If the condition requiring house 6 to be a split–level house is suspended but all other original conditions remain th...

zachmorley2 on October 30, 2020

^ I am having the same difficulty here.

Victoria on November 3, 2020

Hi @ari and @zachmorley2,

Happy to help!

Let's run through the entire question so i can show you how to properly set up the game and comprehend the rules.

We know that a developer will build four houses on each side of the street. Houses 1, 3, 5, and 7 will face Houses 2, 4, 6, and 8, respectively.

So, what does this look like?

_ _ _ _
1 3 5 7
_ _ _ _
2 4 6 8

We also learn that each house will be exactly one of three styles: R, S, or T.

Now let's go through the conditions.

Rule 1 - adjacent houses are of different styles

This means that no two houses that are next door to one another will have the same style.

Rule 2 - no S house faces another S house

Therefore, any S house must face either an R or T house.

Rule 3 - every R house has at least one T house adjacent to it

Each R house must be either next to one T house or surrounded by T houses on both sides.

Rule 4 - House 3 is an R house

This means that House 1, House 5, or both must be T houses.

Rule 5 - House 6 is an S house

So, what do we know so far?

_ R T _
1 3 5 7
_ _ S _
2 4 6 8

Since House 6 is an S house, this means that House 5 must be a T house because two S houses cannot face one another and two R houses cannot be adjacent to one another.

However, the question stem tells us to disregard the condition that requires House 6 to be an S house.

Therefore, all we know is that House 3 must be an R house.

_ R _ _
1 3 5 7
_ _ _ _
2 4 6 8

We are looking for the answer choice which does not represent an accurate list of the styles of houses of houses 2, 4, 6, and 8. This means that our incorrect answers could be true.

Since our diagram is pretty open-ended right now, let's see if we can eliminate answer choices based on the rules alone.

Notice that answer choice (A) breaks Rule 3 because House 2 is an R house, but the only house next to it is an S house.

I think your problem might be that you've confused a couple of the rules in your head. There is no rule which tells us that houses of the same style cannot face one another. All we know is that two S houses cannot face one another and that houses of the same style cannot be next to another.

So, while answer choice (B) has two R houses facing one another, it still meets all the conditions.

We know that any house facing an S house must be either R or T. Since two R houses cannot be next to one another, House 1 must be a T house.

House 5 could be either S or T. Let's make it S. This means House 7 must be T because, if it were R, it would violate Rule 3 as it would not have a T house next to it.

T R S T
1 3 5 7
S R T S
2 4 6 8

Notice that this meets all our rules:

1) No two adjacent houses are of the same style.
2) All S houses face T houses
3) Both R houses (3 and 4) are next to T houses (1 and 6)
4) House 3 is an R house
5) We don't need to consider Rule 5 for this question

Hope this helps clear things up a bit! Please let us know if you have any further questions.