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Complete Question Explanation

The correct answer choice is (C).

Answer choice (A):

Answer choice (B):

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

Answer choice (D):

Answer choice (E):

This explanation is still in progress. Please post any questions below!
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I am having trouble seeing an efficient approach to this question, especially since I wasn't sure whether to start with an even or odd round. After toying with it I see that if you start with 1) even: J and M winning: RJSML 2) odd: L wins: RJSLM 3) L and R win: RJLSM but I'm not sure how to arrive at that answer quickly. Thank you!
 Robert Carroll
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I think the first approach I would take is seeing if any answers choices stand out as involving particularly large changes of position after a single round. Because of the way the game works, a team can change AT MOST by one position after each round. Of course, not every team will - higher-ranked teams that win, lower-ranked teams that lose, and teams that don't even play won't change position in a single round, so changing position isn't ever required. But if a team does change position after a round, it would be by one position, up or down.

If M is going to be 5th after the third round, it must either have already been 5th after the second round, or just got there by dropping one position. Answer choices (A), (D), and (E) have M better than 4th - it's not possible for M to have been better than 4th, then drop to 5th in a single round. So those answer choices can be readily eliminated. Answer choice (B) has R 5th, which couldn't have been the case after two rounds - R is 1st after the third round, according to the local condition. So R couldn't have moved that far in a single round. That leaves only answer choice (C).

Note that I could get rid of every answer by looking for answers that made teams move too far in a single round. If, after checking those facts, I still had more than one answer left, I would have to explore which types of rounds occurred first, second, and third, and see which of the remaining answers was consistent with one such succession of rounds. That's going to be time-consuming - what I expect is that I can eliminate at least some answers by looking at excessive movements of teams. If I can eliminate 4 answers that way, then that's all I have to do, as here.

Robert Carroll

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