Henry Ernest Dudeney/Puzzles and Curious Problems/49 - The Engine-Driver's Name/Solution

Puzzles and Curious Problems by Henry Ernest Dudeney: $49$

Three business men -- Smith, Robinson and Jones -- all live in the Leeds-Sheffield district.

Three railwaymen of similar names live in the same district.

The business man Robinson and the guard live at Sheffield,

the business man Jones and the stoker live at Leeds,

while the business man Smith and the engine-driver live half-way between Leeds and Sheffield.

The guard's namesake earns $\pounds 1000, 10 \shillings 2 \oldpence$ per annum,

and the engine-driver earns exactly one-third of the business man living nearest to him.

Finally, the railwayman Smith beats the stoker at billiards.

What is the engine driver's name?

Smith.

From the last statement, the stoker is not Smith, who therefore must be Jones or Robinson.

The guard's namesake earns $\pounds 1000, 10 \shillings 2 \oldpence = 240 \, 122 \oldpence$ per annum, which is not divisible by $3$.

Hence the businessman (who is Smith) living near the engine-driver cannot be the guard's namesake.

So the guard is either Jones or Robinson.

So the stoker is not Smith, and the guard is not Smith.

Therefore the engine-driver is Smith.

$\blacksquare$

This puzzle became one of Dudeney's most popular.

Such puzzles became known as Smith-Jones-Robinson puzzles.

This puzzle is mentioned in Finnegans Wake by James Joyce, in which Dudeney himself is mentioned in a footnote.