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PrepTest 79, Game 4, Setup


This is PT 79, Game number 4. And here we are told that there are six computers on a network. Exactly one of these computers was infected by a virus from outside the network. And then that virus was then transmitted between computers on the network. Each computer received the virus exactly once.

So this game seems like it is going to be similar to an ordering game because the virus starts with one of these letters, and then the virus is transmitted to other letters. The difference is, you're not just going to have six letters in a row like this, because if you look at the rules, it seems like it's possible for some computers to transmit to more than one computer.

You're not just gonna have one computer go to another computer, go to another one like that all the way to the end. It's theoretically possible that one computer goes to two other computers and then maybe this one goes to another computer. Maybe this one goes to two computers like that. So that's why I say it's similar to an ordering game, but it's not exactly an ordering game.

You could think of this as a rare game type, and we're just gonna have to try our best to visualize the rules because we haven't seen a game that is just like this one before. Let me start by listing our six variables here. One of these computers will get the virus from outside the network. So in other words, it'll be the one that starts with the virus.

And then we have to keep track of who that computer passes the virus to. And then who those computers pass the virus to as well. The first rule says that no computer transmitted the virus to more than two other computers on the network. So that means, you can't have one computer pass to three other computers. This is not allowed.

I'll go ahead and just put it in my list of rules like this. I'm using X because I don't know what computer we're talking about yet, but any computer can only pass to a maximum of two others. The second rule says, S transmits the virus to exactly one other computer on the network. So I'll just write that like this.

S is gonna transfer to only one computer and it must transfer to a computer. So S can't be at the very end of a transmission, it has to pass to somebody else. The third rule says, the computer that transmitted the virus to R also transmits it to S. So that means that R and S have to get the virus from the same computer.

So whichever one gives it to R also gives it to S and vice versa. The fourth rule says, either R or T transmits the virus to Q, and so I'll diagram that like this. Q must get the virus from either R or T or in other words, it's gonna be R passing to Q or T passing to Q. And finally, either T or U transmits the virus to P.

So that means either T is gonna go to P, or U is gonna go to P. So now that we have our rules, and you can see I've just rearranged them over here. Let's start thinking about potential connections between rules. Rules two and three, they both mention the S here. And you see that you could actually put these rules together. There's some computer out there that goes to both R and S and then the S must transfer to exactly one other computer.

So that looks like this. This is a way to visualize a combination of rule two and three. Now unfortunately, there's not much else we can do right now because rules four and five, they each give us options about who passes to Q or who passes to P. And the problem is, it doesn't seem to tell us much. For example, if you're in the world where R is passing to Q, that's great, but that still doesn't tell you anything about whether T goes to P or U goes to P.

And if you're in the world where T goes to Q, that doesn't tell you anything about whether you're in the world where T goes to P or U goes to P. Because theoretically, maybe this T passes to both Q and also it passes to the P. So I'm just gonna have to trust that we're going to go to rules four and five on the questions as necessary. And we should also keep in mind that there's a maximum of two transmissions per computer.

So you can't have one computer passing to three other computers. I'll circle these three rules to remind me that I have to check on them, and now I'm gonna go to the questions.

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