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Hello! I was hoping someone could explain the fastest way to work through this question. My diagrams and inferences didn't seem to give me any tips or clues on how to work through this quickly, but I wanted to know if there was a way to solve this with out just using brute force.
 Robert Carroll
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Because this question is last (and even if it weren't, it seems superficially to require a lot of work, so I might save it for last anyway), we've done a lot of work to this point. We answered #13, and got answer choice (E), so we know the order IFHG works. Also, in a minidiagram I had for #16, I saw that GFIH works. It's very likely you have minidiagrams from other questions that would help. My first thought here is "Have I done what this answer says before?" If I have, I already know it works, so I can eliminate such an answer.

Let's look through the answer choices with the work I already had:

Answer choice (B) was true in the answer to question 13, so it's out.

Answer choice (C) can be made true by modifying the answer to question 13, changing the places of G and H. That change doesn't affect the validity of the order, so it's an easy switch to make to see that this could work. So this answer is out. Now go back to answer choice (A)...the modification of the answer to 13 that made answer choice (C) work here also makes answer choice (A) work. So it's out too.

Answer choice (E) is made true in my minidiagram work for question 16, so I got rid of it right away.

If I was left with two answers instead of just one, I think it's fine to brute force - I'll pick the right answer first and be done, or the WRONG answer first, eliminate it, and select the remaining one without any more work needed. So, with two answers remaining, there's always only one more step!

I really think that, practically speaking, this is an excellent way to do this question - look at what you've done that's an answer here, or that can be made into an answer here without causing an issue. Any such thing could be true, so is out. If that gets rid of 4 answers, I'm done; if it gets rid of 3, the brute force is reduced so much that I think I'd resort to it. If it does no better than that, I think it's still useful - I can now look at my reduced list of answer choices and see if I can find a logical reason why one is more promising than the others. It might be easier to do that with a reduced list than with the list of 5 you start with.

Having templates beforehand could also do some of the work upfront.

Leaving aside those strategies, I might look at the answers and say "putting F and H consecutive can lead to a problem unless they're 2 and 3. If they are 1 and 2 or 3 and 4, the remaining spaces must have G and I next to each other, which doesn't work." That makes answer choices (B) and (D) stand out a bit, and I might go from there, trying one. If it works, I go to the next one; if either of those doesn't work, I have my answer. If they both could be true, well, I'd have to think of something else.

Robert Carroll

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