#23 - Rule Substitution

[Administrator]

Complete Question Explanation

The correct answer choice is (E).

Answer choice (A):

Answer choice (B):

Answer choice (C):

Answer choice (D):

Answer choice (E): This is the correct answer choice.

This explanation is still in progress. Please post any questions below!

[rjhyman]

Hi! I got this question wrong originally because I ran out of time and had to guess, but when I came back and tried to do it untimed I got it wrong again. I thought it was B because I diagrammed the 3rd rule "No two consecutive commercials can be long" as NOT [GK] and this was reflected well in answer choice B: "G's commercial cannot immediately follow K's commercial." Looking back this answer choice was tricky because it didn't specify long vs short commercials, but otherwise, I still think it could be a good answer choice.

Now, I see how E is correct because G and K are always in slots 3 and 5 for this diagram so 2 and 4 are always short. But, any ideas on how to spot the difference between these answer choices and strategies for picking the stronger answer here would be greatly appreciated! Thanks!

[atierney]

One way to look at it is to try to pick the most general-sounding answer, as this will generally capture the breadth of any rule being matched. Here, the specificity of B would make it automatically suspect.

Another strategy would be to look for answers that contain familiar inferences used in the game. For this game in particular, one of the inferences during set up was the exact version of E, mainly that 1,3, and 5 were those slots that could be long, while 2 and 4 must be short. Noticing this in the answer choice of this question really helped to lock on to the correct answer, and, in general, is a good way to "jump" to the probable contenders for rule substitution.

Let me know if you have any questions on this.

[Jeff Wren]

The key to solving a rule substitution question is to find the answer that, when combined with the other remaining rules, will produce the exact same setup as you had with the original rules, neither restricting any variable in a different way than before or allowing any variable to go in space that it wasn't allowed to go in originally.

In the original setup for this game, because rule 2 tells us that the 3rd commercial is Long, we can then use rule 3 (Long commercials can't be consecutive) to infer that the 2nd and 4th commercials must be Short, which we added to our main diagram.

In this question, Answer E produces the exact same result and diagram by just skipping right to the inference that commercials 2 and 4 are Short. Since spaces 2 and 4 are the only "separator" spaces, if they are both Short, then there is no way that two Long commercials can now be consecutive. This produces the exact same effect on the game as rule 3 without changing or restricting the game in any other way.

None of the other answers does this. They either still allow Longs to be consecutive or change the game in some other manner.