Setup and Rule Diagrams

[Jon Denning]

Setup and Rule Diagram Explanation

This is an Identify the templates, Grouping/Linear Combination Game.


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



Main diagram:

C4E2EE1F-3BFF-4ED0-9159-010A005FF113 6.png

[tizwvu34]

How doe we know that Y is with either H or G?

[James Finch]

Hi tizwu,

Y must be with either H or G because of the the conditional chain when either H isn't with Y or G isn't with W: either one forces the F with W and L with Z, which means X and Y must go with H or G. If L isn't with Z, then F is, meaning G then would go with W and H would have to go with Y, leaving L only able to be with X. There is no way to put L or F with Y and not also force H into that spot, thus breaking the rules.

Hope this clears things up!

[gwlsathelp]

Hi, I am not sure how you got the additional conditional rules (bolded) from the restrictions:

Fw Gw + Hy
Gw Fw + Lz
Hy Fw + Lz + Hx + Gy

Can someone explain to me how these are linked?

[KelseyWoods]

Hi gwlsathelp!

The first inference is just the contrapositive of the 2nd rule:
Gw Fw
Fw Gw

The last chain also comes from taking contrapositives and linking rules together.

3rd rule + contrapositive:
Fw Hy
Hy Fw

Per the 1st rule, Z has to be assigned to either F or L. You could potentially diagram that rule as:
Fz Lz
Lz Fz

If F is assigned W, then it is not assigned Z, meaning L must be assigned Z.

Since Z has to be assigned to either F or L and W must be assigned to either F or G, the H must be assigned to either X or Y. Thus, if H is not assigned to Y, then H must be assigned to X.

And, finally, Y can only be assigned to either G or H. So if H is assigned to X, that only leaves G to be assigned to Y.

This game is heavy on either/or rules the first 3 rules all set up an either/or relationship. It's important to make sure you fully understand those rules and what inferences you can (and cannot) make from them.

Hope this helps!

Best,
Kelsey

[lsatdaynnight]

I am having a difficult time setting up the game. Would it be possible to please explain how you set it up? Thank you!

[Rachael Wilkenfeld]

Sure, LSATdaynnight.

We want to list out the variables---the architects (FGHL) and the projects (WXYZ). There's also ANOTHER variable set that's relevant here, and that's numerical order 1-4.

The two boxes pictured are just a representation of the first two rules.

F or L is assigned to Z.
GW FW. Combined with the contrapositive of this rule, this means that either F or G is assigned W

The third rule gets a bit complicated
FW HY
Creating the third box in the image in the first diagram takes a bit of thought. Clearly H can be assigned Y. Who else can? Well, F can't, because that would mean F is not W, which would mean H is assigned Y, not F.
Can G? Sure. you could have Fw, Gy, Lz, and Hx. That works.
How about L? If we put L is assigned Y, that means H is not assigned Y. According to the contrapositive of the third rule, that means that F would have to be assigned W. That would mean L would have to be assigned Z (per the first rule), and that can't happen if L is assigned Y. So we have a contradiction, and L cannot be assigned Y.

Let's combine things a bit. Here's where the chains come in.

When F is not assigned W, we know G must be, and since G is assigned W we know H is assigned Y. That's a combination of the second and third rules.
When G is not assigned W, we know F must be, and since F is assigned W, L has to be assigned Z. That's a combination of the first and second rules.
When H is not assigned Y, we know that F must be assigned W (see the contrapositive of rule 3). We can combine this with the conditional above, and also know that L is assigned Z. Since H isn't assigned Y, H must be assigned X as this is the only assignment left. That leaves G to be assigned Y.

Let's look at the advanced linear diagram. We write out slots 1-4 because we know these assignments occur in an order. H we put in last because of rule 5. The other places we can fill in because of rule 4.. If the order is always FG, we can either put that FG block in 1-2 or in 2-3. Either way, 2 is going to be either F or G. G can't be first, because F is right before G, so our first spot is either F or L . Our third spot can't be F, because there wouldn't be room for G right after. So the third spot is either G or L.

And that's the whole diagram.

[Kenyambo]

Is there a simpler, more "cleaner way" to diagram this game than the one that is currently up?

[Rachael Wilkenfeld]

Hi Kenyambo,

It would help us help you if you could explain what part of the diagram doesn't make sense to you. This diagram contains all the necessary inferences and information. The conditional statements are particularly powerful in this game, and do a good job of guiding your work on the questions.