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 sallyelghdaf@gmail.com
  • Posts: 1
  • Joined: Aug 12, 2021
|
#89659
Hello,

I'm having a difficult time understanding why is R not able to go to house 8?
User avatar
 Bob O'Halloran
PowerScore Staff
  • PowerScore Staff
  • Posts: 61
  • Joined: Jul 06, 2021
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#89809
Hi Sally,
Thank you for your question.

We can determine that House 8 can't be R by combining these two rules:

Every ranch house has at least one Tudor house adjacent to it.
and
House 6 is a split-level house.

Since House 6 is the only house adjacent to House 8, 8 cannot be a ranch.

Let us know if you have other questions.
Bob
 hegna018@umn.edu
  • Posts: 2
  • Joined: Jan 18, 2022
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#94247
can someone please diagram this for me :cry:
 Adam Tyson
PowerScore Staff
  • PowerScore Staff
  • Posts: 5390
  • Joined: Apr 14, 2011
|
#94251
This won't be pretty, but it should help, hegna018:

Draw two rows of 4 blank spaces each, and number them as described in the scenario:

_ _ _ _
1 3 5 7

_ _ _ _
2 4 6 8

Put an R is spot 3 (top row, second space) and an S in spot 6 (bottom row, third space).

To show that no two adjacent houses are the same style, try something like putting XX in a block and crossing it out: XX. The X here is a stand-in for all three types; this is meant to convey that you can never have the same variable beside itself, no matter which type it is. This will allow you to infer that houses 1 and 5 are not R and houses 4 and 8 are not S. If using X is too confusing, then do three not-blocks: RR, SS, and TT.

Make a vertical not-block of two Ss (an S on top of another S, with the whole block crossed out). This will allow you to infer that house 5 is not an S (because 6 is an S). Now you can infer further that house 5 must be T, because it cannot be R or S. That also means that house 7 is not a T.

For the rule about R having T next to it, make it conditional: R :arrow: RT or TR. Every R must have a T next to it on one side or the other or both, so R is the Sufficient Condition here. There is no requirement that every T has an R next to it, though, so don't get that rule backwards or treat it as just a block.

Now an additional inference should come up: house 8 cannot be an R, because if it was then it would not have a T next to it since 6, the only adjacent house to 8, is an S. Thus, house 8 must be a T!

Beware of one possible false inference: some folks mistakenly infer that 4 cannot be an R. But there is no rule against having two Rs face each other the way there is with the Ss, so 4 can be an R or a T, and 2 can be any type.

Put that all together and see what else you can do with it! Maybe set up some templates? Have fun, good luck!

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