The Eternity II (E2) challenge is a well-known instance of the set of Edge Matching Puzzles (EMP), which are examples of combinatorial problem spaces of the worst-case complexity. Transformation of the domain space to consider pieces at the $$2$$ level increases the total number of elements but is shown to result in orders of magnitude smaller search spaces. While the original domain space has uniform cardinality, the transformed space exhibits statistically exploitable features. Two heuristics are proposed and compared to both the original search space and the raw transformed search space. The efficacy of the two heuristics is empirically demonstrated. An explanation of how the mapping results in an overall decrease in the number of nodes in the solution search space of the transformed problem is outlined.