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MATH: What's the Problem? — Text-only | Flash Special Report
Can You Solve the Train Problem?

Over several days, fifth-graders at the summer Elementary Mathematics Laboratory at the University of Michigan worked on a mathematics problem that called for creative thinking and persistent effort. The problem asked them to try to build a train that would meet a set of specific conditions in the arrangement of its cars and numbers of passengers that each could carry. Here’s the problem:

The Train Problem
The EML Train Company makes five different-sized train cars: a 1-person car, a 2-person car, a 3-person car, a 4-person car, and a 5-person car.  These cars can be connected to form trains that hold different numbers of people. 

[graphic of white box] -- 1-passenger car
[graphic of red box] -- 2-passenger car
[graphic of green box] -- 3-passenger car
[graphic of purple box] -- 4-passenger car
[graphic of yellow box] -- 5-passenger car

A customer named Mr. Howe wants to order a special 5-car train that uses exactly one of each of the different-sized cars. He wants to be able to break apart his 5-car train to form smaller trains, one to hold exactly each number of people from 1 to 15. In addition, he wants to be able to form these smaller trains using cars that are next to each other in the larger train.

For example, if he purchased this train:

[graphic of white box, red box, green box, purple box, yellow box lined up horizontally]

He would be able to make a white-red-green train, or a red-green-purple-yellow train, but not a red-yellow train.

Can the EML Train Company fill Mr. Howe’s order?  Explain how you know.

In the end, the students had answered the question.

So how about you? Try the problem yourself and see in more detail the challenge that these fifth graders were facing.