Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is an Advanced Linear: Balanced game.

The game scenario indicates that six people ride a bus together. The bus seats are divided into three rows of two seats each. This creates an Advanced Linear: Balanced scenario:

PT36-Dec2001_LGE-G3_srd1.png

The first rule indicates that G and H form a block in the aisle seats:

PT36-Dec2001_LGE-G3_srd2.png

This rule eliminates G and H from sitting in the window seats, and additionally eliminates H from sitting in row 1 and G from sitting in row 3. Because the GH block must occupy the aisle seats in rows 1-2 or rows 2-3, either G or H always sit in the aisle seat in row 2:

PT36-Dec2001_LGE-G3_srd3.png

The second rule states that if M occupies an aisle seat, then H and L sit in the same row, with H in the aisle seat according to the first rule:

PT36-Dec2001_LGE-G3_srd4.png

The third rule is another odd rule, and states that when G and K sit in the same row, then M is in the seat directly behind I’s seat. The phrase “directly behind” indicates that they are both in window seats or both in aisle seats; however, I and M cannot be in aisle seats because that would not leave room for the GH block, and so I and M would have to be in window seats:

PT36-Dec2001_LGE-G3_srd5.png

More on this rule shortly.

The fourth rule states that when K occupies a window seat, M sits in row 3:

PT36-Dec2001_LGE-G3_srd6.png

The fifth rule states that when K occupies a seat in row 3, I sits in row 1:

PT36-Dec2001_LGE-G3_srd7.png

You may have noted that the rules in this game are extremely varied. This makes remembering the rules more difficult, and increases the difficulty of applying the rules. Not surprisingly, most students feel that this is the most difficult game of the test.

With the basic diagram of each rule in place, let’s consider some of the inferences that can be drawn when the rules are linked together.

The third rule can only be enacted if K and G sit in row 1. Otherwise, there is no room for the IM block. In fact, the rules are so restrictive that when the K and G rule is enacted there is only one solution to the game:

PT36-Dec2001_LGE-G3_srd8.png

The second rule also produces a severely limited scenario. When M sits in an aisle seat, M must be in row 1 or 3 in order to accommodate the GH block. However, with the aisle seats filled, K must sit in a window seat. This enacts the fourth rule, which stipulates that when K sits in a window seat, M must sit in row 3:

PT36-Dec2001_LGE-G3_srd9.png

Further, the third rule ultimately prohibits K from sitting in row 1, and thus K must sit in row 3. Finally, I must sit in row 1:

PT36-Dec2001_LGE-G3_srd10.png

At this point, you might be coming to the realization that there are a limited number of solutions to this game. In fact, only seven templates containing fourteen possibilities exist in this game. Although one approach would be to identify each of these templates, there are likely too many templates to be able to show each within the time limits of the game. Normally, we would prefer to draw out four or five templates at most.

With the variety of rules, you should remember that using hypotheticals can be a very effective weapon. If you find yourself unable to identify the inferences in a game, draw out a few solutions to the game; this approach allows you to work with the rules and at the same time increase your knowledge of the game. For example, the following hypothetical proves correct answer choice (E) on Question #14 and answer choice (A) on question #15:

PT36-Dec2001_LGE-G3_srd11.png

Before moving on to the questions, here is the final setup for the game:

PT36-Dec2001_LGE-G3_srd12.png

[afinelli]

This game took me quite awhile to get through. Is there any trick to setting it up that I missed? All I could really do in my set up was place GH in the aisle seats.
Thanks!

[Dave Killoran]

The rules in this game are pretty varied, and this makes remembering them much more difficult. Overall, it is a tough game.

Take a closer look at the second and third rules: there's only one solution when either the third or fourth rule is enacted. That helps narrow the number of solution to the game (there are only 14 total).

If you don't see how the varied rules fit together to produce limitation (and I'll agree it is not easy to do so), then use hypotheticals to help out on certain questions.

That's a start--let me know if there is anything specific you'd like me to address.

Thanks!

[alee]

Hi guys,

This question refers to Game 3 of the Dec 2001. There are 6 people, G H J K L M, who are to be placed into 6 slots (bus seats, subdivided into 3 rows, each row with a window and aisle seat).

1. What are people's opinions on what is the best variable set to use as the base? Having looked at the rules, I tried using the 2 groups, window, and aisle seats, and then having 3 rows extending vertically from each of these columns (w & a) corresponding to rows 1, 2 and 3. This seems to nicely represent the spatial aspect of the game (i.e. directly behind vs. behind but not directly behind)

2. Next I created 2 templates based on rule 1, which says that H occupies the aisle seat immediately behind G's aisle seat. It's neat because there are only 3 rows so just 2 possibilities for the placement of the HG block.

3. However, this doesn't really seem to lead to a clear way to deal with rules 3-5, which are all conditional. It also doesn't help so much (at least for me so far...) with the first question (Q14), which stumped me as to how to deal with without wasting considerable time.

All

[Jon Denning]

Hey All - thanks for the questions. I've addressed them individually below:

1. I'd likely set this game up just like you did: with two vertical columns of three spaces (numbered 1, 2, and 3 from the bottom to the top), and I'd label the columns W on the left and A on the right (window and aisle). That makes the most sense to me because that's what the scenario described would actually look like if you were looking from the front of a bus towards the back.

2/3. You're right about the first rule creating two possibilities of where you could place that block. However I wouldn't attack this game with templates because those two placements don't really yield a lot of additional inferences; the fact that four of the five rules are conditional would be a big clue to me that there's probably a good bit of uncertainty to this game, so templates are unlikely to be the best strategy.


So I think for the most part your suspicions about this game are correct. One last tip: if you get a question like 14 here (global could be true) to start and you don't feel that you'll be able to quickly spot the answer, skip it and see if the other questions give you some further insights that might help you solve it. It's possible (likely even) that you'll answer a question like 14 as you do the work for other questions, so hang on to it and return later with more information.

Hope this helps!

[SherryZ]

Thank you for your time and patience!

Dec 2001 LSAT, Sec 4, Game 3:

I found this game soooo tricky and time-consuming! I did not time it but I definitely spent more than 20 mins to solve it (Luckily, i got it all right).

Could you show me how to set up this game in most efficient way? Also, I did not make any inference from the conditions, maybe that's why I finished it sooo slowly

Thank you very much!!

---Sherry

[Emily Haney-Caron]

Hi Sherry,

This is definitely a tricky game, with some difficult inferences. Great job answering all the questions correctly!

For this game, you have more information than you think you have, but this is a case where that additional information doesn't necessarily make the questions go much faster. I'll walk through the inferences, though, and see if they are helpful to you.

With Rule 2, we know that if M is in the aisle, then L is in the window seat, because L has to sit next to H and H has to be in an aisle seat. M in the aisle therefore leads to an LH block, and that block can't be in the first row because of Rule 1.

We have a similar inference with Rule 3. If K is next to G, we know that K is in the window seat, because G has to be in an aisle, and we know that KG block cannot be in row 3 (because G can't be in row 3 based on Rule 1). The KG block also can't be in row 2, because that would break up I and M. Therefore, KG is in row 1. From Rule 2, we know that I and M must both be in the window seat, because if M was in the aisle we would need an LH block and we run out of rows. Because H has to go immediately after G, we know that if K and G are in the same row, there is only one possible solution:
KG
IH
ML

We also have some rules that cannot both be triggered at the same time. If Rule 2 is triggered, Rule 3 cannot be - they are mutually exclusive. The same is true with Rule 3 and Rule 5; if one of them is triggered, the other is not. Therefore, in situations where one of those rules is triggered, you have one fewer rule to be concerned with as you try to narrow down possibilities.

This is still a difficult game. In terms of set up, I had three rows top to bottom labeled 1, 2, and 3, and each of those rows had two seats (window seats on the left, aisle seats on the right):
1__ __
2__ __
3__ __
W A

I also indicated on my diagram that H could not go in row 1 and G could not go in row 3, and H and G both could not go in the window seats.

Please let me know if you have any additional questions!

[SherryZ]

Hi Emily,

Thank you for your help! I find that even if use the method you mentioned to solve this game, it is still time-consuming. If we confront this kinda game in real test, should we give up or solve it later?

Thank you!

--Sherry

[Dave Killoran]

Hi Sherry,

If you run into a game you find to be hard at the outset, the best strategy is to push that game to the end of the section. The theory goes that, if possible, you'd prefer to do the easiest games first, and end with the hardest games.

Thanks!