Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Pure Sequencing game.

The game scenario establishes the following basic setup:

PT52-Sept2007_LGE-G4_srd1.png

The four rules each involve sequential elements. The first two rules can be combined to create the following sequence:

PT52-Sept2007_LGE-G4_srd2.png

The third rule is conditional:

PT52-Sept2007_LGE-G4_srd3.png

The contrapositive of this rule is:

PT52-Sept2007_LGE-G4_srd4.png

Note that, between the first three rules, all six variables are addressed, and thus there are no randoms in this game.

The fourth rule is pivotal, and it creates two separate directions for the game. By itself, the rule appears as follows:

PT52-Sept2007_LGE-G4_srd5.png

However, because each possibility is mutually exclusive, the rule really appears as:

PT52-Sept2007_LGE-G4_srd6.png

This rule creates significant restrictions when combined with the other rules. Let us examine both templates.

PT52-Sept2007_LGE-G4_srd7.png

The third rule is still in play, and L’s delivery is uncertain, and thus both items must be tracked carefully when this template is in effect.

PT52-Sept2007_LGE-G4_srd8.png

Because F M, the third rule is enacted and thus L H. Therefore, all of the variables appear in the diagram, and all of the rules are satisfied. The only remaining uncertainty is the positioning of F. This template therefore contains just three solutions.

[stsai]

In this bread truck sequencing game, I got 19, 20, 22 wrong and could not figure out where went wrong with my setups. I came up with two templates. I would put it up but it is kind of difficult on a computer.
Could you please provide your version of setup for me to check mine? Thanks!

[Dave Killoran]

Hey Stsai,

I'll assume your two sequences were generated from the last rule. I agree that the diagramming is tough in these text boxes, but here's what they should look like:

Template #1:

F
G K
M H

In this template, the major uncertainty is the placement of L. L appears to be a random, but L is affected by the third rule, so F, M, and L must all be tracked together.


Template #2:

F
G K M
L H


Please check that against your setup and let me know if you have any questions. Thanks!

[Erice93]

Hi - I see from the previous answers that there are 2 templates that should be used for this question. I’m having a hard time understanding how/why those templates are reached. Could you explain the setup here?

Thanks!

Eric

[Eric Ockert]

Hi Eric!

As Dave mentioned, the basis for these two sequences would be the last rule, because it tells you one of two things must happen. Also, it establishes that the two things cannot BOTH happen. So, the two situations created by that rule are:

#1:

M H, M K

and

#2

H M, K M

When you combine the first two rules into each of these situations, you get the following:

#1:

M H G K

and

#2:

H G K M

In both cases, F is also before G (and therefore before K as well). It is difficult to draw those inferences into these diagrams on our Forum. Also, in the second template, you would KNOW that F is before M, which, according to the third rule, tells you that L must be before H. So, the final templates would look like:

#1

M H G K
(with F G also. L's position in this template is unknown).

and

#2

L H G K M
(with F G also)

Hope that helps!

[johnvm24]

Hello,

I had issues with this game as I incorrectly diagrammed the third rule. I started by diagramming F--M ----> L--H and took the contrapositive as H--L ---> M--F. Based on the diagram and the contrapositive I made two templates, instead of basing the two templates off of the last rule. I understand why I should've based the templates off of the last rule, but can someone explain why the contrapositive of the third rule is wrong? It lead me to get #20 wrong.

Thank You!

John

[Eric Ockert]

Hi John!

Your contrapositive of that rule is correct. The problem is, however, that the original rule and its contrapositive do not create two possibilities. My guess is that your two templates were based around:

#1: F M (in which case L H)

and

#2 H L (in which case M F)

The problem is, what happens if L H? That doesn't prove F M (that would be a Mistaken Reversal of the original rule). So, if you have L H, then F could be either before or after M. This shows that the two instances above are not the only templates in this game.

The final rule, however, give you a construction of "Either A or B, but not both." That creates two distinct possibilities, and no others. That's why this rule is ideal for creating the templates in the game.

With #20, putting M first definitely guarantees that M F. But that is a necessary condition in your contrapositive, not a sufficient condition. So it doesn't prove anything about where H is relative to L.

Hope that helps!

[altheaD]

This thread is very helpful. I just don't understand how in practice you would know by looking at a hypothetical formula, what came first -- the sufficient condition OR the necessary?

For example Eric you state that L--H doesn't mean F--M because that'd be Mistaken Reversal. I totally get that. BUT, how do you know which came first? Is it that you trace which of the conditions comes first in the sequence? But let's say L--F--H--M where elements of both sufficient and necessary conditions are interspersed with each other... then how do you know which came first?

I keep making this error where I assume that a necessary condition resulted from the sufficient condition's presence only to later find out that the order was the other way around. I hope I'm making sense, about what my confusion is... help!!

[Robert Carroll]

althea,

I'm not sure what you mean. The conditions each have a time relation, but it's not as if the sufficient condition happens before or after the necessary condition - the conditionality itself does not have a temporal relationship. In your hypothetical, you have L before H and F before M. So both conditions of the conditional are true. Which "came first" is only a relevant question when asking about two restaurants. The sufficient condition can't come "first" or "second" itself.

Please clarify what you meant so I can answer more fully.

Robert Carroll

[cmnoury1221]

Hello,
I am having difficulty diagramming this game. I knew to use the last rule to create templates, but still struggled with a lot of uncertainty for the variable that are not involved in the last rule.
Help to clear this up would be greatly appreciated!

Thanks
Carolyn