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PrepTest 79, Game 1, Setup


In one week Monday through Friday a library's bookmobile will visit five of the following six neighborhoods H, L, N, O, P, and S. Exactly one neighborhood will be visited on each of the five days, and none of the neighborhoods will be visited on more than one day. The bookmobile must conform to the following conditions, H is visited but not on Friday.

If O is visited, then it is visited on the day immediately before H is visited. If L is visited, then it is visited on Wednesday. N and S are both visited, but not on consecutive days. So we're dealing with a linear game here, and we're trying to determine the schedule of the library's bookmobile when it visits five neighbourhoods. So we have six neighbourhoods to choose from but only five will be visited.

So this is an unbalanced game, meaning we have more variables than available slots. So we're still concerned with order, but we also need to be thoughtful of the one that's always going to be left out. So a lot of rules are dealing with sequencing or when something can occur. So that second rule is telling us that if O occurs, then it's relationship with H spelled out, so we got a mixture of sort of occurence rules and sequencing rules here.

So let's get a grasp on our variables. So, our neighborhoods are HLNOP and S and then Monday through Friday is what we're distributing those variables in so when we're thinking about linear games we always wanna identify our base so that's gonna be your most stable element that you're going to sort all the other variables into. Here the bases are going to be Monday through Friday, is the most stable element is not changing, that is a static sequence, so it's always going to be the same.

So when you're thinking about a base, you're thinking about days of the week, months of the year, seats on a bench, anything along those lines that's pretty stable, that's gonna help you formulate your diagram. So as we look at our diagram, you can see what I was talking about here with the base, we have our days of the week. And then we're gonna figure out the order in which these variables occur, so our variables being our neighborhoods.

Let's look at our rules. Rule number one, H is visited by not on Friday, so we're always gonna have H in our diagram. H just not going to occur on Friday, so we still have these four other possibilities open for H. O wanna go ahead and exclude it from occurring on Friday and do that to our diagram.

If O is visited, then it is visited on the day immediately before Hidden Hills is visited. So if we have O this is conditional rule. If O does occur then we are going to have an O sequence block here. So we gonna have O, whenever we have O we gonna have O and H in that order. Now, we can draw an inference from this, as well.

So, whenever we have O we know that it's gonna come along with H, and H has to be after it. So, O is always gonna need to have a slot after it. So, O cannot go last, since whenever O happens we have H to comes along with it, not enough room. Anyway, let's look at our next rule.

Rule number three, if L is visited, then L is visited on Wednesdays. So we can just write that out as a conditional here, just so we can keep up with this information. If L is going to occur, it must occur on Wednesday, so we can go ahead and exclude it from all these other spots or we can just symbolize it with rule, whatever one makes you feel more comfortable, sometimes, it's easier to see sort of all the possibilities that cannot go in a particularly set and so it's good to write those not lows out as well.

Rule number four, N and S are both visited, but not on consecutive days. So we have N and S both occurring, we can just sort of put these in boxes here to let us know that they're gonna happen, but they cannot happen consecutively. So that means either N coming first and then being followed by S, or S coming first, and being immediately followed by N. So we're gonna have both those variables but they can't be touching each other.

So then we end up with our master diagram, so we have Monday through Friday. We have L not occurring on Monday, Tuesday, Thursday and Friday, H and O cannot occur on Friday. But we're going to have four certain in three of the five spaces, we've already filled them out, we're gonna have N, S and H are current, but H can occur on Friday. Anytime O occurs we're gonna have O and H in that order, so we really only need for any given scenario to find out the variables that match or that we can go along with N, S and H since those will occur, those three variables will occur in any valid arrangement.

So this is our master diagram, not much that we can plug into the diagram. But restrictions on a lot of the rules and some of the spaces like Friday. So we have a bit of information to work with to go through the game questions.

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