Diagram

[stackoutawinner]

I'm looking for a quicker and more accurate solution to the circular style game. After consulting with the LGB in the forgotten few section, I attempted this game. Spending what seemed around 15 minutes (far too long), I still managed to miss 4 of the 7 questions.

The method outlined in the LGB is to modify the numbered list structure into spokes, and begin filling in any contraints where people sit directly across from each other. From there, fill in any chunks. Because the questions tend to contain more local (or question specific) constraints, you're pretty much left to plug and chug. The hope is that by the end of the section that you can use some of previous drawings to help answer the questions.

Either way, it requires copious drawings that burn precious time.

So, given this background information, does anyone have a quicker or more accurate solution to this style game?

FYI, the Q's that I was able to answer were the 3rd, 5th, and 6th. I'm sure I could have gotten them all correct if I had just sat there and brute forced every single option - but what's the point if I can't get through the set in less than 9 minutes or so in an accurate manner?

[dan]

I see two ways to set this game up: 1) put 8 open spaces in a circle (I imagine this is similar to the "spoke" method you described) or 2) put the 8 spaces in a straight horizontal line (just as you would for a standard number line game).

If you use the second method, you need to be very careful in how you read your diagram. Remember that space 1 is technically adjacent to space 8 even though they lie at different ends of the horizontal line (remember, these spaces actually represent a circular arrangement). You'll also need to decide which way, right or left, you'll assign to clockwise. Probably easiest to say that moving to the right on the horizontal line is clockwise. Lastly, two people who sit "across" from each other will have exactly 3 spaces between them on the line.

I find the conversion from a circle to a line a bit complicated for this game, so I prefer arranging the spaces in a circle. One quick way to draw the diagram: put a space at 12 o'clock, at 6 o'clock, at 9 o'clock, and at 3 o'clock. Then simply add a space between each of the ones you've already drawn. This will give you 8 evenly spaced "seats" in a neat drawing.

If you struggled with the time on this game, or if you found yourself struggling to answer the questions correctly, you probably missed the key inferences. Did you see that you could place the O and the I anywhere on the diagram to start, as long as the I sits adjacent to and clockwise from the O? The common mistake would be to read that constraint (Ingrid is next to and immediately clockwise from Olivia) and to think that you CAN'T place them on the diagram because you're not sure what seats they'd go in. The key is to realize that you could put them anywhere. The circular nature of the diagram makes the number of the seats, or the position of any one seat, irrelevant. Because they lie in a circle, the seats are all equivalent. So, start by placing the O and I. Arbitrarily, let's decide to place the O at 12 o'clock and the I in the seat just to the right of the O.

At this point, we can make another inference. Since F and G must be directly across from each other, the F - G pair is limited to two possible arrangements. One possibility is to have the F - G combo in the 9 o'clock - 3 o'clock spaces (directly across from each other). The only other possibility is to put them in the 10:30 - 4:30 positions.

You might even try setting up four frames, or four hypothetical possibilities (for easier reference, let's call the 12 o'clock position "1," and we'll label the rest in order clockwise from there):

1O, 2I, 3F, 7G

1O, 2I, 3G, 7F

1O, 2I, 4F, 8G

1O, 2I, 4G, 8G

Those are the only possibilities to start with. From there, notice that H is very limited (H can't be next to F or K).

So, for just about every question, you want to start by considering where the F/G pair could go, and then use the appropriate frame. Then, consider the H. Where CAN'T the H go? This should help you arrive at the answer more quickly.

Try it again and let me know if this helps.

dan

[dan]

By the way, if you're wanting more practice with these circle games, we've got an interesting circle game waiting in the wings for our fortnightly challenge. Stay tuned. We'll be posting it in a week or two.

[stackoutawinner]

Thank you Dan. I'm going to need as much practice as I can get!

I just re-did this game using frames like you suggested. I timed myself and came in at 18 minutes (!) but only got 1 wrong instead of 4. The one I missed was one I got right the first time through.

Even with the frames, I wound up drawing 8 diagrams, so I'm sure if I polish up my technique I can reduce that down and find a way to just use the frames. From there just spending time doing circular style games would probably help my mind see the inferences quicker.

One way I might achieve this is by figuring out a way to notate what variables can and cannot go in a slot without cluttering up the diagram. Putting the slots in a circle absolutely helps to visualize the situation, but it makes it harder to demonstrate what can/cannot go in a particular space because it takes up valuable real estate...

I'd be curious to see how you would get by this in your diagram.

[rharris1]

I just tried this game and I ran into the same issues of it taking WAY more than the 8-9 minutes a game should take. Is it possible to get some solutions posted with the best way to attack each question?

Thanks in advance,
-- Russell

[stackoutawinner]

Russell,

What kind of diagram did you use?

I'm going to spend some time playing around with this type of question because I have a feeling creating a circular diagram is what's causing my time issues - I'm almost thinking it would be better to use a strict number line (but without the numbers because they do not matter) and then drawing the inferences into contraints.

For example
F _ _ _ G _ _ _
. H . . . . . . . H

Like I said, I'm going to play around with this a little bit in the next day or so, because for me, the circular diagram created almost as many problems as it solved.

[rharris1]

My diagram was probably similar to yours, I went with the "spoke" method. I think my issue was not finding any key inferences with this game, so I was stuck drawing out individual diagrams on most of the questions which was the source of my timing problems.

I just tried to resolve using a strict number line approach and came up with 4 basic templates. Then I applied H as 'not laws' which seemed the next most restrictive.

1 2 3 4 5 6 7 8

O I F _ _ _ G _ (H not in 4)

O I G _ _ _ F _ (H not in 6 or 8)

O I _ F _ _ _ G (H not in 3 or 5)

O I _ G _ _ _ F (H not in 7)


The only other rule that can be applied here is the H not next to K, but drawing out all of the templates would be very time consuming.

I think the only approach after creating your basic templates is to recognize which ones apply to each question and go from there. But, I'm still stuck drawing out multiple diagrams for each question because more than one template applies to each question except for question 19!

-- Russell

[stackoutawinner]

I've worked through this problem about 5 different times using various diagramming strategies.

Russell, I have to disagree with Dan's methodology when he advised using the OI chunk as the one to base the frames around.

The reason is two-fold.
1. The OI chunk is not the biggest chunk given. We're given an 8 space chunk of F&G.
2. Because H is not allowed to be next to F, if you base your frames around F&G, the H not laws apply to the same exact spaces in each frame. This potentially saves you time and reduces potential mental error.

Both ways will work, but I find these two reasons enough to base my diagram on any "across from each other" rule before any adjacent rule. This would hold true whether I'm using a spoke diagram or number line.

Between the two diagram styles, the spoke diagram is at least twice as fast to draw than the number line. Drawing 8 lines in a circle would be my last choice, and even though Dan said he would probably use this diagram style, it was something Dan said in a recent class that tells me not to alter the straight number line into a circle - we want to use consistent strategies among the various games. The number line in a circle means I'm spending just as much time drawing it as a regular number line but cannot take advantage of space on the page - if I'm drawing a circle, I'd rather use the spokes because at least it saves you time.

It's really a choice between the spoke method and the number line for me.

The spoke method, for me, was quicker to draw, but easier to mess up and it relied 100% on plugging and chugging.

The number line took forever to draw out so many times, but it was accurate.

Time wise, both methods were pretty much inadequate. That's mostly because the questions test inferences that will take much longer than 8 minutes to uncover. I was more accurate with the number line, but I'm not sold completely only because plugging and chugging with a spoke diagram is much faster.

I'm surprised that more people aren't posting about this question because it is part of the assigned homework. For those that have done the homework and didn't think twice about this question, please post as to what you did to uncover the inferences and solve the questions so quickly.

Please see the attached solutions that I came up with. And, yes, it took far more than 8 minutes to draw this up, but you'll clearly see the right/wrong answers in looking at my methodology.

After writing up the solutions, I did find some ways to cut time on this question. It requires looking at the answer choices and finding obscure 2nd level inferences... but seeing these in an original diagram, or even frames, would be pretty amazing if done quickly.

[dan]

Hey guys. Great debate. Let me write up how I did the game and I'll post it here. I won't look at your solution until I do my own so that I can avoid being biased by your ideas.

I'll be back...

[rharris1]

Cool, thanks Dan.

[dan]

Hey guys. Here's my solution. A few notes.

1. I numbered the seats for easier reference, but keep in mind that the seat numbers are irrelevant. We're NOT trying to match people to numbers in this game.
2. I would classify this game as a Numbered Ordering/Misc. game. It has numbered ordering properties (namely the constraint types), but the fact that we're putting things in a circular arrangement rather than a linear arrangement makes it slightly "rogue" in nature.
3. I love the fact that you guys are trying this game over and over with many different setups and approaches. This is exactly the process you want to commit to in order to improve. Keep in mind, though, that if a game like this takes you more time than you'd like it may not be because of the type of setup you're using. In fact, if you're struggling to do this in 9 minutes (and you've tried both the circle and line setups), my guess is that the issue is something other than setup. Here are a few thoughts:

a) It's possible that your approach to the questions isn't as efficient as it could be. I think both of you mentioned that you spent way too much time drawing numerous diagrams. In other words, you're probably relying too much on trial and error (trying to make each answer choice "work") and not enough time on following the chain of inferences. Take a look at the attached solution and keep an eye out for how much work was done to make inferences before the answer choices were considered.

b) It's possible that you're not making inferences fast enough. This will come with time and practice. Keep after this game. Take a look at these solutions, and then try it again on your own. Then do it again in a week! With this type of approach, you'll find that you'll start to think in terms of inferences. You'll spot them more quickly, and this will cut down your time.

Again, all of this is to say: setup is only one part of speed and accuracy.

Let me know what you think. Hope this helps.

dan

[dan]

A few more comments on this game...

We've actually had some disagreement in the ranks about how to classify this game. Another one of our instructors sees this as a relative ordering game. Here are his reasons:

"the reason i ultimately categorized it as relative is that all the clues are about where people sit relative to one another. sure, some of the clues are pretty specific, but they are specific in terms of relationships, not in terms of actual positions. as we answer the questions, we never get any idea of specific seat assignments -- again, all we know is relative position -- it's kinda like they are sitting in a spinning cup at an amusement part -- positions can only be described in terms of where one sits relative to others, rather than at the top, or bottom, or left, or right, etc."

I thought of it as a number line game because you can actually solve it using a number line (with no numbers) and because the constraints seemed more numbered ordering-like to me (exactly three between F and G, I immediately next to O, etc.).

This disagreement leads to an important point. When it comes down to it, the LSAT will throw curveballs. If you are well-versed in relative ordering and numbered ordering, and if you're flexible enough to "borrow" components from both, you should have a better chance at success. This game doesn't fit neatly into any category, unless you create a separate category called "circle games," but creating a new category for every type of game that comes up defeats the purpose of having categories!

Again, keep your eye out for out next logic challenge. It happens to involve a circular arrangement of elements, and I'll think you'll find it even more challenging than this one.

[stackoutawinner]

Thanks Dan.

I've printed out your solution and will review it later on tonight.

I happen to agree with you regarding the classification. There's really no reason to say this is relative ordering other than there's no specific numbering. Nearly all relative games feature specific numbering, so it's not as though this is a determinant since even this game bucks the trend of a relative game in that respect as well. The premise does not support the conclusion.

More importantly, every single constraint is a number line type of contraint. There's not a single contraint that's relative.

The H cannot be adjacent to F or K (number line constraint)
F & G have exactly 3 spaces between them in either direction (number line constraint)
O & I must be adjacent and in that order (number line constraint)

There's not a single relative contraint given.

In fact, for a game to be relative, one variable must be able to "come before" another. In this game, there's no first and there's no last. Therefore, this game cannot be relative.

Not that it matters as you're saying, the classification is only part of solving the game, but I doubt anyone could use a tree and answer even one question correctly. If they can, I'd love to see it on paper.

[rharris1]

Thanks Dan, I'll take a look at this in more detail when I get home from work.

I agree with your last two points, especially efficiency towards games. It seems that the setup/diagram/inferences can make or break you in a game, especially when it comes to speed (example: the infamous dino game from June '09).

I'm interested to see what inferences you came up with versus my own. I'll reply back with my observations. Hopefully after this, I can do this next Logic Game Challenge in 8 minutes or less!

Russell

[stackoutawinner]

I'm going to up the ante regarding my argument of relative games.

It's impossible to have a relative game without assigned hierarchy. The reason is because without hierarchy, you can never give a relative constraint. Without hierarchy, every contraint must have defined positions given because of the mere fact that that the lack of hierarchy does not implicitedly give you defined positions on which to relate.

You can never say one variable comes before or after another. You can only define the relationship with numerical spaces between them, and thus, why constraints can never have the nebulous relative nature.

When I said "Nearly all relative games" I should have said "All relative games" have a strict hierarchy built into the model.

My argument can be summed up thusly: The term "relative contraint" is an oxymoron without hierarchy. Therefore, ~ H --> ~ RC; contrapositive = RC --> H

[rharris1]

My observations after going over these solutions and comparing to what I did on my own. It seems that my inferences match yours Dan, but unlike most of the Relative and Numbered Order Games that I am used to, this one seems to have slightly more uncertainty and not a lot of 2nd level inferences to go off of (which I think is what made it more challenging to me).

With that in mind, when I re-did the game, instead of diving into the challenging questions by drawing diagrams for each answer I was uncertain of, I would first work them out mentally with the known constraints and try to picture the answer in my head to see if there were any violations to rules. This seemed to enhance my speed in eliminating wrong answers without having to write them out, but it should be cautioned that this approach could potentially backfire if you forget ANY constraint when forming this mental picture.

I'll sit on this one for a few weeks and then try to re-solve. I'm also eagerly anticipating the next Logic Games Challenge to see if I can tackle this unusual game type with better speed in the future!

Thanks again for the solutions Dan!
-- Russell

[stackoutawinner]

I concur with Russell.

I went through the solutions and really enjoyed the approach. I couldn't really get an accurate guage because the game is so fresh to me at the moment (having worked through it so many times in so little span).

My thoughts echo Russell's... what Dan is showing you how to do in the solution is to use a large chunk of your visualization ability to view the inferences without actually drawing diagrams. This is a skill, and one that can be enhanced with practice. I know I will get stronger at it.

I'm going to sit on this for at least a week like Dan suggested. Then I'll do this again using Dan's approach.

[dan]

Sounds good, guys. I think a revisit in a week is a good idea. You'll be surprised, I'm guessing, by how much your brain will "think" about and process this game over the next week even if you're not actively working on it. That's the beauty of repetition, and tackling things over time.

You're right... part of getting faster is developing the ability to "hold" information in your mind as you're doing a game. In this case, once we put the O and I in the diagram, there are only two things to remember: F across from G, and H not next to F or K. If you can hold on to these rules, and use them as your jumping off point for each question, your speed will increase. You'll obviously have them down in notation form on your paper, but even better if you don't have to remind yourself.

I bet your next shot at it will be much quicker. Keep us posted.

dan

[jdillier]

Does anyone know any other games that are similar to this one?

[stackoutawinner]

There's at least one, I believe, on Preptest 1. It features a 6 person table - the questions and set up are discussed in PS LGB.

Then of course there's another one coming up with the Fortnightly challenge.