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Riddle of Name of the Engineer

Riddle of Name of the Engineer

Riddle of Name of the Engineer: three businessmen with similar names as three railwaymen live in three cities. Given six conditions, find name of engineer.

The riddle

Three businessmen Sen, Roy and Jana live in three cities of Asansol, Durgapur and Burdwan.

Three railwaymen with similar names also live in the same three cities.

Businessman Roy and the railway guard live at Asansol, businessman Jana and railwayman stoker live at Burdwan while businessman Sen and railway engineer live at Durgapur.

The guard's namesake earns Rs.400000.00 per annum, and the engineer earns exactly one-third of the businessman living nearest to him.

Finally, railwayman Sen beats the stoker in chess during the weekends.

This was the time of steam engines.

What is the name of the engineer?

Recommended time to solve: 10 minutes.

About the puzzle

The puzzle in its original form was posed by legendary puzzlist Henry Dudeney of UK. Being first of its kind (reasoning puzzles), the puzzle became very popular. The puzzle is known commonly by the name: Smith-Robinson-Jones puzzle.

Hint: For quick solution, the reasoning puzzle needs careful attention to details and ability to draw logical conclusions from statement of facts.

Do give it a good try. It is not difficult.

Solution to Name of the engineer riddle: identifying most informative statement

Among the six statement of facts, the first three are on living places of the six people. Independently, these won't provide any breakthrough, but together with other statements, a few should be useful later.

Question is: which of the six statements is the most informative? That will be analyzed first.

The statement 5 says: "The engineer earns exactly one-third of the businessman living nearest to him."

It refers to the all important engineer, states his annual earning compared to a businessman as well as provides a clue about who this businessman might be. The statement carries lots of relevant information and can easily be classified as the most informative and so valuable.

First conclusion drawn from the statement,

Conclusion 1: As the businessman nearest to the engineer must be the one living in the same city Durgapur as him, it means, the businessman referred to is businessman Sen

Both Sen and the engineer live in Durgapur.

It follows,

Conclusion 2: The engineer earns exactly one-third the annual earning of businessman Sen.

To know more about the engineer,

Conclusion 3: Annual earning of businessman Sen to be explored further.

Though no information is provided on the earning of businessman Sen, Statement 4 refers to earning, "The guard's namesake earns Rs.400000.00 per annum.”

Important question arises: Can the guard's namesake earning Rs.400000.00 per annum be the businessman Sen?

Exploring the answer should shed further light on who the engineer might be.

Reasoning: The guard's name to be Sen, businessman Sen must earn exactly three times as the engineer. In other words, the earning of the engineer must exactly be one-third the earning of businessman Sen, which would have to be Rs.400000 in this case.

Common sense says, the exact one-third of the figure of 400000 can't be calculated.

Now only the phrase "exactly one-third" attains significance.

When basic math concepts are referred to, the truth is established on firm grounds,

Fact: It is impossible to know the exact value of division of 400000 by 3. 

This is so because 400000/3 = 133333.3333… is a non-terminating decimal number. It can never reach an exact value.

What is the implication of this important clue? It is simply,

Conclusion 4: Sen is not the businessman referred to in the statement 4.

This results in the first critical conclusion,

Conclusion 5: Guard's namesake is not businessman Sen. It means, guard's own name is not Sen.

The only statement left now is statement 6, and that should provide the final clue to the solution of the puzzle.

Statement 6 says: Railwayman Sen beats the stoker in chess during the weekends.

This is the first time name of a railwayman is mentioned and this provides the final clue.

Conclusion 6: As railwayman Sen beats the railwayman stoker in chess, the stoker can't be Sen. Two railwaymen can't be of same name. Names of the railwaymen have to be Sen, Roy and Jana.

By the Conclusion 5, it is already known the guard is not Sen. Now it is discovered the stoker is not Sen.

Out of the three, only the railwayman engineer is left for the name Sen.

Final conclusion: the railwayman engineer's name is Sen.

End note

Though the math concept that exact division of an integer value by 3 is not possible provided a very important clue, solution could be reached step by step largely by logic analysis and drawing conclusions from statements and implications.

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