Setup and Rule Diagrams

[Administrator]

This Advanced Linear game presents a two-variable sequence: the six singers, and the 2/4 split of Recorded/Unrecorded auditions. LSAC is even generous enough to tell us the two recorded auditions, K and L.

So to set this up, use 1-6 as the base with two rows (two stacks) above each number. The lower row we'll use for the singers, K through Z, and the upper to note whether that position is Recorded or not.

The rules are mercifully free of convolution, and, as we'll soon see, lead to some extremely powerful inferences.

The first two tell us that 4 is not recorded, and 5 is. That means 4 cannot be either K or L and we can note K and L as Not Laws beneath 4 (and R in the upper space above it), while 5 must be K or L so we can show K/L in the first row above 5 (and R above that).

Rules 3 and 4 form a chain: W ahead of K and L, and K ahead of T. This, too, leads to Not Laws, which we'll begin to add once we've considered the fifth and final rule.

Rule 5 is a simple sequence with Z --- Y.

Now that we have the rules in place, let's see what we get when we begin to combine them. From the two sequences--the one including W, L, K, T and the other with Z and Y--it's clear that only W or Z can go first, and only T or Y can go last. So spaces 1 and 6 are filled with split options, and must both then be Unrecorded auditions.

We can also see that T has at least two auditions ahead of it (W and K, minimum), so T isn't 2. W is restricted further as well, since it must be before both recorded auditions--K and L--but only recorded spot is open in spaces 4-6 (space 5). So W in either 3 or 4 would force those two recorded auditions into the final spaces where there isn't room for both of them. W in 3 and 4 are both Not Laws then.

Lastly, we have Y. Y is tricky, since it has to appear after Z, but if it's to go up near the front it must also leave room for W. Remember, W can only go in 1 or 2, and if W is in 2 then Z is in 1. So Y in 2 causes problems: it either forces W into 1 and then Y is no longer after Z (last rule), or Z goes into 1 and W goes later than 2, which is also an issue. So no Y in 2.

But what about Y in 3? Consider what occurs: W and Z are in 1 and 2, although we don't know their order. It also means T is in 6. And K and L? They'd have to be 4 and 5, which seems okay until you recall that 4 is an Unrecorded spot and K and L are both Recorded. Uh oh. What caused this conflict? Y in 3, which now becomes another Not Law.

I told you there were a lot of inferences here.

Ultimately the setup I used to attack the questions looked like this:

Game 4.JPG

Here's the thing though: even if you missed a few of these inferences at the outset, or just felt like you were spending too much time setting this up and moved to the questions with an "incomplete" diagram, you'd be fine. Really. Either a missing inference won't be tested or, as happens a few times here, it'll be revealed quite clearly by the questions.

[sbieber1221]

Hi,

I'm a bit confused how we came up with the inference that L can't be the 6th singer from a traditional sequencing diagram. I ended up doing a template for this question based on the dual options for 1 and 5 and discovered L couldn't be in 6 but was just curious how I could bypass making a template to come to this conclusion.

Thanks!

[Alex Bodaken]

sbeiber1221,

Thanks for the question! L can't be 6th because of the combination of two rules:

The fifth audition must be recorded

and

Kammer must be before Trillo (K T)

Because we know that the fifth audition must be recorded, we know that the fifth singer is either K or L (they are the only two singers who are recorded). If we place L in the 6th spot, then that means that K must be in the fifth spot. But if K is fifth and L is sixth, there is nowhere to place T after K, which we must do. Since that is impossible, L ends up not being able to be in the 6th spot.

Hope that helps!
Alex

[deck1134]

Hi PowerScore,

I'm super confused as to how we know that there are dual options on 1 and 6. I couldn't see that during the game, and got BURNED on this one.

Why couldn't it be Z Y W ...? Doesn't that fulfill the Z--Y without eliminating the chain of W, K, T, and L? I have stared and stared, and drawn and drawn, but cannot seem to see the inference between W and Y. Why can position 6 not be recorded?

I got stuck here and really fowled the game up.

[Adam Tyson]

For position 1, Deck, we know that K, T, and L cannot be there, because they are all after W. Y cannot be there, because it must be after Z. That leaves only W and Z available to go first.

6th is a little tougher, but it starts with Z, W and K not going there because they are all before at least one other variable (Z is before Y, W is before K, L, and T, K is before T). So why not put L 6th? Let's see what would happen:

L 6th would force K to be 5th, because those are the only recorded auditions and one of them must be 5th.

K must be before T, so...whoops! If K is 5th and L is 6th, T cannot fit after K! That proves that L cannot go 6th, and so 6th must not be recorded.

Don't forget that rule about 5th being recorded!

[Kelly R]

Hi PS,

I was able to solve this game and made the lion's share of the inferences, but notice that it takes me a bit too long to recognize the more discreet not-law inferences (like the 2 Y not-law inferences in this game, for example). What should have tipped me off to the fact that I ought to look to Y for potential not-laws? These inferences are a bit difficult for me generally, so wondering if you might have any tips for recognizing these kinds of inferences moving forward. Thanks.

[Kelly R]

Hi PS,

I'm a bit confused by the implications of the second rule in this game. I diagrammed this rule using a double-branched sequence, which produced an original conditional statement that read: (H--L)--> M/H--L and the contrapositive (with a double-branched sufficient condition) L--M/H--> (L--H). From this, I was able to deduce that M/H, L was a viable sequence via the original conditional, and L--M/H was a viable sequence via the contrapositive. I'm not sure, however, where the M--L--H sequence came from. Via the contrapositive, L must come before M, so I'm not sure what generates the M--L--H sequence. Have I misunderstood the conditional nature of this sequence?

The implications of these 3 sequences still aren't totally clear to me, either. Do these sequences provide the only 3 patterns to which a viable solution can conform? My intuition was to refer to these rules only when the sufficient condition of the original statement or its contrapositive was triggered, but it seems like these rules were used more as a template than as an active conditional statement.

Additionally, though I now see that the H--L--M sequence is clearly prohibited by the rules, I didn't notice this in my initial set-up and certainly didn't think to examine it for potential not-laws. What should have tipped me off to this in the initial set up/ what should I be looking for moving forward to better identify these kinds of inferences?

I don't generally struggle with games, but had a pretty tough time maintaining control over this one and am wondering if someone might be able to help me better understand the implications of rule 2 and the workings of this game in general. Also, are you guys familiar with any games similar to this one? Thanks so much.

[Kelly R]

Apologies for the double post, one last question!

Will a conditional sequence like this one always provide 3 viable base sequences, and 1 base sequence that is impossible (the H--L--M sequence, in this case)? I just revisited the conditional sequencing section of the LG Bible and am still a bit unsure. Thanks so much!

[Adam Tyson]

Hey Kelly, I think your last two posts on this thread must be about a different game - this thread is for the last game from June 2016, the singer auditions. I think I know which game you meant to ask about, but don't want to make an incorrect assumption, so perhaps you could copy those last two posts into the correct thread for us and we will answer them there (if they have not already been answered in the correct thread)?

Regarding the more subtle inferences about Y, my advice is not to worry about getting ALL the inferences that may be available in a game. Many times, we expect to leave a few undiscovered, and we will find them later if required in order to answer a particular question, like the inferences about Y in question 22. I didn't make those inferences at first either, but the question can still be answered by looking at prior solutions done for earlier questions, and/or by testing your contender answer choices and discovering the problems with some of those placements. We often use the analogy of microwave popcorn - you have to expect to leave some unpopped kernels in the bottom of the bag, because trying to pop them all leads to a burnt mess!

My philosophy is this: you have to get the obvious inferences, like Z not going last and Y not going first. You have to search for at least some inferences that are a little less obvious, like L not going last. But you have to at some point say to yourself "okay, that's enough, I've found some good info and I am not seeing what else to do, so let's go to the questions and see what else we can figure out along the way." If we keep on pushing for more and more inferences, staring at the diagram for long periods of time or just trying things at random to see what else happens, we end up wasting precious time for very little reward. If you miss an inference that you need later in order to answer a question, you will realize that when you get to that question and cannot immediately answer it, and that's when you should do the additional work to suss it out.

Go forward boldly, and don't be afraid to leave an inference or two undiscovered!