Setup and Rule Diagrams

[Dave Killoran]

This game is also discussed in our Podcast: LSAT Podcast Episode 70: The May 2020 LSAT-Flex Logic Games Section

Setup and Rule Diagram Explanation

This is a Grouping: Defined-Fixed, Balanced, Identify the Templates game.


The game begins by introducing two separate variable sets:

• Six Coworkers: F, G, H, J, L, M
  
  Three Successive Games: 1, 2, 3

Because the three games have sense of inherent order, you should select those as the base. And, since two coworkers play in each game, you should create two rows of spaces above each number in the base:

• ___ ___ ___
  
  
  ___ ___ ___
  1      2      3

With the base diagram in place, let's analyze the rules on a basic level. Afterwards, we will dive into some of the interactions that lead to inferences:

• Rule #1: This rule establishes that neither F nor G can participate in the first game (and thus must participate in games 2 or 3):
  
  • ___ ___ ___
    
    
    ___ ___ ___
    1      2      3
    F
    G
  Rule #2: This rule establishes that neither J nor L can participate in the third game (and thus must participate in games 1 or 2):
  
  • ___ ___ ___
    
    
    ___ ___ ___
    1      2      3
    F J
    G L
  
  Rule #3: This rule creates a vertical block with F, which must be with G or H. The nature of the game—where all 6 places are for coworkers—makes it so it does not matter if F is on the top or bottom:
  
  
  G OR   H
  F F
  
  
  Because F cannot play in game 1, this block must appear in game 2 or 3. At first glance, this may seem like just another block rule, but it's actually quite powerful since either game 2 or game 3 will always be fully occupied by one of these blocks. In fact, there are only four possible placement options (FG in 2, FH in 2, FG in 3, FH in 3), which we will later use to show four base templates.
  
  
  Rule #4: This rule creates a vertical not block for G and J. Again, the nature of the game makes it so it does not matter if G or J is on the top or bottom::
  
  J
  G

With the four rules diagrammed, you should notice that M is a random, and that the remaining five variables are linked throughout the four rules. Given that we have only 6 spaces in 3 pairs, this suggests the game is limited. And when you consider the power of third rule, you should make the decision to show four base templates based on the position of the FG/FH block:

• Template #1: FG in 2
  
  When the FG block plays in game 2, then both J and L must play in game 1 since from the second rule they cannot play in game 3. This forces the remaining two variables—H and M—to play in game 3, and results in a template with a single solution:
  
  
  • _L_ _G_ _M_
    
    
    _J_ _F_ _H_
    1      2      3
  
  
  
  Template #2: FH in 2
  
  When the FH block plays in game 2, then both J and L must play in game 1 since from the second rule they cannot play in game 3. This forces the remaining two variables—G and M—to play in game 3, and again results in a template with a single solution:
  
  
  • _L_ _H_ _M_
    
    
    _J_ _F_ _G_
    1      2      3
  
  
  Template #3: FG in 3
  
  When F and G play in game 3, there are no immediate consequences that following. All four rules are satisfied or cannot be violated, and thus H, J, L, and M are free to pair over the first two games:
  
  
  • ___ ___ _G_
    
    
    ___ ___ _F_
    1      2      3
  
  
  Template #4: FH in 3
  
  When the FH block plays in game 1, G is automatically affected since it cannot play in game 1 according to the first rule. Thus, G must play in game 2. This then affects J, because from the fourth rule G and J cannot play in the same game, and so J must play in game 1. This leaves L and M to rotate over the first two games:
  
  
  
  • _L/M_ _M/L_ _H_
    
    
    _J_           _G_ _F_
    1  2      3

And thus, with the four templates in hand, this game can be attacked very effectively and decisively. always look for the limiting options which could lead to templates!