Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Grouping: Defined-Moving, Balanced, Identify the Templates Game.

This is a challenging game because it combines so many different elements: grouping, sequencing, and a two-value system. The initial scenario appears as follows:

pt25_j98_g3_1.PNG

This is a two-value system, and all players must play one of two alternate sports (or values): golf or tennis. Thus, if a player is not playing golf, he or she must play tennis, and if a player is not playing tennis, he or she must play golf. When we examine the final three rules, the presence of this system will have significant effects.

The first two rules helpfully assign two of the people to specific sports:

pt25_j98_g3_2.PNG

The third rule establishes that L is the highest ranked golf player, which will be designated with a subscript “1.” O’s tennis ranking is not established:

pt25_j98_g3_3.PNG

The last three rules are conditional, and each addresses player sport assignments and rankings:

pt25_j98_g3_4.PNG

Applying the two-value system to the contrapositive of each of these rules leads to several interesting statements:

pt25_j98_g3_5.PNG

Since when M plays golf then S must also play golf (rule #4), and when S plays golf then M must also play golf (contrapositive of rule #5), we can infer that S and M always play the same sport. Thus, S and M form a block within the game, and this is one of the critical inferences of the game.

Because this block must be placed into either the golf group or the tennis group, two basic templates apply in the game:

pt25_j98_g3_6.PNG

In template #1, K is the only variable yet to be placed and there are no restrictions on its placement.

In template #2, K and P are the only variables yet to be placed. According to the rules, if K plays golf, then P plays golf, and if P plays tennis then K plays tennis.


These two basic templates provide a solid base with which to attack the questions. The biggest issue then becomes the ordering of the players within each sport.

[amagari]

I did not understand the wording of the conditional rules on this game. How do you know that M triggers all the other variables to go into either category? I interpreted the sequencing rules as additional to the conditional rules. If M and these other variables are in the same category then here is the sequence for them. I don't see how the M rules force all the sequencing rules to occur.

[Emily Haney-Caron]

Hi amagari,

This is a tricky one, especially figuring out how the rules work together. Each conditional rule is saying IF a certain variable is in a certain sport, THEN these other variables are also in that sport, AND they have to be in this certain order. You can see this if you look at the placement of the if and then in those statements.

After that, I think what you need to do here is make sure you've taken the contrapositive of each rule.

So, for Rule 4, we have MG MG > PG > SG
The contrapositive is, SG OR PG MG

For Rule 5, we have MT OT > ST > MT
The contrapositive is, ST OR OT (which I know is not possible in this game, since O has to do tennis, but this would be part of the contrapositive) MT

For Rule 6, we have PT KT > OT > PT
The contrapositive is, KT OR OT (which I know is not possible in this game, since O has to do tennis, but this would be part of the contrapositive) PT

If you look at how those rules work together, you'll see that, if S played golf, S could not play tennis; based on the contrapositive for Rule 4, that would also mean M couldn't play tennis. So, if S plays golf, M has to play golf, which means rule 4 is in effect and P also plays golf. If S plays tennis, S could not play golf, which means M could not play golf. Therefore, if S plays tennis, M also plays tennis.

[VamosRafa19]

Is there a set up of this game available somewhere?

[Dave Killoran]

Yes, I'm not certain why it's not here. Let me see what I can do about having it posted up...

Edit: this has been posted

[yenisey]

How should I define rankings ? I got confused in that part. It says "Paulo ranking lower than Maricella but higher than Shigeru" . I thought higher means higher number like 3, 4 . In logic bibles it says higher numbers are on the right and lower numbers are on the left.
I set the diagram horizontally and got confused in that ranking system

[Adam Tyson]

The difference between "higher number" and "higher ranking" is crucial here, yenisey. When a rule tells you that a certain variable has a higher number than another, that means it is to the right, or after, in a horizontal setup, and could be above or below in a vertical setup depending on which way you ordered your base. For example, if the game involves floors of a building, a higher numbered floor would be above a lower numbered floor, just like in an actual building.

But when we switch to talking about rankings, things get reversed. First place - the number 1 - is a higher ranking than second place. If it helps, picture the platforms for the medalists at the Olympics, with first place, the gold-medal winner, standing literally higher than the silver and bronze (second and third place) finishers.

You also need to pay attention to how the stimulus describes the relationships. For example, in a game in which the variables are ordered by speed, they could tell you to line them up from fastest (first) to slowest (last), but they could also tell you to line them up from slowest to fastest (that would be unusual, but they could do it). You must pay attention to the scenario to see what guidance they give you!

In this game, notice that the scenario, the rules , and the questions never talk about "first" and "second," etc., but only talk about "highest" and "lowest." So it's up to you how you handle that in your base. Our setup put the highest ranking on the bottom, which may be confusing to some folks, but you can certainly choose to set yours up horizontally with the highest rank going on the left (first), or even vertically with the highest rank at the top. Do what works for you!