Linear Setup Practice Drill #11, First 2 Rules

[Dave Killoran]

Earlier today we received the following question:

Hi, I have a question about a problem from your Power Score Logic Games Bible. I was going over linear practice games and cannot figure out the books explanation of question 11 on page 112 in the 2017 edition of the book. The rules for the question state Either T or V must be picked up fifth Either V or Z must be picked up third Does that mean that either T or V can only be placed in the fifth place? And the same can V or Z on be go in the third place? I'm trying to figure out if these to rules are absolutes or if they are conditional. -J

Hi J,

Thanks so much for the question! The first two rules in this game scenario are ones you will see with high frequency, so it’s good to get clarification now, before the actual test. When a rule states something in this form (“this or that must be picked for certain space”), it means that in every solution of the game, one of those two variables will appear in the designated spot. The variable that does not appear in the spot can then go anywhere else (as long as it conforms to the other rules).

So, referring specifically to this example, let’s look at the first rule and see how that works:


“Either T or V must be picked up fifth.”


Thus, in every solution to this game, exactly one of T or V will be in the fifth position. So, in all of the solutions where T is fifth, then in this game V will appear elsewhere. And, when V is fifth, then T will appear elsewhere. No other variable can go fifth.

You made an interesting comment at the end that I wanted to address, namely that you were "trying to figure out if these to rules are absolutes or if they are conditional." They are actually both That's quite confusing, so let me explain. In abstract terms, the rule itself ("either/or") is in conditional form (but it does use an absolute ("must")), and then because of other information we have about the game (namely that each variable fills a single space, and that every space is filled by a single variable, and that all spaces and variables must filled or used), we can draw an absolute conclusion that the 5th space is always filled by exactly one of the two named variables. So, the conditional relationship in each rule is already quite limiting, and reduces down to just two possible outcomes, which is why we diagram with the "T/V" dual-option above the fifth space.

Note that you can diagram each rule separately in several different forms. Each of the following is correct, and it's up to you as to which you'd prefer:

• Representing each by focusing on the variables or the space:
  
  
  T/V 5
  
  5 T/V
  
  
  Or, you could combine those two representations into one:
  
  
  T/V 5
  
  
  Alternately, you could focus on the "either/or:"
  
  
  T5 V5
  
  V5 T5
  
  
  Or last, you could diagram the dual-options right on the diagram, which is what I chose to do.

Please let me know if that helps out. Thanks!