Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Defined-Moving, Balanced Grouping game.

The game establishes that eight counselors will supervise three activities, and the first rule creates a distribution of counselors to activities. Because each activity is supervised by at least two of the counselors but no more than three of the counselors, exactly two of the activities must be supervised by three counselors and exactly one of the activities must be supervised by two counselors, an unfixed numerical distribution of 3-3-2. Because the distribution is unfixed, the best diagram for the game is to show the minimum number of counselors for each activity (2), and then track the distribution throughout the questions:

The second and third rules place one of the counselors, and establish two Not Laws:

The presence of the two Not Laws allows for two additional inferences (these will not be shown as dual-options because that would make it appear that swimming must have three counselors):

The fourth rule contains two negative grouping rules, which can be shown with blocks or arrows. We’ll use arrows for the not-blocks as that has the greatest visual impact:

Combining this rule with the Not Laws specified in the third rule gives us two additional inferences:

The fifth rule establish a conditional relationship when G supervises swimming:

Combining all of the information above leads to the final setup for the game:

[jbrown1104]

Hello PS, quick question about the global diagram!

I understand how the not block of JK yeilds the inferences J(s) K(v) and it's contrapositive K(s) J(v). However, I do not understand why the JN not block does not yield a similar conditional inference.

Could you please explain the reasoning behind this, thank you!

~JB

[Dave Killoran]

Hi J,

Thanks for the question! Two things:

First, that isn't the contrapositive of the JS KV rule. The first part is correct, because if K is not in V, it also can't be in T, and thus it must be in S. However, J has more options than just V in that scenario.

The JN not-block doesn't yield a similar inference because there is no Not Law on J under T. K has that Not Law under T, which is why the JK set of inferences arises. But N has no similar restriction, thus the same set of inferences cannot be drawn. In other words, the linkage between the two rules with K is what makes that happen, and N doesn't have a similar linkage.

Thanks!

[jbrown1104]

Hi Dave!

So I tried diagramming the problem today to see if I could make any inferences I couldn't yesterday and came to the same exact reason that you explained. I now completely understand why the NJ block could not yield the same inference (if only I could've seen it yesterday). For the JK block, would this be an example of hurdling the uncertainty? Thank your for your explanations thus far!

Best,
JB

[Adam Tyson]

You could say that, JB! If we place J in one of the only two places where K could go, then K can only go in the other of those two spaces. Typically, we use the "hurdle the uncertainty" concept to learn about variables that are not mentioned in a given rule. For example, if I must select two of three things, A,B and C, but A and B cannot be selected together, I can then infer that C must be selected. The rule wasn't about C, but it nonetheless told me something about it. That's what "hurdle the uncertainty" is all about.