Setup and Rule Diagrams

[Administrator]

Setup and Rule Diagram Explanation

This is a Grouping game.

This explanation is still in progress. Please post any questions below!

[Dajpol]

Can someone show the setup and diagram for this game? I got caught up in trying to figure out all the Numerical Distributions and wasted too much time.

Thank you!

[Jonathan Evans]

Hi, Dajpol,

It might be helpful to see your work so that we can perhaps get a better picture of what you are doing. It's often more helpful to students to receive feedback on their work rather than seeing a solution presented by someone else.

With that in mind, I would like to respond to your remark about trying to figure out too many numerical distributions. I assume since the groups themselves are fixed, you were trying to determine all the possible distributions of numbers of variables.

Determining distributions in a case such as this is a two step process. First, you notice the possible maximums limited by the restrictions:

Possibly 3 N
Possibly 3 H
Possibly 2 K, definitely 1 K
Exactly 1 J
Exactly 1 M

Possible for variables to be excluded.

Now, if you stopped here and started sorting through possibilities, you would not only waste a lot of time but also neglect the effect of the tight restrictions on the diagram. With the limited slots to fill and the limited options available, it becomes clear that no variable is ever omitted from selection. Further, you are severely underfunded. You need N in at least 2 of the groups, H in at least 2, and exactly 2 K.

Once you make these determinations and observe the powerful restricted possibilities in this game, you need not spend much time at all on working out innumerable permutations of numbers of variables. The possibilities stem from the diagram itself. My advice to you would be not to neglect all the information at your disposal when making deductions/inferences. Also, don't get sucked into a rabbit hole of just spinning your wheels trying to generate information. Assess the game in its entirety and consider all the different components when deciding where your energy is best spent.

[Dajpol]

This is great, thank you.

[RebekkahS]

Hi there,

I'm having a lot of trouble with this question.

My set up looks like:

_ K _
_Js_
_ _ _
x y z

j cannot be in x
k cannot be in z
j cannot be in j

but that is as far as I got. I'm not sure how to see that all of the volunteers are used or how to not spend an unreasonable amount of time on this problem.

[Jennifer Janowsky]

RebekkahS,

What you have is a great start! You can also take it further by looking at the information you have to make a few more inferences:

As you showed, neither K or J can be in group Z. This leaves only 3 letters that could be: H, M, and N. Since all 3 spaces must be used and they can’t be repeated within a group, all three of those letters must be in Z.

Similarly, another inference can be made from here. Since M must be used in Z, and it can only be used once, it can’t be used in either X or Y. Since J can’t be in X, as you said, this leaves only H, K, and N—all of which must be in X.

Lastly, N must be L in wherever group it is in.

That leaves your diagram as follows:

H K H
K Js M
Nl _ Nl
X Y Z

Hope this clears things up a bit!

[T.B.Justin]

Hey all,

Frustrating to admit that (after the fact of running through this game the first time), to me, this is a familiar underfunded and actually quite defined grouping game, perhaps a linear element as the rules refer to one of three positions.

I found that committee X and Z are the most restricted, since J nor M can be in X and K nor J may be in Z. Resulting in N being the leader of both X and Z, while H and K are floaters between secretary and treasurer in X, and the same idea between H and M in Z. Leaving us with committee Y, which we know must contain J as secretary and K as either treasurer or leader, with N as a possibility for leader and H able to be used as a leader or treasurer, in either case we must have one of N or H to fulfill the requirements for committee Y.

This describes in detail one template that I have used to identify the possibilities of this game.

[Ari]

I am a little confused about how we are sure about some of the spots in the diagram. I had:

X Y Z
Leader. N (N/H/K) N
Secretary. H/K J H/M
Treasurer. H/K H/K H/M

Can someone help? Thank you!

RebekkahS,

What you have is a great start! You can also take it further by looking at the information you have to make a few more inferences:

As you showed, neither K or J can be in group Z. This leaves only 3 letters that could be: H, M, and N. Since all 3 spaces must be used and they can’t be repeated within a group, all three of those letters must be in Z.

Similarly, another inference can be made from here. Since M must be used in Z, and it can only be used once, it can’t be used in either X or Y. Since J can’t be in X, as you said, this leaves only H, K, and N—all of which must be in X.

Lastly, N must be L in wherever group it is in.

That leaves your diagram as follows:

H K H
K Js M
Nl _ Nl
X Y Z

Hope this clears things up a bit!

[KelseyWoods]

Hi Ari!

Your setup is correct. However, you might consider adjusting your options for L and S in the Y group to make it clearer that K must be in Y. Otherwise you might think you could have N as the Y leader and H as the Y treasurer and K not in Y at all. I would probably make my diagram more like this, to show that K has to be in Y, but we are unsure if it is the leader or the treasurer:

L        N               K/               N
S     K/H               J             H/M
T     H/K               /K           M/H
          X                 Y                 Z

The above diagram doesn't fill in every possibility for every space--and that's okay! It shows us the information we most need to know to make sure that we have all of our inferences and don't miss important rules.

Hope this helps!

Best,
Kelsey

[christinecwt]

Hi Team - can anyone explain why there is only one J in this set up? Thanks!

Your setup is correct. However, you might consider adjusting your options for L and S in the Y group to make it clearer that K must be in Y. Otherwise you might think you could have N as the Y leader and H as the Y treasurer and K not in Y at all. I would probably make my diagram more like this, to show that K has to be in Y, but we are unsure if it is the leader or the treasurer:

L        N               K/               N
S     K/H               J             H/M
T     H/K               /K           M/H
          X                 Y                 Z