### Setup: Base, Variables, Rules

The key connection is combining rules 3 and 4. Once you see that W has many letters coming after it, it helps to think about how far to the right you can push W. W can’t go in 4 since it needs at least 3 letters after it. W also can’t go in 3, since that would mean either K or L would have to go in 4, but 4 must be non-recorded. So W only fits into spots 1 and 2.

### Setup: Splitting into Worlds

We can split into multiple diagrams based on placement of W in 1 or W in 2. If W is in 2, then K, L, and T must be somewhere after it. Since Z must come before Y, we also know that Z cannot fit after the W. So that means Z must go in 1, and Y would be forced to go somewhere after W.

When W is in 1, things are a lot more open. I would just draw the remaining relationships next to the diagrams to help visualize them.

### Question 18

### Question 19

We can answer this question without drawing anything new. Notice that T must have at least K and W before it. So T can’t go second.

### Question 20

We might be able to visualize this based on our two worlds. Who can go 6th? K can’t go 6, since it must have T after it. L can’t go 6, since that would mean K must go in 5 (as the only other recorded audition). But K must have T after it, which isn’t going to fit in L is in 6. W can’t go 6 since it’s limited to 1 or 2. And Z must have Y after it, so it can’t go 6th. T is the only available answer that can go last.

### Question 21

If K is immediately before Y, then that could happen in both worlds. We’d draw both of those options out. In the first world, the order would be Z W K Y L T. In the second world, the order would be W Z K Y L T.

### Question 22

Based on the first world, you can see that Y could fit in spot 4.

### Question 23

For rule substitution questions, the correct answer (1) must be something that was true under the original rules, and (2) must be something that, if true, would recreate the old rule. Here, we want to replace the rule saying W is earlier than K and L.

We can eliminate (B) since in the second world, W doesn’t have to be next to Z. Z could go in 3 or 4 in that world. We can eliminate (C), since even though this places W before L, it doesn’t force W to go earlier than K. The remaining answers are (A), (D) and (E).

At this point, we may see that (A) fits the two criteria for a correct answer. Under the original rules, Z was the only letter that could go earlier than W. And, if we added (A) as a rule to the game, it would force W to go earlier than K and L (since (A) says only Z can go before W).

(D) and (E) are incorrect since they don’t do anything to force W to go earlier than K or L. For (D), it would still be possible to put K in 1 and W in 2. For (E), you could put W almost anywhere and put one of K or L before it.