[Image courtesy of SharpBrains.com.]

A week ago, we shared a brain teaser sent in by a PuzzleNationer named Brian, who challenged us to solve the following challenge.

Today, we’re going to share not only the solution, but how we got there! Please enjoy this brief solve and tutorial, inspired by one of your fellow PuzzleNationers!

The Smith-Jones-Robinson Problem

Every fact is important. The puzzle is as follows:

On a train, three men named Smith, Jones, and Robinson are the fireman, brakeman, and engineer, but not necessarily in that order. Also on the train are three businessmen who have the same names as the train crew. They will be referred to as Mr. Smith, Mr. Jones, and Mr. Robinson.

• Mr. Robinson lives in Detroit.
• The brakeman lives exactly halfway between Chicago and Detroit.
• Mr. Jones earns exactly $20,000 per year, paid in thousand-dollar bills.
• The brakeman’s nearest neighbor, one of the passengers, earns exactly three times as much as the brakeman, and is also paid in thousand-dollar bills.
• Smith beats the fireman at billiards.
• The passenger whose name is the same as the brakeman’s lives in Chicago.

From the information listed above, can you figure out the name of the engineer?

We’re given one exact number, so let’s start there.

The brakeman’s nearest neighbor, one of the passengers, earns exactly three times as much as the brakeman. Mr. Jones earns exactly $20,000 per year, which cannot be divided evenly by three (in thousand dollar bills), so Mr. Jones is NOT the brakeman’s nearest neighbor.

The brakeman lives exactly halfway between Chicago and Detroit, and Mr. Robinson lives in Detroit, so Mr. Robinson cannot be the passenger who lives nearest to the brakeman. And as we just determined, Mr. Jones is also not the brakeman’s nearest neighbor. That leaves Mr. Smith as the brakeman’s nearest neighbor.

This tells us about the passengers, but how does it help us with the train crew?

Well, the passenger whose name is the same as the brakeman’s lives in Chicago. And neither Mr. Robinson nor Mr. Smith (who is nearest to the brakeman) can live in Chicago. That tells us Mr. Jones lives in Chicago.

This means that the brakeman’s name is Jones.

We can finally turn our attention to the train crew now.

Now that we know the brakeman’s name is Jones, that leaves only Smith and Robinson as possibilities. And we know that Smith beats the fireman at billiards. Smith can’t be the fireman or the brakeman, so Smith must be the engineer.

Did you identify the engineer and outwit the Smith-Jones-Robinson Problem? Let us know in the comments section below. We’d love to hear from you!

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