Futility Closet

Solution to The Smith Jones Robinson Riddle:

We know that the brakeman doesn’t live in Detroit (2) and that his nearest neighbor is a passenger (4). So that passenger can’t be Mr. Robinson, who lives in Detroit (1).

From (3) and (4) we know that the brakeman’s nearest neighbor also can’t be Mr. Jones (because Mr. Jones earns $20,000 per year, which is not evenly divisible by 3).

Thus, if the brakeman’s nearest neighbor is not Mr. Jones and not Mr. Robinson, it must be Mr. Smith.

Now, if Mr. Robinson lives in Detroit (1) and Mr. Smith lives halfway between Chicago and Detroit (as we’ve just deduced), then the third passenger, Mr. Jones, must be the one referred to in (6) and thus lives in Chicago.

That means, also from (6), that the brakeman’s name is Jones. And if Smith is not the fireman (5), then by elimination Smith must be the engineer.