Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Basic Linear Game: Underfunded, Unbalanced, Numerical Distribution.

This is a basic linear game featuring five dignitaries placed in seven meetings. Because there are only five dignitaries, this game is underfunded, but the very first rule establishes that F must meet with Garibaldi three times, and so the composition of the group of dignitaries is precisely defined and balanced.

After reviewing the game scenario and the rules, you should make the following basic setup for this game:

pt44_o04_g1_1.png

Note that the fourth rule involving M is represented by Not Laws on meetings 1 and 7. Let’s take a moment to discuss the second and third rules.

Rule #2. This rule establishes that none of the three meetings with F can be consecutive. At a minimum, then, the three meetings with F require five spaces (meaning that among other things that if the TS block created by rule #3 is placed at the beginning or end of the meeting schedule then the placement of the three Fs will automatically be determined). Given the open-ended nature of this rule, and the fact that it addresses three of the seven meetings, this rule will play a major role in the game.

Rule #3. This rule creates a fixed block involving T and S. Because S is always the next meeting after T, S can never be Garibaldi’s first meeting; because T is always the meeting before S, T can never be Garibaldi’s last meeting. These two inferences are shown as Not Laws on the diagram above.

This game does not present a large amount of information in the scenario and rules, and you should expect to see a high number of Local questions, which will supply the additional information needed to place some of the variables. Given the dearth of information generated in the setup, we have elected to show the triple-options present for the first and last meetings. Since there are only five dignitaries, and the Not Laws eliminate two of those dignitaries from attending the first or last meeting, only three possible dignitaries could attend either meeting.

One other point of note is that R is a random in this game, and R can attend the first or last meeting.

[schnappi]

Game easy with deductions and diagram that made so don't think that missed any did anyone find other deductions that missed?

44-3-2.jpg

[nicholaspavic]

Hi schnappi,

This looks very good to me as an initial set-up. So well done! Note how when that TS block is going to move it makes this game pretty restrictive! But overall, I think this set-up deserves an A+!

Keep up the good work!

[SGD2021]

Hello, I am getting a bit confused about question 4 and 6 associated with this game (page 199 of the 2020-2021 edition of Logic Games Bible). For question 4, I tried to come up with a hypothetical scenario and realized that the following couldn’t occur because of the rules: TSRFMFF. So, I assumed that since I had found one situation where F could not be in the seventh place, that answer choice E could not be the correct answer since the correct answer must be true. However, it seems that this is incorrect reasoning because we can only rule out an answer that must be true when it does not always hold in ACTUAL SOLUTIONS to the problem, as opposed to when it doesn’t hold in what are not solutions to the problem. Would that be the correct understanding?

However, for question 6, which is also a must be true question, the Bible says that we can eliminate answer choices by placing any other variable other than F in the fourth meeting to realize that it will not allow for a workable solution. So in this case, it seems like I can eliminate answer choices as soon as I find that they don’t produce a workable solution. But why doesn’t that same reasoning apply to question 4? I’m sure there is something I am missing in the reasoning here with the way I have explained these two questions, so I would be grateful for some clarification.

Finally, would it also be accurate to represent the rule for this game that Garibaldi does not have any meetings in a row with Fuentes as looking like AT LEAST F__F__F?

Thank you!

[Rachael Wilkenfeld]

Hi SGD2021,

For questions that ask what must be true, they are asking for all answers that are solutions to the game, what has to be true. So it doesn't matter that you can find non-solutions that don't work. You just need what must be true for all correct answers in the situation.

For question 4, you have a TSR block. In order for that to happen, you need to have Fs at the start and end, then M/TRS F TRS/M in the middle. We are unable to definitively place any of the variables in the middle, so we are looking for an answer choice about that F in first/last inference.

For both questions 4 and 6, if you can create a correct solution without an answer choice being true, then that answer choice is not required. So we are trying to see if F is required in 4, we can check by putting the other variables there. We see fairly quickly that F must be in four in order to have the correct placements of F in this local question.

You could draw that F rule in the way you suggest, but I'd worry you'd see it and think that it must be F one space from F, instead of F at least one space from F. The not block clearly says they can't be next to each other, so personally, I'd go with that.

Hope that all helps!

[SGD2021]

Thank you very much for the explanation! Would there be a quick way to realize that, for Question 6, the RM and TS block cannot be next to each other without plugging various things in to check which loses time? I understand the explanation in the book once it is laid out for me, but I'm wondering how I would get to that explanation on my own and quickly on the exam?

Also, to avoid making the mistake of eliminating an answer choice just because it is in a "non-solution that doesn't work," would you recommend that for questions like 6, we always try to come up with all of the possible CORRECT solutions for that question and then eliminate each answer choice by looking at spot 4 and seeing which answer does not have to be in 4, as opposed to testing out the answer choices in a new hypothetical each time and seeing that each time, it does not produce a workable solution? (since the latter way could lead us to accidentally eliminate an answer that was put into an unworkable hypothetical, but the answer choice isn't necessarily wrong, just like the mistake I made with question 4 that I described previously in the second & third sentence of my first post)

[Adam Tyson]

To answer your second question first, SGD2021, no, it would not be a wise use of your time to first come up with all possible solutions under these local circumstances. Instead, focus on what the new restriction requires more generally. Here's what that process looked like for me:

"Okay, we have an RM block in this question, and we still have that TS block somewhere, and I have to fit those three Fs in without being next to each other. How do I do that? Well, if one of the blocks goes first, the Fs would have to be in spots 3-5-7, but that would leave no room for the other block, so since M also can't go first or last, one of the Fs has to go first. Oh, and the same thing would happen if one of the blocks went in the last two spaces, so for the same reason there has to be an F in the last spot. Cool, now what's left? I have five spaces to fill in the middle of the diagram, from 2 through 6, and I need an F and the two blocks. The F can't be at 2 or 6, next to the other Fs, so the blocks have to be in 23 and 56. Hey, that means F must be 4th, and that's the answer! Yay!"

And as for realizing that the two blocks cannot be next to each other, that would also have been a good thing to think about first. When faced with large chunks of variables, I tend to start by trying to combine them in the most extreme ways first to see if it's possible, and putting them next to each other is that kind of extreme idea. Without placing them anywhere particular, my first thought might be "what would this do to the Fs?" And no matter what, I realize that at least two of the Fs would have to be adjacent, which is not allowed. That's how you can get the inference that they cannot be together without going to all the trouble of drawing out a hypothetical solution to the game and finding that it can't work. But keeping them apart is still just a first step before we can figure out what must be in that 4th position, and I think I would still end up back at thinking about whether a block can start or end the sequence.

My mental process was very similar for question 4: we have a TSR block now, and placing it at the beginning or the end of the sequence wouldn't leave enough room for the three Fs to avoid being next to each other. Since the block cannot be at the ends, and M can never be at the ends, there must be Fs in both the 1st and 7th spaces. Without worrying about where anything else goes, that inference answers the question. No need to draw out any working solution, because knowing that certain things cannot happen is enough in this case to tell us what must happen!

Start thinking about extremes as you diagram, and that can help you narrow down possibilities without testing a lot of options and answer choices. Put blocks together, start sequences as early as you can, end them as late as you can, etc. Push things around in ways that might cause problems so you can discover what those problems are! Inferences often come from finding out what cannot happen!