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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.