Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Pure Sequencing game.

This is an unusual game in that it presents a fairly standard sequence, but instead of placing the students in a 1-9 order, it instead assigns them to three groups—level 1, level 2, and level 3—each with three members.

The rules form the following sequence:

Feb94_Game_#1_setup_diagram 1.png

This sequence allows for some immediate inferences. Because I must be first and G must be second, both I and G must be placed in the level 1 class:

Feb94_Game_#1_setup_diagram 2.png

Because J or K must be third, the remaining slot in level 1 must be taken by either J or K:

Feb94_Game_#1_setup_diagram 3.png

Because J scores higher than at least three students (M, H, and N), J cannot be in level 3:

Feb94_Game_#1_setup_diagram 4.png

F, H, K, L, M, and N are the only students who can be placed in the Level 3 class. Note that a variable such as N, which “appears” to have to be placed in the level 3 class due to the fact that it is at the end of a chain, does not have to be in the level 3 class because K, F, and L could have lower scores.

[ginajoy14]

Hi-

I think where I need help is in seeing how they arrived at the answer they did. Like for question 3, couldn't J also go into any of the three classes? For question 4, I am confused as to how this answer was determined, same goes for question 5. I thought I diagrammed correctly...

[Clay Cooper]

Hi ginajoy,

Thanks for your questions. I will start with the general one: did you diagram correctly?

I think the key to this diagram is to make sure that we use the chain-style sequencing rule to its full potential. The first rule tells us that I scores higher than G, or graphically:
I---G.
We can continue to use this notation to add in the other rules as they come; note that they all link up to create a super-rule. What we end up with should look something like this:

I---G---J---M---H---N

Additionally, you could include sub-branches that work in the other information we have, for example that

G---K---F

and that

K---L

as well.

In number 3, no, J cannot go wherever we want, because there are other students who score worse than J according to the rules; Specifically, the rules tell us that M scores lower than J, that H scores lower than M, and that N scores lower than J. Since that is three students who all score lower than J, J could never be in the level 3 class.

For number 4, we need to pick the answer choice that lists a pair of students who, if placed into class two, provide enough information to determine the class into which each student goes. That pair turns out to be J and H. Since we know that J and H must have M between them, placing bot J and H in class two means that M is in class two as well. That forces N into class 3, and since K must score higher than both F and L, F and L end up in class three as well. That leaves only I, G, and K for class one, and our class composition is completely determined.

I hope that helps! Keep working hard.

[Lemorinlaw]

In Game 4 of Lesson 1-

7 of 9 variables fit logically into a sequence. The two that aren't mentioned in the rules (F,L) aren't given ranks ... but in the HW explanation the sequence assigns the two variables to the right of the other variables, after K.

Can you please explain why these random variables are placed here?

L

[Jeff Wren]

Hi Lemor,

I think that you may have missed the sixth and final rule in the game, that "Kathy scores higher than Fred and Laura."

When combined with the first two rules, these rules create a sequencing chain

I - G - K - (F and L)

(The other rules create the other branch of the sequencing chain, J - M - H - N).