505. The Engineer's Last Name. Three businessmen - Smith, Robinson, and Jones - live in the Leeds - Sheffield area. In the same area live three railway workers with the same names. Businessman Robinson and the conductor live in Sheffield, businessman Jones and the stoker live in Leeds, while businessman Smith and the railway engineer live halfway between Leeds and Sheffield. The namesake of the conductor earns 10,000 dollars a year, and the engineer earns exactly three times less than the businessman who lives closest to him. Finally, railway worker Smith beats the stoker at billiards.

What is the engineer's last name?
505. It is clear that the conductor cannot be called Smith, since Mr. Smith is the businessman closest to the engineer, and his income, therefore, is definitely divisible by 3, while 10000 is not divisible by 3. Likewise, the stoker cannot be called Smith, since Smith beats him at billiards. Therefore, Smith must be the engineer, and since he is the only one we are interested in, it is completely irrelevant to us whether the conductor is called Jones and the stoker Robinson, or vice versa.

[This is one of Dudeney's most popular puzzles. It became the prototype for dozens of other logical puzzles, sometimes called Smith-Jones-Robinson type puzzles in honor of Dudeney's original puzzle. \(-M . \Gamma\).