#22 - Local, Could Be True

[Adam Tyson]

In this case, starting off with an odd round may have been a random choice that happened to work out. If it had not, then then next thing to do would have been to try and even-odd-even approach and see if that worked. Let's see!

First round even: J plays R and wins, S plays M and it could go either way. We have a result of either JRSML or else JRMSL.

Second round odd: R plays either M or S, no clue what happens, and L plays the other one of those two, winning and moving up to position 4. Options now are JRSLM, JSRLM, JRMLS, or JMRLS.

Third round even: J plays whoever is in second and wins, and they stay the same. L plays whoever is in third and moves up. Options are: JRLSM, JSLRM, JRLMS, or JMLRS.

We can now eliminate every one of the options that does not end with M in position 4, where it began, because that is a condition of the question. That means a final positioning of JRLMS. So, if we started with an even round and M ended up in 4th, we would have that order - JRLMS. None of our answers are possible in that case, so we have to try the Odd-Even-Odd approach that Jon shared.

Now, Jon's hypothetical was definitely intentional and informed rather than random. Why? Because we were narrowed down to two contenders (see Dave's earlier post to understand why), and we were trying to make one happen. How do you get L up from position 5 to position 2, in order to test answer C? L would have to play in all three rounds to move up three spaces, and that means he has to play in the first round, which means it's an odd round. Recognizing that that is required in order to test C out is an important, time-saving step. If you miss it, you might be casting about randomly and hoping to get lucky. However, you could still do it, as I did, and you'll still get it right.

I hope that makes sense!

[ValVal]

Hi there! I got the question right, and it seems that I followed the same approach that you outlined when I tried to do question on my own. It seems logical to exclude the answer choices that were wrong. However, when I just try to set up a diagram that would reflect the conditions of the question, it does not seem to work out very well.

For example, to place M as #4 at 3rd round, and at the same time to allow J and L win their matches, seems to create controversy:

If L wins 5-4, then M is placed to position 5: RJSLM. Then, to bring it back to 4 would mean to allow round 4-3, where L wins again, and S and L switch positions: RJLSM, and then, in round 3 (which is 5-4 again), allow M to win and occupy 4: RJLMS. However, in this layout J does not get to play.

But if we allow J to play and win, (either in 2-1, when it will be JRSML; or in 3-2, where it win not switch positions), M will move down to 5 (because we have to allow L to win).

Another words, to allow M to keep #4 on top of the fact that it has to lose to L, calls for at least 3 rounds, where J will not be used. Or if J is used, we need more than 3 rounds to allow M to lose and then regain #4.

I know that I may be unnecessary complicating the game, but it's either the conditions are somewhat faulty, or I don't get it (probably the latter . Would you please provide some explanations?

Thank you!

[nicholaspavic]

Hi Val,

This is a hard one. I think what we are really doing to get to the answer choice here is to set up two scenarios of 3 rounds each with "mirrored" even and odd rounds potentially taking place. (At least that was my approach.) So I started just by pure dumb luck with RJSML starting on an odd round which gave me RJSLM in the first round. Then we went to the even round which gave me JRLSM and then back to an odd round to put it into JLRMS. M was at 4 and Answer Choice (C) was the only one that could be true at that point. So to recap, I went odd, even, odd to get to my answer choice. Was that what you did too?

Let me know. This is a tough one.