How to Recognize Limited Solution Set Games

    LSAT Prep

    treeIn last night's Live Online LSAT class, I asked my (awesome!) group for some input about what they would like to see in my post today. The strongest response I got was to write about how to know when to diagram, as part of your initial setup, the limited solutions possible in a logic game with a highly restrictive rule set. Diagramming the limited solutions at the start of a game can empower you, enabling you to dominate the game with increased speed and accuracy. But only if the possible solutions are, in fact, atypically limited. Knowing when this investment in time is appropriate is the first step toward using the technique in a way that helps, rather than hurts, your score.

    The LSAT Logic Games section tests our ability to deduce connections between and among rules. In some games, the rules are so restrictive that only a limited number of solutions remain available. Another way of saying this is that from of all the possible ways in which the variables, without restrictions, could have interacted there are only a few paths remaining.

    The photograph of a tree I've used in this post may help you visualize this process. Think of this tree, with all of its branches, as a logic game. If we take the tree as is, without placing any restrictions on how the branches may emerge, we wind up with many different paths from the trunk outward. However, when we start restricting the branches, we cut off some of those possibilities, and may even wind up with just one or two limbs coming off of the trunk, perhaps with only two or three branches emerging from each. 

    To recognize when a game has only a limited number of solutions, look for a combination of rules that work together to funnel the possible solutions into just a few paths. You will want more than a single rule, even a powerfully restrictive one, to be confident enough to commit to diagramming out the options.

    For example, look for rules that establish a Numerical Distribution.  Pay extra attention to games with no random variables. Remember that real estate is scarce in the games, so rules that form a large block of variables will create reduced spacing options and can even create a duality for a variable or a space. For example, a large block in a linear setup game could so reduce the spacing options that the block's first variable must appear in either first or second position. This is an example of a Power Block.

    Similar scenarios are available in grouping games as well. For example, in a two-group game, if the rules tell you that two variables cannot be in the same group, then reserve a space in both groups so that you can visualize the effect of that restriction. Doing so will reduce the spacing options and might clue you in to the possibility of limited solutions. This process of using uncertainty to generate inferences is an example of our Hurdling the Uncertainty technique.

    These are just a few examples. Their unifying theme is to identify a powerful combination of rules that permits deductive inferences related to limited space, duality, and numerical limitations.  If while applying the rules you find yourself in one or more either/or situations regarding spaces or variables, pause to consider whether the effect of the rule is localized to that space or variable, or whether the rules in combination will permit broader inferences. To be safe, begin with your basic template and only begin diagramming additional possibilities when you can see that there are just two or three paths the game can take.

    While diagramming limited solutions is a time-intensive task, when done properly the return on this investment in time is increased speed and accuracy. If you start down the templating path and discover there are more possibilites than you originially thought, don't panic and don't beat yourself up. Keep your head, take the information you've learned about the game, and move on to the questions, bearing in mind that the options you've diagrammed are not the only ones.

    With practice, you can learn to not only identify limited solution opportunities, but also to diagram the possibilities efficiently and to use your diagrams effectively. In combination, these three skills can earn you a powerful competetive advantage over the competition. 


    Image Attribution: Tree of Life, by Flickr member auntjojo