Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is an Advanced Linear: Balanced, Identify the Templates game.

This game features six animals being assigned to six stalls, one animal per stall. The game is made slightly more challenging because the six animals are divided into two types: lions and tigers. The initial game scenario appears as:

PT16-Sep 1995 LGE-G2_srd1.png

The first rule establishes that the two tigers cannot face each other:

PT16-Sep 1995 LGE-G2_srd2.png

The second rule assigns a lion to stall 1, which eliminates K and M from being assigned to the stall:

PT16-Sep 1995 LGE-G2_srd3.png

The third rule assigns H to stall 6:

PT16-Sep 1995 LGE-G2_srd4.png

This additionally has the effect of removing H from consideration for stall 1, leaving only F, G, or J as candidates for the first stall.

The fourth rule is an important rule in the game, and, for some, a problematic rule. The rule is properly diagrammed as:

PT16-Sep 1995 LGE-G2_srd5.png

One of the mistakes made by many students is to misinterpret this rule as being diagrammed as JK. The rule states that J is assigned to a stall numbered one higher than K’s stall. Numerically, 2 is numbered one higher than 1, 3 is numbered one higher than 2, etc. Thus, if K is assigned to stall 2, then J must be assigned to stall 3. This produces a KJ representation, not JK.

With the addition of this rule, J cannot be assigned to stall 1, and K cannot be assigned to stall 5 (stall 6 is already occupied, and thus it is not the last “open” space). With J removed from consideration for stall 1, we can deduce that F or G must be assigned to stall 1. Of course, with F or G occupying stall 1, the earliest the KJ block could appear is 2-3, meaning J cannot be assigned to stall 2:

PT16-Sep 1995 LGE-G2_srd6.png

The last rule brings an important restriction: K cannot face H, and so K cannot be assigned to stall 3:

PT16-Sep 1995 LGE-G2_srd7.png

This final rule limits K’s options to stall 2 or stall 4. With this limitation, and the other rules in the game, you must make the decision to show the two templates based on the position of the KJ block:

Template #1: KJ in stalls 2-3. When K is assigned to stall 2, M cannot be assigned to stall 5 due to the first rule, and must be assigned to stall 4. F and G rotate between stall 1 and stall 5.

PT16-Sep 1995 LGE-G2_srd8.png

Template #2: KJ in stalls 4-5. When K is assigned to stall 4, stalls 2 and 3 are occupied by M and the remainder of F/G.

PT16-Sep 1995 LGE-G2_srd9.png

The two templates above capture all six of the possibilities in the game. This game can be somewhat difficult without the templates; with the templates, the game is easy.

This game is also the start of some interesting test construction elements used the test makers. Consider the following features of the second, third, and fourth games:

Game #2:     Features two rows, slots are numbered sequentially in horizontal fashion. Numerically, “2” is higher than “1,” etc.

Game #3:     Features two rows, slots are numbered in non-sequential fashion (one odd row, one even row)

Game #4:     Numerically, “1” is higher than “2,” etc.

In the second and third games, the slots are numbered in different ways, and in the second and fourth games, the numerical ranking relationships are opposite. These differences have the subtle effect of keeping test takers off-balance. For example, in the second game the slots line up 1-2-3, and in the third game they line up 1-3-5-7. Psychologically, it is difficult to develop a rhythm when the slots appear similar but are numbered differently. This type of construction is just another example of the psychological ploys used by the test makers.


Returning to this game, using the templates allows you to answer the questions extraordinarily quickly.

[Shar14]

I created three hypotheticals because based on the rules my understanding was that J must come immediately before K which therefore limits the amount of spaces where J and K can go:

1st hypothetical: J K _
_ _ H

2nd hypothetical: _ _ J
K _ H
3rd hypothetical: _ _ _
J K H

The could be true questions made most of the answer choices look possible so I figured something has to be wrong with my diagramming but I am struggling to see what it is. Please help.

[Jeremy Press]

Hi Shar!

The big problem you're having here (which is a common problem on this game!) is that you misinterpreted the rule about J and K. The rule says that "J must be assigned to a stall numbered one higher than K's stall." Let's say, for the sake of argument, that we place K in stall 2. What is the stall that is "numbered one higher than" stall 2? It's stall 3. That's because the number 3 is "one number higher" than the number 2. Tricky rule, but if you follow it, what it means is that J actually has to come immediately after (not before) K. So your templates are actually not possible under the rules. Here's a global diagram that better captures that rule (plus the other rules). I've also sketched out the only two possible templates that fit with the correct understanding of the rule about J and K. Let us know if this clears things up!

Global diagram:

Screen Shot 2020-09-30 at 10.52.16 AM.png

Templates:

Screen Shot 2020-09-28 at 11.34.55 AM.png

[ltowns1]

Why can’t K be in 3 and J be in slot 4? Took me a minute to figure that it can’t, but I don’t see anything in the rules that say it cant?

[ltowns1]

Why can’t K be in 3 and J be in slot 4? Took me a minute to figure that it can’t, but I don’t see anything in the rules that say it cant?

answered my own question! Lol I see it now, I just totally ignored the last rule which says k can’t face H, which is 6.