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Five railway employees (Posted on 2009-04-02) Difficulty: 4 of 5
Ten players from a bridge tournament find themselves in the same train, five being passengers and five being railway employees.

The passengers are called Smith, Jones, Clark, Stone, and Black, while the five railways employees - an engineer, a fireman, a guard, a chief guard, and a mail clerk - bear the same five names in some order. It is further known that:

1. The passenger Smith won $10.60 more than the chief guard did.

2. There is a difference in age between the passenger Black and the engineer, of 5 years to the day.

3. The passenger Clark is not related to the guardīs namesake, even by marriage.

4. Last week, the fireman was punished for failure to report to work. While the newspaper article about this identified the offender only as a railway employee and by his last initial, the chief guard could not possibly have been suspected.

5. The passenger Black is precisely as old as the engineer was when the passenger Jones was as old as the railway employee Stone was when the engineer was as old as the railway employee Stone now is. Moreover, the passenger Black is precisely as old as the railway employee Stone was when the passenger Jones was as old as the engineer was when the passenger Jones was as old as the engineer now is.

6. One of the passengers is the son of one of the railway employees. The mail clerk is married to the mother of the passenger in question.

7. The engineer is a neighbour of the firemanīs namesake.

8. The guard and his maternal grandfather celebrate their birthdays on the same day.

9. The fireman differs in age by less than 2 ― years both from his namesake and from the engineer.

10. The chief guardīs youngest grandson is married to the mother of the engineerīs namesake.

11. The passengers Jones and Stone live in Bridgeport.

12. The mail clerk had winnings exactly one quarter of his namesakeīs winnings, and the chief guard had winnings exactly one fifth of his namesakeīs winnings.

13. The chief guardīs namesake celebrates his birthday one week before the railway employee Stone.

14. The guard is married to a daughter of the passenger Smith.

15. The railway employee Stoneīs motherīs father was born on the same day as the passenger Clark.

16. One of the passengers is the father of one of the railway employees.

17. The engineer differs less in age from the mail clerk than from any of the eight other persons.

18. The railway employee Stone won $2.80 more than the railway employee Smith did; the railway employee Clark won $3.25.

19. The railway employee Smith lives in Stamford.

20. Two of the railways employees won $6.60 each.

What are the names and the winnings of the railway employees (engineer, fireman, and so forth)?

See The Solution Submitted by pcbouhid    
Rating: 3.0000 (1 votes)

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Solution ...I think! | Comment 3 of 4 |

There certainly are many 'red-herrings' liberally sprinkled throughout this problem as Dej Mar points out, ambiguity about who might actually share the initial 'S', and even more ambiguity about whether certain references to 'birthday' relate to a particular day of the year or actual specific dates. 

Nonetheless, following on tomarken's start... since the mail clerk is the father of a passenger (6) and is closest in age to the engineer (17), from (5) as well he won't be father to passengers Jones or Black.

From (10), the chief guard must indeed be a great-grandfather (i.e. 1st generation).  His grandson (3rd generation on the maternal side no less, since we don't have three individuals in this problem with the same surname) is the father of the engineer's namesake (4th generation).  That great-grandson wouldn't be passenger Smith, who already has a married daughter (14) and which essentially results in a 5 generation scenario here.  Not terribly likely that the patriarch of 5 generations is still working the railway as a chief guard.  The engineer is therefore not Smith.

From (10) as well, if the engineer's namesake were either passenger Jones or Black, all would be 4th generation, as would the mail clerk (17) who is father to a passenger (again yielding 5 generations if that son were to be passenger Clark or Stone, or even 6 generations if the son were to be passenger Smith).  The engineer can't be Jones or Black either, which now means he can only be Clark (who won $3.25).

So to this point we have the following:

Engineer:  Clark

Fireman:  Jones, Smith, Stone

Guard:  Jones Black Smith Stone

Chief Guard:  Smith Stone

Mail Clerk:  Smith Stone

Now by simple elimination, Black must be the guard, Jones is the fireman, and the chief guard/mail clerk could each be either Smith or Stone.

Also given is that one of the passengers is the father of an employee (16).  Passenger Smith could not be the father of either the chief guard Smith (i.e. 5 generations again), or mail clerk Smith since, from (6), he could only be the mail clerk's son.  Stone can't be the father of the chief guard Stone (13) creating another 5 generation problem, and he couldn't be both father and son to the mail clerk either!  Jones can't be the father to fireman Jones because the two actually have an age difference of less than 2.5 years (9). 

Since the chief guard's grandson is the father of the engineer's namesake (10), passenger Clark is not likely to be engineer Clark's father, which in this case would create a 6 generation problem.  That only leaves passenger Black as father to guard Black, who is married to passenger Smith's daughter (14).

We know passenger Black, engineer Clark, employee Stone and the mail clerk are all close in age and basically of the same generation.  If the mail clerk was Smith, he'd be father to passenger Smith who, with guard Black, would be second generation.  Guard Black is married to passenger Smith's daughter (third generation) however, so we then have a cross-generational marriage thing happening.  Possible?  Yes, but not terribly likely in a logic puzzle!!

My money is therefore on the mail clerk being Stone (father to passenger Stone), leaving the chief guard as Smith.  From (12), the chief guard's winnings are 1/5th of his namesake Smith's, who in turn won $10.60 (i.e. 4 times) more than the chief guard.  Therefore, chief guard Smith won $2.65, mail clerk Stone won $5.45 ($2.80 more), leaving guard Black and fireman Jones winning $6.60 each.  

Edited on April 5, 2009, 12:08 am
  Posted by rod hines on 2009-04-05 00:06:06

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