By now, we all know that the game section of the June 2014 LSAT was a brutal endeavor, comparable in many ways to the World Cup semi-finals between Germany and Brazil (where you were not Germany). Two weeks ago, I wrote a blog post discussing the causes (and the potential effects – positive or negative) of such curveballs on the test. This week, we get to talk about the type of game that threw every June test-taker into a fit: Pattern games.
Here’s a typical scenario of a Pattern game:
For the Fall 2014 production of Hamlet, three actors—Peter, Ramon, and Stephan—must be assigned to play the roles of Fortinbras, Gertrude, and Horatio. After the initial assignment of actors to roles, the casting director makes two reassignments so that each actor plays each role exactly once during the season. The following conditions apply:
This is a difficult Pattern game because it is built around a complex concept: the assignment (and subsequent reassignment) of actors to roles. The interaction between the actors helps establish a pattern that exists in every game solution; creating a setup that captures this information is crucial. The first important decision in this game is how to display the assignment of actors to roles. Since each of the three actor must play each role exactly once, there will be a total of three assignments of actors to roles (one initial assignment, and two subsequent reassignments). Here’s an easy way to represent this:
Now that we have a basic setup, we need to figure out the pattern in which the assignment of actors to roles will be made. The first rule stipulates that the actor initially assigned to play the role of Horatio cannot play the role of Fortinbras until after the actor initially assigned to play the role of Fortinbras has played the role of Horatio. This rule has several implications:
2. Whoever is assigned to the role of Fortinbras first must be reassigned to the role of Horatio second, and to the role of Gertrude – third:
3. This leaves us with only one possible sequence of the three actors assigned to play the role of Gertrude:
Next, consider the rule about Ramon: he cannot be assigned to play the role of Gertrude until after he has played the role of Horatio. Clearly, this means that Ramon cannot be assigned to play the role of Gertrude first, nor the role of Horatio last. Consequently, there are only four ways in which the actors can be initially assigned to each role:
Given the three patterns described above, each of these templates has only one possible solution:
By analyzing the implication of the two rules, we have established a single pattern that governs the assignment of actors to roles. Uncovering this pattern is critical to conquering a game like this. Yes, Pattern games seem daunting at first, because their setup often contains no starting point for analysis, and the rules are difficult to diagram. However, once you uncover the pattern in which the variables interact, the questions virtually solve themselves.