We can also see three major clusters on the left-hand side of Figure 9(c). These clusters are further away from the goal than the start state, indicating that the players moved away from the solution to reach them. A fourth major cluster can be seen in the lower right, on the path to the goal. An example of a state from each of these clusters can be seen in Figure 10. Clusters 10(a), 10(b), and 10(d) represent logical hypotheses. Of these hypotheses, 10(a) and 10(b) are incorrect, but 10(d) is correct and is along the most commonly taken path to the goal. Cluster 10(c), on the other hand, is a collection of states where pieces have been placed with no effect on the lasers. Even in this more complex example, our visualization is able to draw the user's attention to these clusters, providing clues as to why players seemed to struggle with this level. Furthermore, this example shows how our tool can be used to discover common player strategies.