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February 17, 2011

Linear Logic Game Diagram and Explanation

LSAT Blog Linear Logic Game Diagram Explanation FijiMy Basic Linear LSAT Logic Game has been without an explanation for far too long.

By popular demand, I'll demonstrate below how to create a diagram for it.

We have 7 variables: ABCDEFG. (I wasn't feeling creative that day.)

Here are the rules, numbered for quick reference:

1. Jandra must visit exactly two countries before her visit to China but after her visit to Bahrain.

2. China cannot be the last country she visits.

3. Jandra cannot visit Bahrain until she has visited Australia.

4. She cannot visit England immediately after she visits Djibouti, nor can she visit Djibouti immediately after she visits England.

5. Fiji must be visited either 4th or 5th.

***

The rules are not primarily about 1 variable going before or after another, as in a Pure Sequencing game. Instead, we have rules that refer to specific spaces, like rule 5, and other rules about immediacy/adjacency, like rule 4.

As such, I consider this game as a Basic Linear game and diagram it as such, with 7 spaces, numbered 1-7:





Rule 1 tells us we have 2 spaces between C and B. Those 2 are before C, and B's even before those. As such, we'll have B _ _ C . We can put a box around it to indicate that there are exactly 2 between them.

Rule 2 tells us C can't be last, so we can place C with a slash through it under the 7th space.

Rule 3 tells us B can't go before A goes. Because no 2 countries are visited simultaneously, we can say that A must go before B. We can diagram this as A - B. Since we already know that we have B _ _ C, we can combine the 2 rules to indicate that A is before B _ _ C, giving us:




Rule 4 tells us D and E can't be adjacent (touching). As such, I'll draw them touching in both orders and put a slash through each ordering. I'll also put a box around them to indicate that their adjacency is what isn't permitted.

Rule 5 tells us F must be 4th or 5th, so I'll put F/ on 4 and /F on 5, to indicate that we either have F on 4 and something else on 5, or we have F on 5 and something else on 4.

I know that's a lot to swallow, so here's a diagram to clear things up for you:






You could simply move on to the game's questions at this point. However, I prefer to instead make some major inferences.

The B _ _ C rule is like the 800-pound gorilla taking up too many seats on the subway/bus/airplane/spaceship. By figuring out the limited places it can fit, we can make some major deductions about where everyone else goes.

B can't start off on 1 because A's got to go before it. B can't end up on any of 5, 6, or 7 because we've got to fit "_ _ C" after it.

As such, B is limited to starting off this enormous unit on 2, 3, or 4, and we can create 3 separate stacked possibilities to represent those options. We can have B on 2 and C on 5, we can have B on 3 and C on 6, or we can have B on 4 and C on 7, generally speaking. Here's what it initially looks like:







(I've temporarily removed Rule 5 - the one regarding F - from the image, but I'll discuss it now.)

In the top possibility, because C's on 5, we'll need to have F on 4. We also know that A must be on 1 in order to go before B, due to Rule 3.

In the middle possibility, because neither B nor C is on either 4 or 5, F could be on either 4 or 5. We can now break this possibility in 2, based upon whether F goes on 4 or 5.

In the bottom possibility, F would have to be on 5, but this possibility is invalid because C can't be on 7, due to Rule 2. As such, this option is eliminated.

So far, this might have been drawn as this:







However, I'll now draw it as:







In the top possibility, we'll need to have one of D or E go on 3 so that they're not together on 6 and 7, which would violate Rule 4. The remaining spaces will feature G and whichever one of D or E didn't go on 3. Either we'll have G on 6 and one of the E/D pair on 7, or we'll have G on 7 and one of the E/D pair on 6.

In each of the bottom 2 possibilities, A must be on either 1 or 2 to ensure that it goes before B, due to Rule 3. Because of this, we know that whatever happens, D and E will never be adjacent in either of these diagrams. That's because 1 and 2 are the only remaining empty adjacent spaces in those diagrams.








The top diagram is pretty much fleshed-out now. The bottom 2 diagrams lack only D, E, and G, which can go pretty much anywhere at this point, since we're no longer in danger of having D and E be adjacent, and since G can always go anywhere.

As always, some of you will likely be thinking that this is way too much time invested up-front.

Is it possible to solve this game without a huge fancy diagram, simply using the basic diagram I drew earlier? Of course.

However, I'm all about showing you the deeper inferences so that you have a bird's-eye view of the game whenever possible. This gives you a stronger jumping-off point from which to create hypothetical diagrams over the course of the game.

***


The text below contains the answers to the above Logic Game.


1. A
2. B
3. D
4. D
5. C


***

The "Difficult Version" of this Logic Game is logically-equivalent, just with different variables, so I'm not going to bother creating a diagram for it. Just use the explanation in this post to understand my approach for it.



12 comments:

  1. Good to be the first to comment here... Good job on drawing the diagrams! They must have cost lot of time...

    Just a question for you, Steve: I just wrote the Feb LSAT, but I had a hard time on the LG section.I knew it was not that hard (I usually got 20+ LG questions correct in my PrepTests) but in the actual test, I just sit there with absolutely NOTHING in my head. I knew this was not good, and I tried to figure out what's happening, but the more time I spent on calming myself down, the more anxious I got because of the obvious time pressure.

    I have to take the June test, and I don't want that same "blackout" to happen again. What should I do to avoid it?

    Thanks a lot, Steve!

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  2. Practice and re-practice individual games and sections at different times of the day so it becomes reflexive and not a thoughtful process. I used to imagine Steve as a drill sargent yelling, "Drop down, and give me 24, soldier!" in my face unexpectedly, and my complying without thinking. (The 24 being the 24 questions in an LG section.) It worked. Do you like LGs? It is important.

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  3. I see great diagrams but still don't see the answers to the questions posted when I click on the white highlighted area.

    ReplyDelete
  4. Liah - highlight over the white area (don't just click, click and drag).

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  5. steve,
    thanks for all the wonderful work you are doing.
    i have two questions.
    in the game above,shouldnt B be anytime before the 2 countries and china?
    ie, the rule can be interpreted as B_ _ _ C or B _ _ C , since from the statement it looks like B can appear anytime before the visit of china and the two contries and not immediately before the two countries. please explain.
    similarly,when a rule says, B works two days after A does. i think it implies A_ _ B but rule says A_B. can you explain this too?
    thanks again.

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  6. Steve, i made the deeper inferences of this problem and got all the questions right, however, I cant seem to finish the problems within the 8:45 time limit. Usually takes me 10mins. I wonder if its because i spend too much time on the deductions, however the deductions help me with getting the answers correct and i go through them faster. I just cant seem to cut my time on the diagrams (i use all the shorthands and abreviations). What would you recommend: just use the initial diagram and start going through the questions, or spend more time on deductions knowing i'm going to take longer?

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  7. For the difficult version of this game, can you please provide an explanation for question #1? I narrowed it down to A and D but couldn't seem to find anything wrong with either of the options based on the limitations provided in the question.

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  8. Since you narrowed down B, C, and E, I won't bother explaining them.

    First off, A is the correct answer. I'll now explain why D isn't. D has Athena written twice, and Ares is absent. Isn't that simple? :)

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  9. This comment has been removed by the author.

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  10. Grant, thank you for explaining that. I did not post the question, but I have been stuck trying to figure out the answer for an embarrassingly large amount of time.

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  11. I'm sorry, I'm lost as to where the answers are located.

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  12. I'm preparing for the June 2014 test, paid for the 4-month study schedule, and am one Day One today. I'm working through the problems (I've taken the test once and bombed it, so I'm familiar with what is required test-wise) and am glad to have found this blog. However, like others, I'm not seeing a "white area" where I'm supposed to click for the answers. ??

    ReplyDelete