## Favorite Math Problem

In mathematics, problem solving is an essential skill that is developed through instructional activities. Riddles like the one below get students thinking outside the box and allow students to apply problem solving skills to other aspects of the world. Riddles allow students to reason through a problem through logic and reasoning, which is a very important skill to allow your students to practice.

On a train; Smith, Robinson and Jones are the fireman, the brakeman, and the engineer (not necessarily respectively). Also, aboard the train are three passengers with the same names; Mr. Smith, Mr. Robinson, and Mr. Jones. The following facts are known:

- Mr. Robinson is a passenger. He lives in Detroit.
- The brakeman lives exactly halfway between Chicago and Detroit.
- Mr. Jones is a passenger. He earns exactly $20,000 per year.
- The brakeman's nearest neighbor, one of the passengers, earns exactly three times as much as the brakeman.
- Smith is not a passenger. He wins against the fireman in billiards.
- The passenger whose name is the same as the brakeman's lives in Chicago.

**Who is the engineer?**Fact #4 states: The brakeman's nearest neighbor, one of the passengers, earns exactly three times as much as the brakeman.

From this fact you can determine:

From this fact you can determine:

- The brakeman's nearest neighbor is not Mr. Jones because Mr. Jones' salary of $20,000 per year is not a multiple of 3.

Fact #5 states: Smith is not a passenger. He wins against the fireman in billiards.

From this fact you can determine:

From this fact you can determine:

- The fireman is either Jones or Robinson

Fact #5 states: Smith is not a passenger. He wins against the fireman in billiards.

From this fact you can determine:

From this fact you can determine:

- The fireman is either Jones or Robinson