Diagram

[kevmillva]

Hi,
Does anyone have a good representation of the conditionals (rules 3-4) for this game, or a good idea for conditionals on sequencing games in general? This game took a really long time to mentally chunk through the rules, mostly because I brute-forced it, particularly on Q22 and Q23.

Thanks,
Kevin

[ManhattanPrepLSAT1]

This is a tough one, and I think that it's really important. Attached is the setup with 2 frames you can establish before you begin the questions. If you don't have them, the game can be much harder.



Also, I've worked through question #22 so that you can see how having the information organized initially can make a big difference. Try applying this to question #23 and let me know what you think.

If you want to see a couple other examples of games very similar to this check out...

PT53, S2, G2
PT51, S4, G2
PT50, S3, G4
Feb 2000, S1, G2 available in the SuperPrep released by the LSAC and available at Amazon for $15.

[kevmillva]

Thanks, mshermn.

It makes a lot more sense now. I eventually grasped that Q22 relied on the contrapositive of Rule #3, but it took me about 2 minutes too long to get there while working the game. And now I see that Q23 falls naturally out of the insight that M cannot fall between H and K, meaning it can't be in the fourth position.

Interestingly, though, just struggling through this once helped a lot. About 20 minutes after bombing this game, I worked PT53, G2, and was much more successful. I notice that both games have at least one question which exploits an inference that some piece cannot fall between two other pieces. In PT53 G2, question 8 exploits the exclusionary nature of rule 2 (G not between J and L). Once you are tuned into dealing with that kind of idea, it is easier to see next time.

- Kevin

[lisahollchang]

For this question, I ended up with three frames. Let me know what you think of my process:

Rules:

H/F .... G ....K

F-M --> L-H

I combined this inference with the last rule.

If M-H there are two possibilities:

1) F -M leads to only one solution:
*FMLHGK
2) If not F-M then leads to the following setup:
M ... H/F ... G ...K (L is a floater)

If K-M then there is only one possibility, which would be my third frame:
3) L-H/F....G....K....M

If K-M then M cannot come before F.

These three frames helped speed up my answering the questions.
Also, I've found the either/or rules to be difficult game types for me and making frames does help a lot.

Let me know what you think!

[ManhattanPrepLSAT1]

I like the approach but not the results. It's tough to read precisely, but I think you're missing possible solutions within your frames. If you make a slide using powerpoint and the regular Tree Setup similar to the one I used in my slide attached to an earlier post, I'd be glad to check again.

I know that typing in games is not as easy as drawing games. Try drawing it, and then I'll check again.

[lisahollchang]

Hi mshermn,

Thanks for taking the time to revisit this one.

I'm attaching the slides that show my work.
I should comment that I found some more possibilities on my first frame which is now reflected in the slides
I can't attach documents so you'll have to follow the links:

Slides one and two:
[deleted links]

While time consuming, this was really fun!

[ManhattanPrepLSAT1]

That's fine. I had no problem following the links. Not sure you want to have public links over to what appears to personal pictures. I've edited your message to remove the links.

I checked your work and it appears great. Your process was different than mine for piecing together the Tree elements, but it was solid, great work!

[lisahollchang]

Thanks!

[marc.herman39]

Hi,

I tried a different way to diagram them out, please tell me if it's okay?

Instead of incorporating the H M K in to the diagram, I left this off to the side and incorporated the contrapositive statement instead of the HMK rule... basically my diagrams looked like this;

1. F-G-K

* F before M
*L before H
*H before G

2. F-G-K

*M before F
*H before G
*H before L

If you can see,my first diagram had the 'if FM' whilst my second one had 'if MF'. Is deducting that if F isn't before M then M must be before F okay? or is that contravening the rules of the contrapositive?

Sorry if there is confusion...

Marc

[ManhattanPrepLSAT1]

I like the attempt to find another way of setting up the frames. Unfortunately, your second frame incorporates a common error in conditional logic. It's called a negation.

According to the 3rd constraint:

F -- M ---> L -- H

The contrapostive of this is:

H -- L ---> M -- F

According to your second frame, you've interpreted the contrapositve to read:

M -- F ---> H -- L

Be careful! That's not a valid manipulation of the conditional relationship. Let me know if you have further questions on this, as it's a tricky step and one full of opportunities to make an error that can cost you the whole game!

[kdeclark]

Hey mshermn. I came up with the same two frames as you, but then I split frame 1 into two of its own frames, one with F-M and L-H, and the other with M-F and L as a floater. Is there anything wrong with doing it this way?

So I ended up with these three frames. The last two are your "frame 1" divided into two possibilities, around the F-M rule (ignore the periods. I need them to keep the letters on the second row in place):

L - H - G - K - L - M
......F /

F - M - H - G - K
......L /

M - F - G - K L (floater)
...\ H /

Let me know if that doesn't make sense. I have no way to upload the image.

[ManhattanPrepLSAT1]

Hi kdeclark!

That looks good to me. The interesting things about frames, is that there is some degree of preference involved. Some may prefer to have more frames with more clarity, others prefer to have fewer frames and more ambiguity.

I generally try to limit my framing to 2-4 frames. By that rule, your options look great. Just to clarify, you have L as the floater in your 3rd frame?

M - F - G - K L (floater)
...\ H /

[kdeclark]

Thanks mshermn! That's right. The formatting is bad. Thanks for your response.

Because of some confusion I've been having about the best way to approach these RO problems, I've posted a action sequence for attacking these problems, and I'd like to know whether you think it's sound. Primarily, I'd like to make sure that I'm not assuming I'll get a exhaustive list of possibilities when in fact what I'm getting is a partial list.

The explanation is on the forum for Game 2 (Architect game) from PT 53. If you have a chance to look at that, I'd appreciate it.

[abigailsean]

I'm a bit confused. I thought for contropositives you were supposed to negate and reverse? But you didn't negate the contropositive you did...

Explain?

[timmydoeslsat]

If A is before B, then Y is before Z.

To show the contrapositive we have:

Z - Y ---> B - A

This is a matter of placement. It is either the case that A comes before B or that B comes before A (Since this game does not have ties). The contrapositive will be triggered in the hypothetical rule above when we have a situation of A coming before B.

In short, the logic of this contrapositive is not any different than what you normally see. Technically what is going on is this:

[Z-Y] ---> [B-A]

We are switching the [B-A] to the left side and negating it, which is how we come up with A-B.

[schmid215]

EDIT: The spatial framework of my trees became much different when I posted, so it might be harder to read them. Sorry about that, MLSAT Geeks.

I came up with three possible trees for this game and worked off of those. I got all the questions right, but I am wondering if what I did was the most efficient approach, or if something is wrong with my trees and I just got a little lucky to get all of them right. Clearly, I was doing something right, but I'm not 100% sure if I'm doing this optimally, primarily b\c I am not very good at LG.

After the first two rules, I had:
H
F-G-K (Line from H-G, no other lines)

From the third rule, I created two possible trees
L-H
F-M--->L-H: F-G-K (H-G, F-M, no other lines)
M


H---L
Contra: M-F-G-K (H-G, no other lines)

The fourth rules gives us M before K and H, or H and K before M, so I tried to incorporate those two possibilities into the two trees I had to come up with master trees that would give me all the possibilities.

M before K and H applied to the tree derived from F-M--->L-H:

L-H
F-G-K (Line from M-H, and M-K, no other lines)
M


H and K before M applied to the same tree:


L-H-----M
F-G-K (Lines from H-G, K-M, and no others)


Now, M before K and H applied to the tree deriving from H-L--->M-F

H--L
M-F-G-K (Line from M-H, and H-G, no other lines)

H and K before M can't be applied to this tree, because it has M-K, leaving me with three trees to answer the questions.