Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

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

The game scenario creates a five day linear scenario:

J96_Game_#2_setup_diagram 1.png

The first rule establishes that the two days of each workshop are consecutive, resulting in four blocks:

J96_Game_#2_setup_diagram 2.png

The second rule establishes that on each of the five days, there is a minimum of one workshop and a maximum of two workshops. This results in an unfixed 2-2-2-1-1 numerical distribution.

The third rule creates a sequencing relationship:

J96_Game_#2_setup_diagram 3.png

While this rule creates several Not Laws, the better decision here is to bypass showing the Not Laws, and use the information in the three rules to Identify the Templates. Based on the position of LL, only two major templates exist:


Template #1: LL on Tuesday-Wednesday:

When LL is in session on Tuesday-Wednesday, Both PP and RR must be in session on Thursday-Friday. SS, the only remaining unplaced workshop, must then be on Monday-Tuesday because Monday must have a workshop in session:

J96_Game_#2_setup_diagram 4.png

Template #2: LL on Monday-Tuesday:

When LL is in session on Monday-Tuesday, there are a greater number of possibilities. PP and RR can be in session only on Wednesday, Thursday, and Friday, so no matter what configuration they are in, they will each be in session on Thursday, and their “remainder” will be in session on Wednesday or else on Friday (this is the Overlap Principle at work):

J96_Game_#2_setup_diagram 5.png

Because Thursday must have a P and an R session, S cannot be in session on Thursday (that would lead to three sessions on Thursday, a violation of the second rule). That also means that S cannot be in session on Friday. Thus, S must be in session on Monday-Tuesday, or Tuesday-Wednesday, leading to two more templates:


Template #2A: LL on Monday-Tuesday, SS on Monday-Tuesday:

When SS is on Monday-Tuesday, then one of P or R must be on Wednesday, and the other must be on Friday in order to conform to the second rule. Both P and R can never both be Wednesday-Thursday because that would leave Friday without a workshop.

J96_Game_#2_setup_diagram 6.png

Template #2B: LL on Monday-Tuesday, SS on Tuesday-Wednesday:

When SS is on Tuesday-Wednesday, P and R could both be on Thursday-Friday, or one could be Wednesday-Thursday and the other could be Thursday-Friday.

J96_Game_#2_setup_diagram 7.png

Template #1, Template #2A, and Template #2B capture all six of the possibilities in this game, and with them (or any variation, such as two main templates instead of three), the questions are relatively easy.

[rsj]

I'm really confused on how to go about diagramming this question. Infact, I think I'm having a hard time understanding it.

I know that LL> RR and PP

but does this mean that the conditions with overlap?

Is there any way you can just explain how to produce the initial diagram to this.

I'm not having trouble with the other advanced linear games but for some reason this one is confusing me.

Thanks in advance!

[Nikki Siclunov]

Hi RSJ,

You have 4 two-day workshops, and the two days on which a given workshop is in session are consecutive. So, you will have the following four blocks to line up over the course of five consecutive days:

LL
PP
RR
SS

The base should be the variable set that has an inherent order to it, which - in this game - are the days of the week:

M T W Th F

On each of the five days, at least one, but no more than two, of the workshops are in session. Since we have a total of 8 workshop days (two for each workshop), the numerical distribution of workshop days to week days would be 2-2-2-1-1.

The third rule can be diagrammed as follows:

LL > PP and RR

LL cannot overlap with either PP or RR, but of course PP and RR can overlap. As a result, the LL block will fall either on Monday and Tuesday, or else on Tuesday and Wednesday (either way, there will be a Lighting workshop on Tuesday).

From this point on, I'd make two templates:

Template 1: LL on Tuesday and Wednesday

This pushes the two RR/PP blocks to be on Thursday and Friday. Also, the SS block must now be on Monday and Tuesday; otherwise, there will be workshop on Monday.

Template 2: LL on Monday and Tuesday

Although the PP/RR blocks can now be on either W/Th or Th/F (giving you two additional templates), in either case they will overlap on Thursday. Since you can have at most two workshops on a given day, the SS block will now need to go on Monday/Tuesday or Tuesday/Wednesday - either way, the SS block will overlap with the LL block on at least one day (i.e. on Tuesday).

Hope this helps!

[bella243]

Is this question considered as challenging/difficult in general?

[Adam Tyson]

I wouldn't say so, bella, especially not if you do the templates as Nikki suggested in this thread. This game should be one of the easier ones on this test. But difficulty is a relative thing, personal to each student, and what one person finds easy might be very challenging to someone else, and those same two people might feel just the opposite about some other game. So don't worry about what we think about the difficulty of this game - think about what YOU felt about it. If you found it challenging, why, and what can you learn from that experience? What new tools can you bring to bear on it that would make it easier, such as using the template approach, or diagramming the variables as paired blocks rather than as single letters?

Find what makes a game challenging to you, and then study ways to make it less challenging. Then you can apply those new ideas and skills to other games, which will become easier as a result. You've got this!