This is a fun game, driven by three possible templates. To set it up, we are going to create an advanced linear diagram, with F as one line, and G as the other, with slots 1 2 and 3 going across.
Drawing.jpeg
When we draw this out, we notice that we have six slots for four cities. Since the game tells us that the representatives only visit each city once, and every city has to be visited at least once, we can determine the numerical distribution fairly easily. We can't have any city visited more than twice, and every city is visited at least once. That means that we have a 2-2-1-1 distribution, a fairly common distribution for a 6 slots for 4 variables game.
To write the rules, we write them as conditionals. It's important to use conditional rules because it makes it clear that the relationships are tied to the sufficient condition's occurrence. If anyone visits M, they visit T immediately afterward is drawn with an MT block to show that it will take up that amount of space. That rule also indicates that M can never go last, so we draw a not law under 3 for M.
The next two rules are really critical for the game. If H is visited by G, then M (and thus T) are visited by F. If H is visited by F, then F must visit H sometime afterward. One thing to notice here is that H is either visited by F or G (or potentially both). Therefore, these two conditionals together give you all the possible solutions for the game. This is a key indicator for a templating game, and I recommend templating here.
Let's start with the scenario where G visits H, and F visits MT. F is more filled there, so we can start with F. The final city F would visit would be either S or H. We know it can't be H, because if F visits H, then they also must visit S, and that would be 4 cities in this scenario. So here, F visits MT and S. G then has two options. G could visit H MT or HTS.
The other scenario would be where F visits H. Here, we know F would visit H then S at some point based on our rules. The final city for F couldn't be M, because F doesn't visit T here (at least yet). So the only possible final city for F would be T. G would have to have M so that M is visited, and it would also then have T. For the final city for G, it can't be H (or it would trigger all the consequences in the paragraph above) so it must be S.
In summary, we have the following 3 possible templates. Note that the commas separate the variables where we don't know the order of those variables. These templates mostly show the cities visited by each.
Template 1: F: MT, S G: MT, H
Template 2: F: MT, S G: H, S, T
Template 3: F: H-S, T G: MT, S
A few notes on these templates. First, T is visited by both reps in all three templates. That is a global inference we can note. Also, in each template, one rep visits MT and S in some order. That's a second major global inference we can use.
The questions in this game move fairly quickly with the templates drawn, especially with the global inferences that you can note across the templates.
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