## PrepTest 78, Game 4, Setup

### Transcript

This is the fourth game from Pt 78. And here we are told that there is a director auditioning 6 different singers. We're also told KNL are recorded auditions while the other 4 are not recorded auditions. So we have characteristics for each of these variables some are R and four are not recorded.

So that's why I'm gonna choose to draw the setup like this, where we have 6 different auditions in a row. And I'll just note which ones are recorded or not recorded by drawing R or N, for not recorded, above them. The first rule says fourth audition cannot be recorded, so that means fourth is gonna be an N.

And of course, since fourth has to be an N that means it can't be K or L. The second rule says the fifth audition must be recorded. And so that means the fifth audition has to be K or L since it has to be recorded. The third rule says W has to be earlier than the 2 recorded auditions and the 2 recorded auditions are K and L. So I'm gonna diagram that like W before K and also W before L.

The fourth rule says K has to be earlier than T, so that looks like this. And of course you'll we can connect that. I'll go ahead and do that in a moment, W before K before T. The final rule says that Z has to be earlier than Y. So that means Z to the left of Y. So now let's go ahead and make some deductions.

I noticed earlier that the third rule and the fourth rule both mentioned K, so you could actually go ahead and just put them together. That means our full relationship is W before L and also K which is before T. And so right now rule 3 is done, rule 4 is already done because we've combined it over here, the first two rules 1 and 2, those are also handled because we drew them directly into the diagram.

The only rule that's left is Z before Y. I'll just go ahead and recopy that over here. So I just need to focus on this area and these slots. I don't have to worry about any of these rules anymore because we've already accounted for them on the main board, or we've drawn them in these chains in this area.

And now we are ready for the questions.