Fixed Grouping Setup

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Transcript

Okay, we are back for our next lesson on fixed grouping logic games and in this video we will be doing the setup. In the next video we will be tackling the questions. So without further ado, we'll be using the June 2007 prep test game for from section number one. So at this point, take a moment, pause the video, read through the game and its rules and hit play when you are ready to begin Okay, so as always, we wanna start off by reviewing our method for how to approach the setup of a logic game.

As usual, it's a four step process, where we first ID the game type, second, we draw our master diagram. Third we diagram the rules. And fourth, we make inferences. So let's start off with Step 1. Identifying the game type.

In this particular game, we are told that we will be distributing five different types of materials among three recycling centers. And I think of those recycling centers as sort of like bins that we're just going to kind of chuck materials into, okay? Secondly, we the materials, can be used more than once. So we're not limited to only one of each letter.

And finally the rules group the materials together or separate them from each other. So these are all clues that we're dealing with a grouping game, and in this particular case, a fixed grouping game. Why? Well, that's actually somewhat debatable. Many people might view this as a floating grouping game because the exact number of spots per bin is not specified.

I'm sticking with a fixed grouping game, because that approach allows us to diagram the game much more effectively. And you'll see that on the next slide. So really this is kind of a reminder that the different types of games, there's some blurry lines between them. And again, I recommend going back and watching the videos in the game types section for a little bit further of an exploration into the different types of games and why they really kind of overlap with one another.

And it's much more about being flexible and adaptable than it is about getting to hung up on the exact type of game. But let's go ahead and work on our master diagram. So step two, we draw our master diagram. In this particular case, we're gonna drop bins, and we're gonna assign spaces in each.

So we have some relevant info that we wanna keep in mind. First, the game told us that there's three recycling centers. Labeled simply 1, 2 and 3. There are 5 materials, glass, newsprint, plastic, tin, and wood. And finally that there are two to three materials recycled per center. So that's. That's some really helpful information in that two to three materials per center is why this is kind of arguably a fixed versus floating game.

I'm going to say that it's fixed because they tell us that it's either 2 or 3. Others would say it's floating because we don't know whether it's 2 or 3. Regardless, here's our three bins. Let's go ahead and label them, 1, 2 and 3. And let's next draw in those potential spaces that we're gonna fill. So you notice, I've drawn three spaces into each center, but we don't actually know whether that third space will be used or not.

Therefore, I would kinda put a little question mark next to it to signify that there might be something in that space, but it might also be empty. So here's a nice simple master diagram that I can now add to according to the rules that are provided. So step number three, we diagram the rules. Let's go ahead and get them up on the screen, and let's get our master diagram up there as well.

And as usual, we're gonna try to incorporate each rule directly into the diagram. But when we can't do that, we will just write them in a separate little column or list somewhere where we can easily see them and write them symbolically. For our first rule, any recycling center that recycles wood also recycles newsprint.

So we want to think for a moment about what this really means. What it's telling us is that if we see wood at a recycling center, that we should also see newsprint somewhere at that same recycling center. In other words, wood is the trigger material. It triggers the presence of newsprint, okay? This really creates an if then statement.

If w, then n. if you haven't already watched the videos in the formal logic section of the logic games lessons, I really recommend that you do that before we proceed any further, because these if then statements are gonna be very important in this game and in most logic games moving forward. So I would go back to that first.

But the key here is really to recognize that wood is the trigger, not newsprints. Some of you might be tempted to write this rule as if N then W, or to simply have a W and N together kind of rule. But the thing is here that new if we see newsprint at a recycling center, it doesn't actually tell us that wood is there. You could have newsprint without wood.

But you can't have wood without newsprint according to our rule, okay? So if W then N. Next, every kind of material that Center 2 recycles is also recycled at Center 1. So we can't draw this directly into the diagram because we don't know what materials are at any of the centers yet. But again, we can write this as an if-then statement.

And in this particular case, Center 2 is the trigger. If something is in the Center 2, then we also know that it's in the Center 1. If in 2, then in 1 we do not know that the reverse is true. Center 1 is not a trigger. The rule does not tell us that something recycled at Center 1 must also be recycled at Center 2.

So be careful of that one. And finally, rule three, only one of the recycling centers recycles plastic, and that recycling center does not recycle glass. Okay, this is kind of a complicated rule. And personally I would actually break this up and write it as two separate bullets in my list.

So first, I would say only 1 P. We can't see multiple P and P's in our diagram. Secondly, if P then no G, so that recycling center that recycles plastic does not recycle glass. So again, plastic is the trigger here. If we see plastic, we know that we can't have glass Okay, but no glass is not a trigger.

In other words, the fact that a recycling center does not recycle glass does not mean that it does recycle plastic. So again, be careful of those if-then statements and go back and watch the formal logic lessons if you haven't already. But at this point we've diagrammed all of our rules. And we're ready to start making some inferences here.

So step 4, we make our inferences. So let's get our master diagram up there. And let's get our list of rules. In this particular case, the simplest inferences to make are those based on our formal logic if-then statements. We are going to take the contrapositive of each one of these rules, or wherever it's applicable.

Remember that for a contrapositive, we negate each term in the if-then statement, and then we reverse them. So for example number 1, if W then N, the control positive is if there's no N then there's no W. And if you think about it it's logical. Wherever there's wood, there's also newsprint.

That's what the rule tells us. So if there's no newsprint, then there can't possibly be any wood, right? So if no N, then no W. So notice that no N becomes a new trigger. But that in by itself in other words, the presence of newsprint is not a trigger.

It's the absence of newsprint that triggers us to recognize that there must also be an absence of wood. Likewise, we can take the contrapositive of our second rule. And if into then in one becomes if not in 1, then not in 2. If something's not present at the first recycling center then there's no way it can be present at the second recycling center.

Because everything at the second recycling center is also at the first recycling center, okay? So hopefully that's making sense so far. Next there's only 1 P. Well, there's not really much we can do with that yet except if you take a moment to combine it with this rule.

So let's just see what happens when we combine these. If something is in the second recycling center, it's also in the first recycling center. But there can only be one plastic. So combining those we can infer that there can't be plastic at the second recycling center.

Therefore, P is not in 2 and this is something we can actually draw directly into our diagram. So I'm just gonna put a no P down there under column 2 or under bin number 2. As a reminder that I can't put a P there. And then finally our last rule If P then no G, taking the contrapositive that turns into If G then no P.

So, if we see glass then there can't be any plastic. In other words P and G are mutually exclusive. If one is present, the other is absent. But remember that our triggers are the presence of plastic and the presence of glass, not the absence of either one. It is possible that a recycling center could have neither G nor P in it, okay?

So that kind of carries us through the end of our making inferences. And this is where I would expect most students would probably end the inference process, although there are technically further inferences that could be made in this game, but they're really not necessary. So if you got more, great congratulations. But if this is as far as you get, then you're still in really great shape.

The bonus one here really is that if glass is in bin number 2 or recycling center number 2, then plastic has to be in bin number 3. That's the one that you really might have recognized if you took this a little bit further, because if you think about it, if I put glass here in bin number 2. Then that means the glass is also in bin number 1 and therefore a plastic must be over here in bin number 3.

So that's where that came from. But, really, again, kudos to you if you got that far. It's not a necessary inference to make at this point in time, and we really should be happy with what we've got here on the screen right now. So there's our final version of our diagram, and we're gonna quickly review the steps before we tackle the questions.

Our 4 step process for fixed grouping game setup begins with step 1, identify the game type. This is an important step because it helps us determine what type of Master Diagram we're gonna draw. For a fixed grouping game, you're typically going to want Bins with spaces in them, To illustrate how many different items will be placed in each bin.

Once we've drawn our Master Diagram, we diagram the rules. Remember, we wanna add them straight into the master diagram where possible otherwise list them symbolically along the side of your master diagram. And finally, number 4, make inferences and in this particular game our inferences came from using the contrapositives of our if then statements. And from combining some roles.

We didn't find any limited options in this one and that's fine. You don't always have limited options in a logic game. And finally, your bonus step, just take a minute to imagine some cute puppies for a few seconds and de-stress. That's an important process in the LSAT is making sure that you're de-stressing, breathing, calming yourself as you go.

Otherwise you will get anxious and stressed out and that is helpful to no one. Thanks for listening the video and I'll see you in the next one when we tackle the questions for this game.

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