Hey Lawrence,
Thanks for the question! Ron has posted a link to a prior discussion of it that you should definitely check out, but I figured I would add a few additional thoughts as well (particularly on rule 4)
This is a tricky game because, while the setup seems fairly straightforward at first (a series of four stops at four places with one of the four passengers exiting at each stop), the second and fourth rules contain language that makes the situation more challenging that it might initially appear.
To set it up, use a base of 1-4 and show two spaces above each base position: one space for the stop (F L M S) and another for the passenger (G J R V). Then you can begin to represent rules and inferences around this eight-position structure.
Let's look at rule 2 and rule 4 and try to make sense of what they're saying:
Rule 2 - essentially this tells us that R does not exit before stop M. R could then exit at M, or after M, just not before M. The best way to show that is M ≥ R.
Functionally, this rule is tough to track because once stop M is reached, R is not obligated to exit at that point, and can still exit at a later stop. However, there are some inferences that can be drawn from this rule.
For instance, if R exits at the first stop, that stop must be M. Similarly, if M is the last stop, R must exit at that stop. These could prove important, but note that unless we have R first or M last there will still be some uncertainty about the relationship between R and M.
Rule 4 - This is the most challenging rule of the game. The first part of this sentence creates a conditional relationship that indicates that if J is still on board when the van reaches S, then G must still be on board when the van reaches S. One representation for this portion of the rule is:
F > J
S > G
Of course, the contrapositive for this portion would be:
G > S
J > F
The second portion of the rule indicates that if J is not still on board when the van reaches F (J > F), then G is not still on board when the van reaches S (G > S), which can be diagrammed as:
J > F
G > S
By combining the contrapositive of the first portion with the diagram for the second portion, we arrive at:
G > S
J > F
This diagram means that the two conditions must always occur jointly. Conversely, if one of the two conditions does not occur, the other one will not occur either. In a nutshell, either both conditions happen, or both do not happen.
With the second and fourth rules now (hopefully) better understood, take another look at this game and see if you are better able to address the questions. And please let me know if you are still having trouble.
Thanks!
Jon
