Setup and Rule Diagrams

[Dave Killoran]

The same way you would with any distribution--check the numerical possibilities, and then compare them to what can occur with the rules. There's a lot of information here, so you can see immediately that some thing are impossible (all 1s, for example). That narrows the process down considerably, but aside from straight counting/addition, there is never a magic bullet that tells you that you've discovered everything.

Glad I could help, thanks!

[cornhusker37]

Why does a 3-2-2 distribution not work? I see that it could work with KP-LS-RTV

[Nikki Siclunov]

Hi cornhusker37,

A 3-2-2 distribution of the type you suggest definitely works. The possible distributions in this game are:

• 1-1-2-3
  1-2-2-2
  2-2-3

In the third distribution, one of the two doubles is comprised of KP, while the other one must contain L (because L is a fourth-year student who does not live in a triple). Since L and R must live in separate rooms, R must go to a triple. How you divide the remaining three students between the double and the triple is up to you. KP-LS-RTV is just one of several possibilities.

Hope this helps! Let me know.

[cornhusker37]

Yes, very much thanks!

[justpeachy]

Soooo, I tried to do a timed section of LG using the December 1996 exam, Section 1 and it was well, interesting. With the time pressure, I froze and could not figure out how to properly diagram Game #1 (questions 1-6). Even when I went back to try to do it un-timed I could not figure out the proper setup. I thought that the answer would be to figure out all the possible triple-double-single room combinations that would not violate the rules, but even after I did that I was still not able to solve the game. I definitely think there's something I'm overlooking but I can't figure out what it is.


Help please!

[Nikki Siclunov]

Hi justpeachy,

Thanks for your question. This is a grouping game in which you need to figure out the assignment of students to dorm rooms. The variable set is further subdivided into three groups:

4th year: K, L
3rd year: P, R
2nd year: S, T, V

There are only single, double, and triple dorm rooms. The scenario doesn't specify precisely how many rooms of each type must be used, but you can - and should - figure that out. Of utmost importance is the combination of the first and fourth rules here: since K and P must be in the same room, but K is a 4th year student who cannot be assigned to a triple, it follows that K and P must share a double. Hence, you need to have at least one double.

What about the singles? Since no 2nd year student can be assigned to a single, and K and P are sharing a double, the only students who can occupy singles are L and R. So, at most two single rooms can be used (but it is possible that none are used). Similarly, with only five students remaining once K and P have been accounted for, at most one triple room can be (but need not be) used.

With this in mind, there are only three Numerical Distributions of students to rooms, where KP always occupy one of the doubles:

2-2-3
1-1-2-3
1-2-2-2

You can take each distribution a step further:

In the first distribution, L must occupy a double, and R - a triple, because they can't be in the same room (third rule), and L is a 4th year student who cannot be assigned to a triple.

The second distribution is completely determined. Do you see why?

The third distribution is the most open-ended, which is fine.

Distributions often lead to a Templates-based approach, because each distribution places an extreme limitation on where each variable can and cannot go. With only three distributions in place, the questions should not be terribly challenging. Give them a try and let me know if you have any further questions.

Thanks!

[srcline@noctrl.edu]

Hello

So I read over the explanations and I am still pretty lost. How would I even begin to set this game up, I understand that you have to keep separate the numerical distribution from the types of rooms. Everything about this game is confusing me.

I understand the rules, would rule three make this game a vertical setup? Can someone please explain this game.

Thankyou
Sarah

[Clay Cooper]

Hi Sarah,

Thanks for your question. Numerical distributions can be challenging.

I am not sure I can do a better job explaining this game than Nikki does in the post immediately above yours - she nails it. I can answer your questions, though, and maybe that will help.

First, let me note where you mention that you know we have to keep the type of room separate from the numerical distribution. That statement confuses me - what do you mean by type of room? If you mean whether it is a single, double, or triple, then in fact that statement is incorrect - the numerical distribution is not separate from the types of rooms, but is our attempt to understand everything we can about which types of rooms must be used.

Second, does rule three make it a vertical setup? No, the third rule (that L and R cannot share a room) does not affect the basic layout of the game; it is simply a not-block that tells us any permutation in which L and R appear in the same room won't work. Since this game is a grouping game, to call a setup vertical or horizontal doesn't seem really to be necessary or helpful; instead, we are focusing on who goes with whom, regardless of where they land in relation to another group.

I hope that helps. Keep trying!