Setup and Rule Diagrams

[bella243]

Is this is an underfunded game? I do understand that nothing in the rules explicitly suggests that a professor was hired in EACH year, just that they were hired between 89-95. But for the sake of clarity and categorization, is this basic linear game underfunded or balanced?

[CodeyD29]

I do not understand the set up to this game at all. Any clarification would be helpful. Thank you!

[Jeremy Press]

Hi Bella and Codey,

This is a basic linear game with a couple little twists away from the norm. First, to answer Bella's question, even though the game is technically properly labeled as balanced (7 professors, 7 different years), it's not a 1-to-1 distribution style of basic linear game. In other words, not every year has to have a professor hired in it, and not every professor is hired in a different year from every other professor (some professors could be hired in the same year as each other).

The strangest element about this game is the notion of the specialties. All professors have at least one specialty. But you don't have to figure out what the specialties are, because the game never specifically identifies them! So what's the point of the specialties? They determine who can be "with" each other (hired in the same year as each other) and who can be "next to" each other (i.e. hired in consecutive years to each other). If a professor has the same specialty as another professor, then she cannot be hired in the same year as that professor, nor can she be hired in consecutive years with that professor. Where do we get that? From this language: "any two professors hired in the same year or in consecutive years do not have a specialty in common."

How does that affect the game? Take a simple example. Nilsson shares a specialty with Robinson, and we know from the first rule that Robinson was hired in 1991. So what does that rule tell us about Nilsson? Nilsson could not have been hired in 1991 (cannot be hired in the same year, because any two professors hired in the same year do NOT have a specialty in common), and Nilsson could not have been hired in 1990 or 1992 (cannot be hired in years consecutive with 1991, because any two professors hired in consecutive years do NOT have a specialty in common). Basically, the rule about specialties is allowing us to create some Not Laws in the game.

Take Orozco and Sarkis. They cannot be hired in the same year (meaning Sarkis can't be hired in 1990). And they cannot be next to each other (meaning Sarkis can't be hired in 1989 or 1991). Since Sarkis was hired at least one year before Madison (who was hired in 1993), this means Sarkis must have been hired in 1992 (big inference!). That also means N, which has to be ahead of S, has to be hired in 1989, because that is the only possible year left ahead of 1992 that N could've been hired in. P is then allowed to be hired any year between 1990 and 1992 (the only variable with any flexibility in this game, as you'll see from what follows).

Take Madison and Togo, who also share a specialty. That means Togo cannot have been hired in 1993 (when Madison was hired) or in 1992 or 1994 (the years consecutive to Madison's hiring).

From the second rule, Togo also shares a specialty with Orozco. That means Togo cannot have been hired in 1990 (when Orozco was hired), or in 1989 or 1991 (the years consecutive to Orozco's hiring). So, Togo must have been hired in 1995 (our final big inference!).

The following is what we can determine from the rules (with P possibly being hired in any of 90, 91, or 92):

89: N
90: O
91: R
92: S
93: M
94:
95: T

I hope this helps!

[vangorgc]

This game gave me fits and my biggest confusion was with representing the rules - I think I got the overall base and setup right. Not sure if this blog is still monitored, but if anyone could help that would be amazing. Could you do a full set up or show how to best represent the game?

[KelseyWoods]

Hi vangorgc!

This game is a little weird, but the rules are actually fairly simple to diagram. It's just a bunch of Not Laws and Not Blocks, and a couple of sequencing rules!

Here's one way you could diagram it:

Screen Shot 2020-11-23 at 12.12.36 PM.png

Whenever you know that two professors share a specialty, what that really tells you is that those two professors cannot be hired in the same year or in consecutive years. So if they have a specialty in common, you do a vertical Not Block for those two profs (because they can't be in the same year) and a horizontal Not Block (because they can't be in consecutive years). Then, since we know the exact years in which some profs were hired, we should add Not Laws on our diagram. For example, T and O each have a specialty in common with M and we know that M is hired in 1993. So that means that T and O cannot be hired in 92, 93, or 94. Rule #4 is just a sequencing rule. P and S are after N and before M. Again, we can add Not Laws based on these sequencing rules. Some of those Not Laws end up forcing variables into one specific slot. And we end up with a setup in which we know the year in which every professor was hired except for P (who is limited to just 3 possible years).

Hope this helps!

Best,
Kelsey

[Gcg99768@uga.edu]

Hi! What other games that are similar to this would you suggest trying!

[evelineliu]

Hi there,

Here are some other linear games to practice:

PT 40 [June 2003], Section 2, Game 2 (linear with a twist because there's an out group)

PT 59 [December 2009], Section 1, Game 4

PT 63 [June 2011] Section 2, Game 4

Best,
Eveline

[ivan.l99]

Although seemingly obvious now, one thing that I was unclear of when drawing a set up, was whether more than one could go in each year. After rereading "two professors hired in the same year," the set up was more feasible.