car was behind the engine.
Then the problem really got started. The problem says the cattle car was between the milk car and the lumber car. This didn't tell me enough to figure out where these cars went in the train. There were two different ways I could order these cars: milk, cattle, lumber OR lumber, cattle, milk.
or
But the next sentence says the open box car was right behind the milk car and right before the flat car. That told me everything. If the previous three cars were in the order milk, cattle, lumber, then the cattle car and not the open box car would be right behind the milk car. So the previous cars must have been in the order lumber, cattle, milk. Now the train looked like this:
Then the open box car had to come right after the milk car and the flat car came right after the open box car. In other words it looked like this:
Finally at the end of the train was the caboose.
My Answer
My train was in this order: engine, coal car, lumber car, cattle car, milk car, open box car, flat car, and caboose.
3. Evaluation
I felt this problem was interesting. I liked working on it because it had something to do with a train. Figuring out the second part of the problem was the hardest part. I didn't learn anything. I am proud that I got a solution.
