Size Minimizing Strategies for Removing of Redundant Expressions From a Superset

A British gameshow titled “Countdown” has contestants generate mathematical expressions using arithmetic operations and a randomized set of values. The goal is to generate an expression which evaluates nearest to a target quantity given a random set of operators. To simulate contestant’s answers permutations and other strategies generate an exhaustive superset of possible solutions for the given parameters. However, the solution set is huge, filled with redundancies, and needs to be pruned. Our research identified and removed unnecessary expressions based on associativity and commutativity, and further defined a process for deleting operations that nullify a previous operation. The minimized list of expressions will be used for future research on the relative difficulty of evaluating each of these expressions for humans