Linear Games Rule Diagramming Drill #2 and #5

[marieallen]

#2 - The answer key indicates Z should be placed in slot 1 (Z/) and 2 (/Z). Because Z in slots 1 and 2 are above the slot, it must be true that Z is either in slot 1 or 2. The answer key also indicates Not Laws should be placed for Z at 3, 4, and 6. I realize the additional clarity this may provide but seems redundant or am I missing something?

#5 - I understand the rule here to be a Rotating Not Block: T cannot be before or after P. I also represented this rule as:
Block T-PT; similar to the answer for Question #8. Would my representation lead me down a wrong path?

[Francis O'Rourke]

Hi Marie!

I personally would not place four additional not Z symbols underneath spaces 3, 4, 5, and 6. However, as you say, doing so provides extra clarity. For many students this extra clarity will meaningfully improve their performance on the exam. If you find yourself making mistakes or missing inferences that may have been caught with these four additional not Z symbols, then try placing them in the future. If this is merely redundant for you, then there is no need to place them there.

Drill number five is a bit more complicated. I understand the shortcut you took here and it will likely be fine to symbolize the rule in the way you explained for the game this drill was taken from. However, there are a significant number of games in which your symbolization will lead you astray.

For example, imagine that instead of seating Tom and Pat in a row of seats, we were asked to place Toms and Puma brand shoes on a display shelf. In the example provided in the book, there is onyl one Tom and only one Pat. In the example of placing shoes on a display shelf, there may be three different Toms brand shoes and two different Puma brand shoes (as well as a few Reebok and Nike shoes most likely).

In games in which variables repeat, diagramming the rule "Toms brand shoe may not be placed immediately before or after a Puma brand shoe" as TPT with a box around it would be ambiguous. This is because the diagram that you are describing would tell me that we may never have a P surrounded by T on both sides. In this case the diagram tells me that it would be fine to place a T immediately before a P, as long as an R or N would follow that P.

Let me know if my explanation here is clear enough. Since you have a very good chance of seeing a game in which variables repeat, you should try to avoid the diagramming you suggested and list out two separate diagrams, as shown in the book.

I hope this helps!

[marieallen]

Thank you for the clarity on Question 2 and 5! Re question 5, you provide clear advice not to take the shortcut I took as it may lead to a wrong path for repeated variable games. I get that now. However, since both #5 and #8 are similar in structure, wouldn't the same advice hold for Question 8 as well? In the end, I want to develop good reliable methodology rather than just simple quick shortcuts that would not always work. Thanks for your response!

[Francis O'Rourke]

That's right, the same advice does hold for number eight. That is why we have a pair of diagrams for rule, just like we had in number five. Is there something inconsistent in this diagram that I am not spotting at the moment?

[marieallen]

I think I'm getting it now - for #5, perhaps better methodology would be to diagram as:

Block T-PT. I'm thinking this representation would be proper for both #5 and the hypothetical you provided earlier?

And you're right, I get now that #8 is really 2 separate diagrams - not 1. Thank.s

[Jonathan Evans]

Hi, MarieAllen,

Thanks for following up! I believe you've got it right. Just to make sure, compare your diagram to the one below:



The things to note about this Not Block are that:

• You can't make any Not Laws from it. T or P could still be 1st or 6th.
• As noted in the discussion earlier, it's a good idea to write it out both ways to make sure that the rule is not ambiguous.

Please follow up with further questions!