Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Basic Linear: Unbalanced: Balanced game.

The game scenario establishes that six saxophonists are scheduled for six separate auditions, creating a Balanced scenario:

PT56-Dec2008_LGE-G1_srd1.png

Rule #1. This rule establishes a simple sequence:

PT56-Dec2008_LGE-G1_srd2.png

As with any two-variable sequence in a Basic Linear game, this sequence produces two Not Laws:

PT56-Dec2008_LGE-G1_srd3.png

Rules #2 and #3. These two rules establish a block-and-sequence diagram:

PT56-Dec2008_LGE-G1_srd4.png

Alternatively, this rule could be represented as:

PT56-Dec2008_LGE-G1_srd5.png

The operational effect of the rule is that K cannot audition first or second, and L and G cannot audition last:

PT56-Dec2008_LGE-G1_srd6.png

When the Not Laws from the first three rules are combined, we can infer that only F, H, or K can audition last, which will be shown as a triple-option on the final diagram.

Rule #4. This rule creates a split-block:

PT56-Dec2008_LGE-G1_srd7.png

By itself, this rule is automatically restricted because it requires three spaces. So, for example, if L or J were to audition second, then the remainder would have to audition fourth. Similarly, if L or J were to audition fifth, then the remainder would have to audition third. In addition, because neither L nor J can audition last, if either L or J auditions fourth, then the remainder must audition second.

Because L appears in both the third and fourth rules, you should carefully monitor the interaction of the variables, G, L, and J. Although there are a number of configurations for these three variables, one inference we will discuss is that L cannot audition fourth. This inference will be discussed in more detail in the discussion of question #6.

Combining the information above leads to the final diagram for the game:

PT56-Dec2008_LGE-G1_srd8.png

[christos]

after setting up the game, I have that J is ahead of H and L, while L with G is ahead of K. In question 3 we need to determine the earliest K can begin, which I think is 4 pm, but apparently the correct answer is 3 pm. Why is that? J goes to 1, L to 2/3, G to 3/2, K to 4. How can K go to 3?

[David Boyle]

after setting up the game, I have that J is ahead of H and L, while L with G is ahead of K. In question 3 we need to determine the earliest K can begin, which I think is 4 pm, but apparently the correct answer is 3 pm. Why is that? J goes to 1, L to 2/3, G to 3/2, K to 4. How can K go to 3?

Hello christos,

glkjhf gives you k in 3rd place.

Hope this helps,
David

[bethavedon]

Hi,

I ended up creating four different templates for this set-up, which got me through the game, but was very timely. Is there a more time-efficient way you'd recommend moving forward?

My templates were based on the rules of GL or LG and J_L or L_J so my templates were:

1. If JGL
2. If GL_J
3. If J_LG
4. If LGF

Thanks!

[Adam Tyson]

Good question, Beth, and one I have pondered myself. I tend to try templates on most games, and find them to be the right approach for me on about half of them.

This one, though, looks like templates would be more of a waste of time than they are worth. Getting the J_L and LG orders sorted out is nice, but where do I fit the H and K? What about F, my random? After considering them briefly and realizing that there is still so much room for H, K and F to move around those JLG blocks, I felt that it was best just to move on with a more basic diagram, including the appropriate not-laws, One inference I might get, but might not without a little playing around (asking myself what-if questions, like what if J is 4th or what if G is 5th), is that L cannot go 5th.

Others may disagree, but I think they take too much time here. For example, if I want to try the order JGL, I have to try it with J at 1, and then with J at 2, and then with J at 3 (which won't work). Same thing with the order J_LG - I have to do two more templates now. Then again with each of the other two possible orders. Too much!

So, I would diagram the rules, do the obvious not-laws, try a couple of what-ifs, and then be off to the races. I think in the long run it will prove worth it. Give that a try and see if you can't do away with the template approach this time.

Keep on plugging! Consider templates whenever you think they might be useful, but if you see that they aren't working out all that well, abandon that approach without looking back and move on to attacking the game another way.

[lina2020]

Hello,

I had quite a bit of trouble with this game in terms of setup. I was able to quickly diagram all of the rules but had trouble connecting them together so I had no choice but to move on to the questions. Can you please write out the most efficient approach for this game including how to go about connecting the rules in the final diagram and also the inferences that should be made?

Please advise.

[Jeremy Press]

Hi lina,

That's not an uncommon problem on this game! There isn't much "connecting" you can do, because the rule involving J and L is uncertain (we don't know which comes first in the block), and the rule involving L and G is also uncertain (again, we don't know which of L or G comes first in the block).

Other than the simple rule depictions, plus the basic Not Laws, there is one inference involving the second and third rules. Whichever way G and L are arranged in their block, K will have to come after both of them. That means neither G nor L can come 6th, and K cannot come 1st or 2nd. I've included a diagram of all of this below.

Global Diagram:

Screen Shot 2020-07-27 at 2.43.58 PM.png

[angelsfan0055]

Hi,
So another inference I made in this game is
J__LG- K, is this a correct inference to make? I wasn't entirely sure how much it helped me when I was doing the game, but I think it may have prevented me from recognizing that K can go 3rd. Also, I think the fact that GL can be interchangeable may have confused me?

[Adam Tyson]

I wouldn't call that an inference, angelsfan0055, but just one hypothetical positioning of those variables that works. When we talk about making inferences, we are talking about things that absolutely must be true, rather than just things that could be true.

Your hypothetical setup would indeed work, and it was one of the ones we covered earlier in this thread. If that was the relationship between J, L, and G, we would have to put either F or H in that space between J and L, and that would then influence where the remaining variable could go. Here are the possible solutions with that setup:

FJHLGK
JHLGFK
JHLGKF
JFLGHK
JFLGKH

You can probably see why we would not want to pursue an Identify the Possibilities approach with this game, or even a Template approach, because there are just so many ways to solve it! But you do have to be aware that the JL relationship could go in the opposite order, as could the LG relationship, and that K could therefore end up earlier in the order. As shown in the diagram that Jeremy provided, this game could have the first four variables in order be GLKJ, followed by F and H in either order.

Coming up with possible orders is great, but it's crucial to be flexible in your thinking and account for other possible orders too! Whether you do that with templates or not is sometimes a difficult call, but just be sure not to box yourself into thinking a game must be done a certain way when there may be alternatives.

[emilyjmyer]

Hi!

I had some trouble with this game. I diagrammed all of the rules correctly and identified almost (but not all) of the not laws. After diagramming all of the rules I tried to combine all of the rules. I thought that was something we wanted to do. But I see that the PowerScore set up did not do that. And, I wonder if that was the source of my difficulty with completing the questions.

I made a diagram that was something combined the GL/LG rule with the L_J/J_L rule and then had -H and -K coming off of them diagonally to show that H and K both had to come after GLJ.

Is that incorrect? Why do we not want to combine the rules? Also, I know that it is hard for me to describe my diagram without a picture so my apologies.

Thanks for your help!