Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is an Advanced Linear: Unbalanced: Underfunded game.

The game scenario establishes that five members of the Kim family attend an opera. There are six seat options, with three seats in two rows. Thus, this is an Advanced Linear game. As there are only five family members for the six seats, the game is Underfunded, and one seat will always be empty, which can be designated with an “E”. This maneuver transforms the game from Unbalanced: Underfunded to Balanced. E is then treated like any other variable.

O01_Game_#3_setup_diagram 1.png

The first rule is a bit difficult to parse, but the operational result is that the empty seat cannot be the middle seat in either row:

O01_Game_#3_setup_diagram 2.png

This rule effectively means a KEK block (“K” stands for Kim) is impossible, and that each Kim family member is always next to at least one other family member (shown as a KEK not-block).

The second rule assigns T and U to row H, so two side Not Laws can be shown on row G:

O01_Game_#3_setup_diagram 3.png

The third rule creates a sequence:

O01_Game_#3_setup_diagram 4.png

This sequence eliminates T from sitting in seat 1 in either row, and S and U from sitting in seat 3 in either row. Because T cannot sit in row G or seat H1 (row H, seat 1), T must be in seat H2 or H3:

O01_Game_#3_setup_diagram 5.png

The fourth rule creates a block involving R:

O01_Game_#3_setup_diagram 6.png

Because T and U both sit in row H, we can infer that R, and Q or S or both, must sit in row G. When this inference is combined with the fifth rule, which states that R sits in seat 2, we can infer that R sits in seat G2. And, because R, S, T, and U cannot sit in seat G3, only Q or the empty seat can be seat G3. This results in this setup for the game:

O01_Game_#3_setup_diagram 7.png

Several important inferences remain, based on the placement of certain family members:

• T must sit in seat H2 or H3. Thus, by applying the second and third rules, if T sits in H2, then U must sit in H1 and S must sit in G1.
  
  Seat H3 cannot be occupied by R, S, or U, and thus H3 is occupied by Q, T, or E.
  
  If E is in seat G3, then seat G1 is Q or S; If E is in seat G1, then seat G3 is Q.

Combining all of the prior information results in the final setup for the game:

O01_Game_#3_setup_diagram 8.png

[srcline@noctrl.edu]

Hello

I initially set this game up as

G: 1 2 3

H: 1 2 3

and this is how far I got in my setup

G; T RS 3 *no T

H; T RS U

Is this the right set up?
I am lost from there
Thankyou
Sarah

[Nikki Siclunov]

Hi Sarah,

Thanks for your question. You have the base right, but I'm having a hard time understanding the rest of your setup. For instance, why do you have (T RS 3 *no T) for the G row, and (T RS U) for the H row? I'm a bit lost here.

What you really need to do is, first, identify all the relevant Not Laws:

• 1. The second rule requires T and U to sit in row H. This produces side Not Laws for T and U in row G.
  2. The third rule prohibits S and U from sitting in seat 3, and it also prohibits T from sitting in seat 1. That's three more Not-Laws.
  3. The last rule produces a Dual Option for R in seat 2 in either row. You can also represent this information using Not Laws for seats 1 and 3.

Once this is all done, focus on the power variable here, which is R. Why? Because R is subject to two powerful limitations: it must be in a seat numbered 2, and it also must be adjacent to either Q or S. A quick hypothetical reveals that R cannot be in row H, because both T and U must be in that row. If R were there, you'd be unable to create the RQ or RS block required by the fourth rule. Therefore, R must occupy seat G2.

Hope this gives you a good place to start.

Thanks!

[ivan.l99]

The only thing that threw me off about this game was the rule regarding the lower numbered seats. I thought the rule applied to the individual row and not the two rows as a whole. After correctly applying the rule to set up, it made more sense. For example, when I misunderstood the rule, I thought C was correct on question 13.