Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Grouping: Partially Defined game.

At first, this game appears to be fairly standard: nine sessions are being filled, and three employees are available to fill those sessions. The first rule then establishes that each employee can attend only two of the sessions. This rule makes the game appear Underfunded, which is not a concern because we can create three empty spaces (E) to balance out the game. But, the final rule reveals that employees can attend sessions together, and this leaves the number of sessions attended by the employees uncertain. Because we can determine that the employees attend a maximum of six different sessions or a minimum of four sessions, this game is Partially Defined.

Because the employees can attend a maximum of six different sessions, at least three of the nine sessions will be “empty” for our purposes. These can be designated with “E,” leading to the initial setup, which is based on the game scenario and the first rule:

D02_Game_#2_setup_diagram 1.png

The second rule eliminates M and S from attending an investing session. This information is best shown with side Not Laws. The third rule eliminates T from attending any session on the third day, which can be shown as a standard Not Law. Of course, the combination of these two rules causes a problem for the investing session on the third day: neither M, nor S, nor T can attend that session. Thus, that session must be unattended, which will be designated with an E. The consequences of these two rules are shown below, along with a note regarding the fourth rule:

D02_Game_#2_setup_diagram 2.png

[Sdaoud17]

Can you explain how can you have 4 is the min number of sessions attend by at least one capital Employee ?

I prefer and if you dont mind to show me how through a digram.

PS: from the first rule I can see that you can have a max of 6 sessions that attend by at least one Employee ?


Thank you so much

[Lucas Moreau]

Okay. Picture a diagram that looks like this, approximately:

H _ _ _
I ._ _ _
R _ _ _
...1 2 3
MMSSTT

Um, approximately.

The trick is the first and the second rule. You need to combine their interactions. A minimum interaction would look something like this:

H (M/T) .S _
I .._ .... _ ._
R (S/T) .M _
...1 .... 2 .3

If that's not clear, Day 1 H has Maria and Tate, Day 2 H has Suki, Day 3 H is empty. I is wholly empty. Day 2 R has Suki and Tate, Day 2 R has Maria, Day 3 R is empty. All the periods are for spacing. Sorry if it's confusing.

It simply cannot collapse into less total sessions than this. Any arrangement where two people are each on one session would violate a rule. Suki and Maria could not join up on Day 2 without being on the same session twice, and neither Suki nor Maria can join Tate in an investing session to avoid this problem. Any arrangement runs into this difficulty, and thus, 4 is the minimum.

Let me know if you have any more questions.

[ellenb]

Dear Powerscore,

This seemed a very confusing game, I thought that one person must do two sessions.
Thus, there should be: MMSSTT (thus 2 of each)

However, in question 11, only on M is used on the first day, how about the second M, it is not used. ( we just have first day: M,T, second day: S and T, third day: S (why we did not use one more M ?)

Also, in question 10, we just used on of M and S for the first day, what about the rest of them?

For question 9, answer choice B did not make sense, I thought that the answer choice is saying: that they all attend 3 sessions, ( 1 plus 2). So, I am a bit confused to what it is saying.

Thanks in advance!

Regards

Ellen

[KelseyWoods]

Hi Ellen,

Thanks for your questions! This game is a bit tricky.

For question 11, we know for sure that M and T are on the 1st day, S and T are on the 2nd day, and S is on the 3rd day. You are correct, we need another M, but that M could be on the 2nd day or the 3rd day--we don't know for sure which day to put the 2nd M on. In the explanation, they are just giving you what we know must be true.

Similarly, in the explanation for question 10, they are showing you what we know. We don't know where the other M, T, and S go.

Remember that in Local questions, you won't necessarily be able to figure out where all of your variables go based on the Local rule. In your diagrams, you just need to include as much as you do know and answer the question from there.

In question 9, answer choice (B) means that exactly TWO employees have to attend each session that any employee attends. It's not saying that if there is one employee, there are also two others. It's saying that it there is at least one employee, there are exactly two employees. Essentially, it's a strange way of telling us that you can't have an employee attend a session by him/herself and you can't have all three employees together in a session. The reason that they word it that way is to be clear that there could still be sessions which ZERO employees attend. Again, the rule is basically: if any employee is attending that session, there are exactly two employees attending that session.

Hope this helps!

Best,
Kelsey

[Jiya]

Hi there,

I struggled a bit with the set up of this game. I had 1-2-3 as my base, with the three sessions stacked vertically for each day, but I think I am simply not able to get my head wrapped around this one .

For example, why can't Maria and Suki attend a session together on Day 3 per correct answer for 8? Could MS not attend a session on day 3, and one of M or S attends a session alone on Day 2, the other attending a session alone on Day 3? Similarly for Q 10 - why can't T be the only one attending a session on Day 2 and MS attend a session on Day 3, making that session the second one for each of them?

Can someone please help? I feel I am missing something very fundamental here.

Thanks!

[David Boyle]

Hi there,

I struggled a bit with the set up of this game. I had 1-2-3 as my base, with the three sessions stacked vertically for each day, but I think I am simply not able to get my head wrapped around this one .

For example, why can't Maria and Suki attend a session together on Day 3 per correct answer for 8? Could MS not attend a session on day 3, and one of M or S attends a session alone on Day 2, the other attending a session alone on Day 3? Similarly for Q 10 - why can't T be the only one attending a session on Day 2 and MS attend a session on Day 3, making that session the second one for each of them?

Can someone please help? I feel I am missing something very fundamental here.

Thanks!

Hello jiya,

One helpful inference to make is that since m and s can't do investing, and t can't do anything on day 3, then the investing session on day 3 must be empty.

That actually helps with question 8. Only regulation and hiring are open on day 3, so if two sessions are to be filled, m and s must each attend one of those sessions. Also recall, "Each conference participant attends exactly two sessions, which are on different topics and on different days." That means that if m and s attend regulation and hiring (in whatever order), they can't ever be in the same space at the same time, since they can't be in investing.
That helps with question 10, too. The first day, t must be in investing, so m or s must be in regulation or hiring. Again, that means m and s can never both be in the same spot on any day.

Hope this helps,
David

[lsatstudier]

Hi!

I was wondering if someone could help me understand how to figure out the maximum number of sessions attended as well as the minimum number of sessions attended (or more specifically, question #6). Looking at the previous responses to this question, I think I understand how to set up the question, but I can't figure out how you get a minimum of 4 sessions. Why is it not that S, for instance, would be counted as going to no more than two conferences? I know they can pair up, but don't the employees have a limited number of options (why do they go to the hiring conference more than twice?)

Thank you so much in advance!

[Kristina Moen]

Hi!

I was wondering if someone could help me understand how to figure out the maximum number of sessions attended as well as the minimum number of sessions attended (or more specifically, question #6). Looking at the previous responses to this question, I think I understand how to set up the question, but I can't figure out how you get a minimum of 4 sessions. Why is it not that S, for instance, would be counted as going to no more than two conferences? I know they can pair up, but don't the employees have a limited number of options (why do they go to the hiring conference more than twice?)

Thank you so much in advance!

Hi lsatstudier

To start with, Question 6 is asking about the maximum number of sessions attended by at least one Capital employee. The first rule says "Each participant attends exactly two sessions." Since there's three employees, the maximum number of sessions before reading any other rule is six. So I can eliminate Answer Choice (E) which is seven (that would mean at least one participant attended three sessions). However, I also know from the fourth rule that "At most, two Capital employees attend any given session together." So I know that Capital employees can attend sessions together, which means that the maximum might be less than six sessions if they have to double up. So I ask myself - can I set up a scenario where the employees each attend their own session? Try it out! You can! Which means that six sessions is the maximum - and the correct answer choice is (D).

Now, to answer your question about the minimum. If everyone doubles up, then that's three sessions (since you can't have more than two people per session). Is it possible to make a scenario where they double up on all the sessions? Try it out, and let me know what you find out!

[ehlers.christopher]

I still can't get past the first question.

The first rule says that each participant attends exactly two sessions.

So how can a participant attend EXACTLY two sessions and a minimum of 6 sessions? These ideas seem incompatible and I haven't seen anything that addresses this specifically.