Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

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

This game is more challenging than the first game. Although the setup is straightforward, there are some interesting inferences. Let’s take a look at the game by examining each rule.

The first rule reserves one space in each group for an officer:

Of course, if an officer must be assigned to each committee, then all three supervisors can never be assigned to the same committee:

The second rule establishes the minimum assignments—one per employee—in a numerical distribution. With six employees, that minimum translates to 1-1-1-1-1-1. Thus, there are three additional assignments remaining. All three cannot be assigned to the same person as that would result in four total assignment when there are only three possible committee assignments, so the three assignments must either be split 2-1 or 1-1-1. Adding those to the minimums produces two separate unfixed numerical distributions:

The third rule very nicely fills the Policy Committee with all three officers:

The fourth rule is a negative grouping rule between G and L. Because this game contains fixed groups in a vertical array, we will show this rule as a vertical not-block:

Because G and L cannot be assigned together, and from the second rule each must be assigned to at least one committee, we can infer that neither G nor L can be assigned to all three committees:

As G is already assigned to the Policy Committee from the third rule, this means that G cannot be assigned to both the Quality and Sales Committees. L, who cannot be assigned to the Policy committee because it is full, must then be assigned to either the Quality or Sales Committees, or both:

The fifth and final rule assigns K to the Sales Committee. Because K is a supervisor, K will be placed in the second available slot, in order to reserve the first slot for an officer per the first rule:

Combining all of the rules and inferences leads to the final setup for the game:

[xishao3]

Hi,

For LG #2 of the December 1995 LSAT, was the best approach the template approach before moving onto the questions? I applied the template approach during my blind review of the exam, but did not find that it helped me move through the questions quicker. Is there a better approach and/or critical inferences that dominated this game and would have helped increased my efficiency?

Many Thanks,
Amy

[Dave Killoran]

Hi Amy,

Thanks for the question! This isn't a game where we use a template approach, and so instead we make a basic setup that then gets used to attack each question. Consequently, we use hypotheticals to solve certain questions, such as #7, #9, and #11.

Please let me know if that helps. Thanks!

[AJH]

Is there a better way to set up the game or make more inferences to get more information out of it? I set up the game with the following diagram, but feel like I don't have enough to be able to attack the questions. Any help is appreciated!

H ___ ___

G ___ ___

F ___ K
_______________________
s q p

The main rule: G<--|-->L

[nicholaspavic]

Hi AJH,

The first thing I notice is that you have FGH all under Sales when they should be under Policy. So that's a problem.

As Dave has also noted you need to do Templates here, specifically for the supervisors because there's only 2 possibilities. Can you show me how you would represent that with the correction to the Policy column I mentioned?

Let's start there and keep talking!

[LSAT2018]

On the Classifications page, this game was identified as Grouping: Defined-Fixed, Unbalanced: Underfunded, Numerical Distribution. I know that when a game is underfunded, so the variables must be repeated. But I was unable to figure out the Numerical Distribution here, so do you mind explaining this part? Was the Numerical Distribution part of the inference here?

[Adam Tyson]

For sure, LSAT2018! The Numerical Distribution is about how we can go about spreading the 6 employees around into those 9 spaces. Let's start with the basics: every one of the 6 employees must be used at least once, so that gives us this starting point:

1-1-1-1-1-1

That's only 6 spaces accounted for, though, so now let's create the most extreme distribution we can by adding as many of the extra, unaccounted for spaces to just one of our employees. There are three more spaces to deal with - can I give them all to one person, so that they have a total of 4 spaces? I cannot, because there are only three committees. That means the maximum number of committees that one person can sit on is all three. So, this gives me this change to the distribution:

3-1-1-1-1-1

That's 6 people into 8 spaces with everyone going at least once. But that leaves one empty space still that I have to fill, so I have to do one more thing to build my most extreme distribution, and that's add that one extra space to one of my six employees, like so:

3-2-1-1-1-1

Now I have all nine spaces accounted for, and this means one person is on all three committees, one is on two of the three, and the rest are on one committee each. That seems like it will work, and I might even try a hypothetical with it. The person who goes three times has to be an officer, since only officers sit on committee P. It cannot be G, because then G and L would be sitting on at least one committee together, violating a rule. So, in the 3-2-1-1-1-1 distribution, the 3 can only be either F or H. Conveniently, that inference answers question 8! (although we could probably have answered that one without the distribution, just based on the G/L rule)

But now we have to consider another distribution, one that is a little less extreme. What if I take one of the extra spaces away from that person who is in all three committees, and give it to someone else? Now I have this distribution:

2-2-2-1-1-1

That's more evenly distributed, and also looks possible, if a little less interesting. At least two of those 2s are going to be officers, because I need an officer on P and also on Q and I need a different officer from P to also be on S. The last person to double up could be the remaining officer, perhaps, or it could be a supervisor. Just beware of keeping G and L apart!

When the numbers do not match, consider whether a numeric distribution is called for. Start with the most extreme and then work your way towards to more even. Give that a try on a few other games and see how that goes. Good luck, and have fun!

[Mastering_LSAT]

Hello,

I would appreciate it if you could clarify the following.

The game rules do not prohibit the same employee to be assigned more than once to the same committee. All we have on this subject is: “…exactly three employees per committee…”. However, we do not know for sure and cannot make any assumption as to whether the same employee can/cannot be counted more than once for the same committee if the rules are silent about it. Otherwise, we would have had a rule similar to: “No employee can be assigned more than once to the same committee.”

What game rule is suggesting that the same employee can serve only once on the same committee?

Thanks for the help!

[Adam Tyson]

That's not so much a rule, Mastering_LSAT, as it is a common sense/language usage issue. If I select you to play on my kickball team, and then I select you a second time to be on that same team, did I pick two people or just one? I didn't clone you, so no matter how many times I said "I want Mastering_LSAT on my team" I still only get one of you, right?

It's the same here. If I say that my committee is made up of H, K, and H, do I have three people on my committee, or just two? Looks like just two to me, no matter how many times I say that H is included.

Now, if I said I needed a Chairperson, a Secretary, and a Treasurer for each committee, and there was no rule against one person holding two positions or requiring three people per committee, I might be able to have a committee made up of just one person holding all three jobs. That would be an odd way to make a committee, but it might be something LSAC would pull just to make our lives more difficult interesting. But that's not what's going on in this game. "Exactly three employees per committee" can only mean three different people, because that's the plain meaning of the language in this case. Any other interpretation would be an unreasonable twisting of the meaning of those words.