#23 - Global, Rule Substitution

[Jon Denning]

Perhaps the section's biggest surprise occurred not with the games themselves (which were as standard as they come), but with the appearance of a second Rule Substitution question in #23!

This question type is vanishingly rare, appearing more frequently in the past several years but still skipping whole tests and never really occurring more than once (if memory serves) per exam, so to get two is a head scratcher. Perhaps this was LSAC's last-ditch attempt to add some difficulty to a section that was otherwise pretty tame.

Regardless, we end with one, so if you missed my discussion of them for question #6 let me reiterate it here:

"While not necessarily the hardest thing you'll see in LG, Rule Sub questions are among the most unique, in that they typically occur at most once per test (if at all; although as we'll see this particular exam had two!) and ask you to replace one of the original rules with an answer choice that would yield an identical game situation. That is, produce this exact same game with all of its consequences and inferences and possibilities and Not Laws and interactions by means of a swap, where you'd put an answer in place of a rule and never know the difference.

I won't go into a full breakdown of this type here—although I think you'll find this question analysis helps you better understand them—however if you're reading this as a PowerScore course student or an owner of the Logic Games Bible, there is a lengthy discussion of these questions in the LGB, and in the L11 Homework/Supplemental area in the Online Student Center for the Full-length and Live Online classes."

The rule we're asked to replace in this question is rule 2, where F and H cannot visit the same city. So the first thing you want to do is consider the effects of that rule, both immediate and secondary.

The immediate effect is that F and H must be kept apart, always, which is simple enough, and the secondary/inferential effects are, most critically, that I has to go to S at all times (that was only because G couldn't go there AND we had to keep F and H apart; without the direct FH rule we could theoretically put them together at S, and that's something we'll want to test in the answers). Similarly, things like if G goes to M and H is at T then F cannot be at T, and if F is at T then G cannot be at M, and so on. So any answer choice that allows F and H to visit a city together is instantly eliminated, as are any that permit those secondary inferences/implications to be different. But noting that I is no longer locked in place at S is huge here!

To further complicate matters, you also can't have an answer that imposes conditions that weren't a part of the original rule set, where something that was allowed under the original rule no longer is. So if an answer said, for instance, "F can't go to S" it would be wrong, as that was allowed even with the original rule in place.

In short, everything needs to stay exactly the same as before. More freedom of movement, or less, instantly eliminates an answer.

Let's test them.

Answer choice (A): G and I could go together in M previously (as seen in a number of question, like 18). So this is out.

Answer choice (B): Consider, was it always the case that F to S meant H to T? Could we have avoided that in our original? The answer is yes, we didn't have to follow (B) under our original rules:

I F F
H I G
M S T

That's F to S without putting H on T while still following the rules we've had until now. If it didn't have to be true originally, then it can't be the correct answer. Replacements only work here if the original holds up.

Answer choice (C): Well we originally knew the F and H couldn't both visit T, or any city together, and interestingly it was also true that T always had to have one of F or H (we saw that tested as wrong answer (B) in question #20!)...but would this answer allow F and H to go together somewhere else and thus violate the original rule? Yep:

I F H
G H I
M S T

We still have our two Is and our G on M H on T rules in place, as well as the new rule from (C), and yet we're able to put F and H together. Clearly then (C) doesn't achieve what the FH Not Block does.

If we can break the original rule, then it can't be the correct answer. Note we're having to test both sides of it though: can we potentially break the original rule (like here)?, and can we avoid the answer's new condition under our original terms (like in answer choice B)? Either is enough to remove the option.

Answer choice (D): Well we know straight away this wasn't true originally, since plenty of situations, including our analysis of answer choice (A) in this question, allowed for G and I to be together at M. So it was never the case that either F or H always had to be one of the two visitors, meaning this doesn't match with our initial conditions.

Answer choice (E): This is tricky, but as we'll see it makes perfect sense. What (E) says is that either I or G, and maybe both, visits every city. What does that mean? It means that F and H can never be together, because I or G has always taken at least one of the city's two spots! This both produces the same result (F and H not together), and is entirely in line with what we originally had (look at every diagram and you'll see either a G, and I, or both on every city at all times; they have to be to keep F and H from being together!).

Tough question to wrap this up, but on the whole this section was still far easier than average.

[abby1285]

Hi! I got this question correct but pretty much guessed between A and E because they seemed to do the exact same thing to me. I understand why E is correct- because it puts I in two cities and G in one city (leaving no cities for both F and H to go to) but doesn't A do the same thing? If G and I cannot go to the same city, as the answer choice states, then I has to go to two cities (as stated in the conditions) forcing G to go to the third city. With this approach, doesn't it also restrict F and H to different cities? I also see in your explanation that you wrote A is incorrect because, in question 18, G and I visit the same city- I thought the whole point of rule substitution questions was that it's a new rule entirely and doesn't matter what set-ups may have occurred in the questions before. Logic games is my strongest section (this is the only question I was confused about) and I'm really trying to get a perfect score in the section to make up for my scores in the other sections. Thanks in advance!

[KelseyWoods]

Hi Abby!

Rule Suspension suspend a Global Rule and sometimes substitute a new rule in its place. For those, past diagrams are likely not going to be very useful. But this is a Rule Substitution question which is asking us to replace a Global Rule with a new rule in the answer choices that would have the same effect as the original rule. In this type of question, we're not ignoring our previous work. We're looking for a rule that maintains all of the same restrictions as the original rule without adding any new restrictions. So if there is an answer choice rule that violates something we've already seen in a previously diagrammed possibility, we want to eliminate it. Our goal is to substitute a rule that would have the exact same effect as the original rule and thus all of the previous possibilities should still be possible. So the fact that in our original diagram it was possible for G and I to visit the same city means that we have to eliminate answer choice (A). We want the new rule to have the exact same effect in determining the assignment of managers to cities. If the new rule adds a restriction we didn't previously have, then it does not have the exact same effect in arranging our variables and is, thus, incorrect.

Hope this helps!

Best,
Kelsey

[rjulien91]

In this question, is I still required to be in S? Given G can't be in S, that means, I must still be one because we want to keep F and H apart?

Would be helpful to help visualize this.

Perhaps the section's biggest surprise occurred not with the games themselves (which were as standard as they come), but with the appearance of a second Rule Substitution question in #23!

This question type is vanishingly rare, appearing more frequently in the past several years but still skipping whole tests and never really occurring more than once (if memory serves) per exam, so to get two is a head scratcher. Perhaps this was LSAC's last-ditch attempt to add some difficulty to a section that was otherwise pretty tame.

Regardless, we end with one, so if you missed my discussion of them for question #6 let me reiterate it here:

"While not necessarily the hardest thing you'll see in LG, Rule Sub questions are among the most unique, in that they typically occur at most once per test (if at all; although as we'll see this particular exam had two!) and ask you to replace one of the original rules with an answer choice that would yield an identical game situation. That is, produce this exact same game with all of its consequences and inferences and possibilities and Not Laws and interactions by means of a swap, where you'd put an answer in place of a rule and never know the difference.

I won't go into a full breakdown of this type here—although I think you'll find this question analysis helps you better understand them—however if you're reading this as a PowerScore course student or an owner of the Logic Games Bible, there is a lengthy discussion of these questions in the LGB, and in the L11 Homework/Supplemental area in the Online Student Center for the Full-length and Live Online classes."

The rule we're asked to replace in this question is rule 2, where F and H cannot visit the same city. So the first thing you want to do is consider the effects of that rule, both immediate and secondary.

The immediate effect is that F and H must be kept apart, always, which is simple enough, and the secondary/inferential effects are, most critically, that I has to go to S at all times (that was only because G couldn't go there AND we had to keep F and H apart; without the direct FH rule we could theoretically put them together at S, and that's something we'll want to test in the answers). Similarly, things like if G goes to M and H is at T then F cannot be at T, and if F is at T then G cannot be at M, and so on. So any answer choice that allows F and H to visit a city together is instantly eliminated, as are any that permit those secondary inferences/implications to be different. But noting that I is no longer locked in place at S is huge here!

To further complicate matters, you also can't have an answer that imposes conditions that weren't a part of the original rule set, where something that was allowed under the original rule no longer is. So if an answer said, for instance, "F can't go to S" it would be wrong, as that was allowed even with the original rule in place.

In short, everything needs to stay exactly the same as before. More freedom of movement, or less, instantly eliminates an answer.

Let's test them.

Answer choice (A): G and I could go together in M previously (as seen in a number of question, like 18). So this is out.

Answer choice (B): Consider, was it always the case that F to S meant H to T? Could we have avoided that in our original? The answer is yes, we didn't have to follow (B) under our original rules:

I F F
H I G
M S T

That's F to S without putting H on T while still following the rules we've had until now. If it didn't have to be true originally, then it can't be the correct answer. Replacements only work here if the original holds up.

Answer choice (C): Well we originally knew the F and H couldn't both visit T, or any city together, and interestingly it was also true that T always had to have one of F or H (we saw that tested as wrong answer (B) in question #20!)...but would this answer allow F and H to go together somewhere else and thus violate the original rule? Yep:

I F H
G H I
M S T

We still have our two Is and our G on M H on T rules in place, as well as the new rule from (C), and yet we're able to put F and H together. Clearly then (C) doesn't achieve what the FH Not Block does.

If we can break the original rule, then it can't be the correct answer. Note we're having to test both sides of it though: can we potentially break the original rule (like here)?, and can we avoid the answer's new condition under our original terms (like in answer choice B)? Either is enough to remove the option.

Answer choice (D): Well we know straight away this wasn't true originally, since plenty of situations, including our analysis of answer choice (A) in this question, allowed for G and I to be together at M. So it was never the case that either F or H always had to be one of the two visitors, meaning this doesn't match with our initial conditions.

Answer choice (E): This is tricky, but as we'll see it makes perfect sense. What (E) says is that either I or G, and maybe both, visits every city. What does that mean? It means that F and H can never be together, because I or G has always taken at least one of the city's two spots! This both produces the same result (F and H not together), and is entirely in line with what we originally had (look at every diagram and you'll see either a G, and I, or both on every city at all times; they have to be to keep F and H from being together!).

Tough question to wrap this up, but on the whole this section was still far easier than average.

[Robert Carroll]

rjulien91,

Yes, I must still be in S. Here is a diagram of what answer choice (E) says:

I G

Contrapose that:

G I

Thus, any place not visited by G must be visited by I. Sydney is still not visited by G, so answer choice (E) forces Sydney to be visited by I, as required.

Robert Carroll