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PrepTest 73, Game 2, Setup


Game two, the scenario for this game is a little bit complicated. We have five speakers that have to be split into two groups, those who are gonna be in the Gold room and those in the Rose room. That'll be enough to allow us to build some categories and to make a roster of the things that are going to be used in the game. But the slots are a little more complicated.

We're told that there will be exactly one speech at 1 and one at 2 in each of the rooms. So that would allow us to put in four spaces, but the final space is a little bit up in the air, there's gonna be a speech of 3 PM, but we don't know which room it's in. So we can add that to the sketch by sort of hovering it in between the two categories there, there is a speech at 3 but we don't know what room it's in.

And that's about all we can do before we go to the rules and we have three rules. The first rule puts M and L into the same room and says that M has to be earlier than l. That second part is easy enough to put in place, M is in front of L, but we do need a symbol to indicate that M and L are in the same room. Normally we would put a little box around them to say that they are definitely next to each other, but we need to accommodate the possibility that we could put someone in between them.

So, they're in the same room, which means they're gonna be on the same half the sketch. So, I would just put a line underneath them like that to indicate they're together, though I don't know they could be in Gold together or in Rose together and someone else could be together with them as well. Additionally, if it was in front of L, we know that M can't be last and if M is in front of L, we know that L can't be first, so we could notate that directly underneath the spaces.

Rule 2 just has a couple of exclusions. It tells us two things that are not allowed to happen, we're not allowed to have Y in front of Z and we're not allowed to have X in front of Z. Don't confuse this rule,iIt doesn't mean that Z is definitely in front of them. Z could come in the same time as them, he just can't come after them. This rule does allow us to make a deduction, about when Z goes.

Think, we know that Z won't be able to go third or in the 3 PM block because if it went at 3, both Y and X would definitely be in front of it. The question is, could it go at 2? I think if Z were to go at 2, we would need two different people to be in front of it going at 1 PM because there's two spots at 1 PM. L can't go there because he's never allowed there, M could go there.

But if Z were at 2, Y and X would not be allowed to be in front of him, which means that there would only be M left over for that first block. So since there aren't two people available to go in front of Z, Z is definitely gonna have to be up front. It's definitely gonna have to be at the 1 PM hour. And that's gonna be a big deduction in this game.

The final rule here is a conditional rule, it says if L is in the Gold room then X and Z have to be in the Rose. And of course, if they were in the Rose room it would be in that order. Z would be in front of X cuz X is never allowed to be in front of Z. So whenever you have a conditional rule, write it into shorthand using the arrows shorthand.

If L is in the Gold and Z and X are in the Rose, make sure to make the contrapositive for that rule. If Z and X aren't in the Rose, which because this is a binary game, which just means that there's only two options, you're either in the Gold room or in the Rose room. If Z or X isn't in the Rose, which would mean if they're in the Gold room, then L has to not be in the Gold room, which would mean L was in the Rose room.

If everybody has to be in one of two categories, not one category means in the other category. But once we have our original and our contrapositive, we're done with that rule and that's pretty much where we're gonna leave the sketch. There aren't any main deductions beyond what we've already written, so we're gonna go on to the questions now.

Remember, we're gonna do the questions in the order that's most useful to us, which here is gonna be to go 8 skip 9, go to 10, skip 11 go to 12, then double back and pick up 9, 11, and 13. We wanna do the solution question first, then the locals and then everything else. And we're definitely gonna put questions like 13 a rule change question off till the very end.

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