Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Grouping: Defined-Fixed, Unbalanced: Overloaded, Identify the Possibilities game.

The initial scenario establishes that two lawmakers and two scientists will form a four-person panel in each of two years:

S98_Game_#4_setup_diagram 1.png

The game is complicated by the presence of a chairperson on each panel, in part because the chairperson can come from either group and because there is a relationship between the chairperson of each panel.

The basic representation of the three rules is fairly straightforward:

S98_Game_#4_setup_diagram 2.png

Since V appears in two of the three rules, V is a logical starting point for our analysis. If V serves on a panel, then neither G nor I can serve on that panel. Because exactly two lawmakers must serve on the panel, it follows that if V serves on a panel, then F and H must serve on that panel:

• V F, H

Of course, if H serves on the panel, then Y cannot serve on that panel:

• V F, H Y

Because Y cannot serve on the panel, and there must be two scientists on the panel, Z must serve on the panel:

• V F, H Y Z

This is an extremely important inference because of the rule that states that each year either I or V serves on the panel. When V serves on the panel, the other three members are always F, H, and Z. This relationship pattern also reveals an underlying inference of the game: because V and Y can never serve together, we can infer that Z must always serve on the panel. This inference is tested in question #24.

The panel membership is also restricted when I serves on the panel. Because I cannot serve with V, and there must be two scientists, when I serves on the panel we can infer that Y and Z serve on the panel. And, because H and Y cannot serve together, the remaining member is F or G. Thus, when I serves on the panel, the remaining members are always Y, Z, and F or G.

Because I or V, but not both, serve on each panel, there are initially four possible combinations:

1. I serves on the panel in the first year, V serves on the panel in the second year.
2. V serves on the panel in the first year, I serves on the panel in the second year.
3. I serves on the panel in both years.
4. V serves on the panel in both years.

However, if V serves on both panels, the rule stating that the chairperson in the first year cannot serve on the panel in the second year is violated. Thus, there are only three combinations of I and V, and the game should be attacked by showing the three templates that Identify the Possibilities:

S98_Game_#4_setup_diagram 3.png

The three templates above encompass the only six solutions of the game. The only remaining consideration is the chairperson of each panel. For example, the third template will work only if F or G is the chairperson in the first year. If F is the chairperson in the first year, then G must serve on the panel in the second year, and I, Y, or Z is the chairperson in the second year; If G is the chairperson in the first year, then F must serve on the panel in the second year, and I, Y, or Z is the chairperson in the second year.

Overall, the game is very difficult. The Identify the Possibilities technique makes the game manageable, but it requires some insight in order to apply the technique.

[RinMan]

" if V serves on both panels, the rule stating that the chairperson in the first year cannot serve on the panel in the second year is violated"

How do we know that V is the chairperson the first year?

[Rachael Wilkenfeld]

Hi Rinman,

We don't! It's not that we know V is the chairperson if he's on a panel. It's that if V is selected, we know EVERYONE else that has to be there. The panel is set. One of those people has to be the chairperson, and that person couldn't be on the panel the second year.

If V is on the panel, G cannot be and I cannot be. That means FH must both be on the panel. And once H is on the panel, Y cannot be on the panel. That means the last slot is Z. So when V is on the panel, it must be FHVZ. Every time. So no matter which one of those four you select to be the chairperson in year 1, you'd have the same four people on the panel in year 2. Meaning the chairperson for year 1 would also be on the panel for year 2.

Hope that helps!

[valegria]

Hi,
How were you able to make the deduction that F/G can be chairpersons?
This game confused me because there are 7 members, 2 years and each year has a total of 4 members. I understand that there's one repeat but I assumed that the repeat will always be a scientist since there are 3.

How is it that on the lawyer's members, there can be a repeat? If there's a repeat you just basically exclude a member?

[Hanin Abu Amara]

Hi! So it's important to note on this question that we don't have to use all seven variables. When we're doing a game, we want to check to see if the test-makers told us that we have to use all the members. When they don't tell you that you have to use every member, you absolutely can exclude a member.

With that in mind, F/G can be chairperson because you can exclude one of them.

Hope that made sense