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Setup and Rule Diagram Explanation

This is a Grouping, Numerical Distribution, Underfunded, Underbalanced, Defined-Fixed game.

This explanation is still in progress. Please post any questions below!
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Is there any way to see a more detailed game set up here?

The current way i have set up the game is i recognize this is a 2-2-2-2-1 and i also know the conditional M -> L and have N on friday and a not P under saturday.

Is there anything more i could have done to set myself up to succeed?
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 Dave Killoran
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Hi Why,

It's coming—now that things have slowed down just a bit I have been working backwards through 2019 posting setups for each game. November is done, and 3/4 of September (I just finished September 2019, Game 1 this morning).

I'll turn to June 2019 soon but in any event this was a tough game. You can add that L must work on Saturday to your inference list: without P, Friday must be three from L, M, N, and Q, and if you remove L you cant have M, which wouldn't be enough. So, L has to be there too.

More soon!
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Any chance we get a diagram on this soon? This game was definitely tough but at least one of my guesses panned out :lol:
 Paul Marsh
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Hi tfab! I'm sure that Dave will post an official explanation and diagram soon, but until then I'll do a quick run through of it.

We have 5 prospective volunteers: L, M, N, P, Q. They are grouped into 3 days. Each day has 3 spots. Like so:

T: _ _ _
F: _ _ _
S: _ _ _

As always with Grouping games, I want to take note of the number of spots available (9) and how those spots can be filled. Initially, we have basically no limitations on how the spots can be filled. Can any of the people be assigned to all 3 days? What about being assigned to 0 days? Luckily, the first rule is very helpful in this regard.

Rule 1: No volunteer works every day. (No need for short-hand, I'd write this rule out in its entirety)

This means that each of the five volunteers can only work a maximum of 2 days. How many of the volunteers will work the maximum 2 days? We can figure out the answer - since there are 9 spots available, four of the volunteers must work two days. The fifth volunteer will work one day. It is not possible for any of the volunteers to work 0 days. So we have a strong inference: four volunteers work two days, the fifth volunteer works only one day.

Rule 2: M :arrow: L (contrapositive: L :arrow: M)

Since there are only 3 spots per day, this rule is important to keep in mind since it means M always takes up 2 of those 3 spots (M and L) on any day it appears.

In addition, we can make one inference based on Rule 2 and our inference about the number of volunteers: L cannot be the volunteer who only works one day (if L only works one day, then M could only work one day and we wouldn't be able to fill all 9 spots).

Rule 3: N = F

Rule 4: P =/ S

If P does not work on S, that means we're left with only the four other volunteers (L, M, N, Q) to fill those 3 slots. However, from our contrapositive of Rule 2, we know that if L is not present, then M cannot be either. That would leave only 2 variables (N and Q) to fill the 3 spots on S, so that doesn't work. That means L must work on S.

Since L works on S, we are limited in where the M + L block(s) can go. This means the placement of M can be very instructive. For example, if M (and, because of Rule 2, L as well) goes on Thursday, then we know that M can't go on Friday (because that would mean L would have to be used all 3 days, which can't happen). That leaves us with only 2 volunteers to fill in the open Friday slots: P and Q. Similarly, if M (and therefore L) goes on Friday, we know that M and L can't go Thursday, which means Thursday has to be filled by the three remaining volunteers of P, N, and Q. And since P can't go Saturday, and we've already used N twice, the last two Saturday spots have to be M and Q. I don't think we can write down an exact inference about this, but the takeaway is that the placement of M is something to watch very closely.

Anyways, our final diagram will look like this:

T: _ _ _
F: N _ _
S: L _ _ (P)

Along with two rules not represented in the diagram:
- M :arrow: L (and we know it's a rule to watch very closely!)
- Rule 1, which is more helpfully expressed as our inference that four volunteers get used exactly twice, and the fifth volunteer (which cannot be L) exactly once.

From there, the questions become easier to answer.

Hope that helps!
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Thanks for your explanation, Paul! Could you please provide the final diagram with all the inferences? Thank you!
 Jeremy Press
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Hi v,

The diagrammed setup below is deceptively simple, but it contains all the key inferences that Paul worked into his very good (and detailed) post. Use Paul's post as your key to decipher how we derive this diagram (it's also at least worth a thought to build some templates around the placement of L--assuming you had enough time for that at the end of this section). Thanks!

Screen Shot 2020-05-11 at 1.35.36 PM.png
Screen Shot 2020-05-11 at 1.35.36 PM.png (28.29 KiB) Viewed 1901 times
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I do not understand why L has to be on Saturday specifically. I understand why it has to go more than once but why is it always on Sat?
 Adam Tyson
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One of the best ways to test an inference like this is to try to violate it, LSAT-Learner, so let's do that. What if L is NOT on Saturday? We already know from the rules that P cannot go there, and we only have 5 variables to choose from, so that would leave us with a Saturday grouping of MNQ. But wait, there is a rule that says that L has to work any day that M works, so an MNQ solution violates that rule! Thus, we have to put L in and take someone else out.

Put another way, with four variables to choose from (LMNQ) for Saturday, we have two options to choose from with regard to the rule about M and L. Either M is not among the three variables chosen, in which case L must be (LNQ would be the only three available), or else M IS among those chosen, in which case L would still have to be (because M requires L). One way or another, L must be included in the Saturday group!

And finally, here's one more way you could have gotten there: testing combinations. With 4 variables available for three slots, try all the combinations (there are only 4 possible ones to consider, so that won't take too long). Here they are:

LMN - works fine
LMQ - works fine
LNQ - works fine
MNQ - whoops, broke a rule! Has to be one of the others, and L is always in them.

A challenging inference, perhaps, but one that turns out to be pretty crucial and well worth the effort to find it.
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 Tami Taylor
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This game is very challenging for me. My initial diagram is very simple (as is yours). Whenever I play this game, I find myself needing to draw out several different scenarios for every question, which takes a lot of time. Even then, I find myself placing variables in spaces that violate the rules, so then I need to fix the mistakes (more time!). I'm not sure why this question was so, visually, challenging for me. I want to practice more games like this. Can you recommend similar games from other PTs?


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