Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Basic Linear Game: Balanced, Identify the Possibilities.

At first glance, this game appears to be a standard Basic Linear game. However, the second and third rules combine to create a powerful block-sequence:

Oct 94_M12_game#1_L9_explanations_Limited game#1_setup_diagram_1.png

By itself, the GS portion of this super-block-sequence can only be placed in days 1-4 or days 2-5 (days 3-6 are unavailable because S U). By itself, then, this formation would suggest creating two base templates. However, the addition of the first rule (J H) and the fourth rule (J 1/3) further limits the possibilities, and the best approach is to Identify the Possibilities. Let’s examine each:


Template #1: GS block scheduled for days 1-4

• When the GS block is scheduled for days 1-4, then from the second rule U must be scheduled for day 5 or 6, and from the last rule J must be scheduled for day 3:
  
  Oct 94_M12_game#1_L9_explanations_Limited game#1_setup_diagram_2.png
  Due to the first rule J H, H must be scheduled for day 5 or 6, and T, a random, must be scheduled for day 2:
  
  Oct 94_M12_game#1_L9_explanations_Limited game#1_setup_diagram_3.png
  
  This template captures two solutions to the game.

Template #2: GS block scheduled for days 2-5, J scheduled for day 3

• When the GS block is scheduled for days 2-5, then from the second rule U must be scheduled for day 6. When J is scheduled for day 3, the following setup results:
  
  Oct 94_M12_game#1_L9_explanations_Limited game#1_setup_diagram_4.png
  Because from the first rule J H, H must be scheduled for day 4, and T, a random, must be scheduled for day 1:
  
  Oct 94_M12_game#1_L9_explanations_Limited game#1_setup_diagram_5.png
  This template captures one solution to the game.

Template #3: GS block scheduled for days 2-5, J scheduled for day 1

• When the GS block is scheduled for days 2-5, then from the second rule U must be scheduled for day 6. When J is scheduled for day 1, the following setup results:
  
  Oct 94_M12_game#1_L9_explanations_Limited game#1_setup_diagram_6.png
  The remaining two students—H and T—are then scheduled for days 3 and 4, not necessarily in that order:
  
  Oct 94_M12_game#1_L9_explanations_Limited game#1_setup_diagram_7.png
  This template captures two solutions to the game.

As all of the possibilities for the GS block have been explored, the five solutions above represent the only five solutions to the game.

Combining all of the information above leads to the final setup for the game:

Oct 94_M12_game#1_L9_explanations_Limited game#1_setup_diagram_8.png

Although creating this setup takes some time, with all of the possibilities in hand the questions can be destroyed at a high rate of speed.

[annabelle.swift]

I am confused about Rule 3, "Steve's lesson is exactly three days after Grace's lesson." My gut instinct in diagramming this rule is G __ __ __ S. Why is G __ __ S correct?

I ran into a similar problem on p. 3-15 of the course book where they diagrammed the rule "O is scheduled to perform two performances before P" as O__ P. I would have thought that that rule would be diagrammed as O __ __ P.

Thank you!

[Robert Carroll]

annabelle.swift,

Don't rely on gut instinct. If S is immediately after G, then S is one day later than G, right? If S is immediately after T, who is immediately after G, then S is two days later than G. If S is immediately after J, who is immediately after T, who is immediately after G, then S is three days after G. So:

GTJS

is a situation where S is three days after G. Therefore, since I was just using T and J as placeholders, and they could in theory have been anyone, let's use blanks:

G __ __ S

has S three days after G.

There is a huge difference between saying "there are three days between A and B" and saying "B is three days after A". To confirm you've got it diagrammed right, make sure what you diagram matches what the rule actually says.

Robert Carroll

[shanekoch1]

Question on Logic games if anyone can help.

Game #1 on page 9-20 ( October 1994 - LG 1) is a linear game. In class we were showed how to "split" a rule. We split in class the "G_ _ S-U" rules. on page 9-20. On page 3-26 ( December 1997 - LG 2) is also a linear game. How do you know what rule to split for these types of problems?

Thanks everyone and good luck

[Adam Tyson]

The decision to split a game into multiple templates, or even to draw out all of the possibilities, is typically going to be based on some aspect of the rules that severely restricts the initial setup. In this game, that G _ _ S - U combination is extremely limited - it can only fit in two places - and it has a big impact on the rest of the board because of the limitations on J and H. Look for combinations like that, which have a sort of domino effect on other things.

In that game from Lesson 3, there are a few limitations that might make you think about doing templates. The KJ block, for example - blocks are often a good place to start templates. But that block looks like it could go just about anywhere, and it only occasionally impacts anything else directly (like if it's in the first two spaces, P is forced to go 5th). P has only two options, 2nd or 5th, so you might look there to start templates, but it also appears to have very little impact on many other things (if P is 2, M is 1, but when P is 5 the M could be in any of the first 4 spaces).

If you are even unsure about doing templates, try finding the most powerful, restricted (or restricting) rule or combination of rules and give it a try. If you get some powerful results, fantastic, it's a templates game! If you don't, you can always stop as soon as you realize it isn't paying off and just move to the questions. As you practice this more and more you'll get better and better at spotting what makes a good templates game, and you will spend less time doing trial and error. You'll know it when you see it!