Evolving Number Sentence Morphing Puzzles

Number sentence morphing is an example of a type of edit puzzle. Edit puzzles choose a class of objects and a collection of editing operators. The goal of the puzzle is to change an initial configuration into a final one, using the edit operations, with the intermediate objects remaining within the selected class of of objects. Changing one English word into another by changing single letters, with all the intermediate steps also consisting of English words, is a typical example of an edit game. A number sentence is a well formed mathematical object, which can be used to generate a type of edit puzzle called Number sentence morphing. This puzzle has the player transform a false number sentence into a true one by removing and replacing symbols from a number sentence while leaving the sentence well formed. This type of puzzle is intended for teaching students the notion of well-formation in a game setting as well as providing practice with basic arithmetic. An evolutionary algorithm is used to construct number sentence morphing puzzles while certifying that they can be solved and requiring a minimal number of steps in a solution. The search for number sentences is template driven so particular forms of sentences are searched for in their own sets of runs. An unexpected outcome of this study is that the search landscapes for different templates are very different.