Henry Ernest Dudeney/Puzzles and Curious Problems/49 - The Engine-Driver's Name/Solution
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Puzzles and Curious Problems by Henry Ernest Dudeney: $49$
- The Engine-Driver's Name
- 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?
Solution
Smith.
Proof
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.
$\blacksquare$
Historical Note
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.
Sources
- 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Solutions: $49$. -- The Engine-Driver's Name
- 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $521$. The Engineer's Name