## PrepTest 78, Game 2, Setup

### Transcript

This is PT78 game number two and here we're told that there are four students who are assigned to a history project and they're gonna search archives from the years 192119221923 and 1924. Each of these years is gonna have one student assigned to it and there are a total of six students. So because we're selecting four out of these six students to be assigned to these projects, you can think of this as a fixed grouping game.

But since we're also told that there's an ordering to the years, 21 22 23 and 24, this actually becomes a hybrid game. It's a combination of fixed grouping, and sequencing. So that's why I'm gonna go with an in and out setup. But I'm gonna label the in group slots with one two three four to represent the years, since we know there's exactly four in that means there's got to be two of the students that are left out.

Now let's take a look at the rules. The first rule says that only L or T can be assigned to 1923 So that means that the third slot is gonna have either l or T. It's much more important not to put it in your list of rules like this but to actually represent that directly in your diagram with L slash t and 1923. The next rule says that if Molly's assigned to the project, she's got to go in either 1921 or 1922.

So I've written that like this, if Emma's in she's got to go in one or two. The important takeaway from this is that m is never gonna go in slot number four. So that means M only has three options M is either gonna go in 1921, 1922, or M is gonna go out. The third rule says that if Tiffany is assigned to the project, then Ryan must also be assigned to the project.

So that is a conditional statement that looks like this. If you put T somewhere in our for in group slots, you also have to see R the contrapositive is if you don't see R, then you can't see T or in other words if R is in the out group if R is not assigned to the project, then you also have to put T in the out group. Be careful not to read this rule backwards.

This doesn't mean that R automatically brings T. You're allowed to have R without T. It's just that if you have T, you must have R with it. The final rule says that if Ryan is assigned to the project, then Onyx must be assigned to the year immediately prior to Ryan's. So what that means is If you put an R in the in group, then you have to see an O immediately before that R.

In other words, if R goes in the in group, you have to have an O R Block. The contrapositive means that if you don't have an O R block, then R cannot be in. Now notice what that means for where R can go, because there's only a couple of spots left one, two and four. If you were to put an R in slot number one, there's no room to put the O before we have to see an O before it but R is in the very first spot.

And so what that means is R actually cannot go in slot number one. If you put R in slot number two, that does work because there is room for O, do immediately before the R, but if you put R in slot number four, there's no room for the O immediately before it because l or T must always be in 1923 based on the first rule, so that means R cannot go in four. So what we've just figured out based on this rule is that R is never gonna go in one and R is never gonna go in four the only options for R are either slot number two, or out.

So we've diagrammed our rules. We've made deductions based on our rules particularly about where R can go based on rule number four. As well as where M can go based on rule number two. And at this point let me go ahead and just circle our floating variable y there's no rules about Yoshio.

So Yoshio is gonna be the least constrained and at this point we are ready for our questions.