## June 2007, Game 4, Question 20

### Transcript

Question 20, question 20 is a local question because it gives us a new if condition that we have to add to the game just for this one question. That usually means writing a new sketch. So write a new sketch with the new condition. The condition here is that Center 2 gets three things. If Center 2 is doing three things, that immediately means that Center 1 is also doing three things.

Because everything that's done in 2 has to be done in 1. And that's going to mean that plastic is going to have to be done in Center 3. Center 1 is now doing the same three things that Center 1 is doing. So anything in 1's column is gonna be shared in 2's. So the plastic, which we only get one of, is gonna go to Center 3. And since this question, the rest of it, is simply asking, what is it that Center 3 must recycle, we already have our answer.

The answer is answer choice C, it has to do p. Now, I'm a big fan of finishing out your if sketches, it only takes a second to add the rest of the things. And in this game, it's gonna teach us something that's gonna be useful for the remaining questions. So think, if 3 is doing plastic, it now can't do glass.

By rule three, since you have to do glass somewhere, you'll have to do it in both Centers 1 and 2, because they're doing the same things as each other. And now, consider the two remaining spaces in Centers 1 and 2. So we started out with five things, g, n, p, t, w. We've already used as many g's and as many p's as we're gonna be allowed to use. So we have three items left, n, t and w, for those two spaces.

Now this is where rule one is gonna become very important. So rule one's contrapositive says if you don't use n, you're not allowed to use w. So imagine if we were to try to get away with not using an n in the 1 and the 2 column. If you get rid of n, you have to get rid of w, and that leaves you with only t, but t can't fill both spaces by itself.

A center can only recycle ten 1s. So that means that we can't actually get rid of n, we're going to have to use it. So here we'll have to use it in both Centers 1 and 2. Now, the remaining space in Centers 1 and 2, well, it could be either w or t, we can't say. Remember, don't confuse the rule one to mean that if you have n you have to have w, it only works the one way.

If you have w, you have n, n doesn't trigger w, but whatever it is that Center 1 and 2 have, they will have the same thing. So if one has ten, 2 will get it, and vice versa. If 2 has wood, 1 will get it, and vice versa. And then whichever one we don't use in Center 1 and 2, we'll have to use over in Center 3.

So completing the sketch takes a couple extra seconds, but it taught us something about those two spaces that we're gonna see in subsequent questions. Let's get on to the other questions.