## PrepTest 73, Game 3, Setup

### Transcript

The scenario for this game describes a standard floating grouping game. We have three groups, which are the three families, the Tents, the Williamses, and the Yandells, and they have to split up five buildings between them. That's not to let us begin the sketch, we make our categories. I'm using two letters for the categories here to make sure I don't confuse them with the things that we're moving around.

And a list of the things we're moving around, F, G, I, M, and S. We do know one thing about the groups, and that is that they have to have at least one slot in them, because every family owns at least one of the buildings. So we can go ahead and put one set of slots by each of the buildings, and that's about as far as we can go with the sketch before we hit the rules. There are three rules, and they're not terribly complicated.

The first rule says that the Williamses have to own more buildings than the Yandells. Asking to do two things, of course, first, we need to put it into shorthand into our notes. But the two things it's gonna do, first, it's going to give us an extra slot for the Williamses.

Because the Yandells already have one, so the Williamses need a second one to stay ahead. But that's four of our slots, and we only have five slots total, which means that we won't be able to give a slot to the Yandells. Because if we did give them a second slot, the Williamses would need three, and that would be five slots total, leaving nothing for the Trents.

So we know for sure that the Yandells are going to have exactly one building. That extra slot could go to either the Trents or the Williamses. The Trents could have two and the Williamses two, or the Trents could have one and the Williamses three. And a second rule just gives us a couple of exclusions. It tells us that we can't have the inn or the mill grouped with the forge, so no MF, no IF.

And then the third rule tells us something that has to happen or at least one of two things has to happen, either the Trents get the stables or the Yandells get the inn, or both. To begin, we can write that in shorthand, Trents have S or Yandells have I. And the question might become, does that or both matter in the game? And to tell the truth, it doesn't.

On the outset, the word or is always non-exclusive, which just means that it never implies not both unless explicitly stated. So they didn't actually need to say or both here, they could have left that off and the rule would run exactly the same. We could the Trents with S and the Yandells not with I, we could have the Trents not with S and the Yandells with I, or we could have the Trents with S and the Yandells with I at the same time.

And that's pretty much it. The rules don't interact very well with each other directly. There's a lot of ifs in the questions. So we're gonna move on with the questions and not look for additional deductions. When we go to the questions, we'll go in the usual order, which is solutions, locals and globals, with any rule change questions thrown in last.

There aren't any rule change questions in this game, so we're gonna hit 14 first, then do 16, 17, and 18 are locals, and then double back to pick up 15 R1 global. So on to the questions.