How to Produce BlockSum Instances with Various Levels of Difficulty

We propose a framework that yields instances of certain combinatorial puzzles. To explore such a framework, we focus on certain types of puzzles that ask an assignment of numbers to the cells of an n × n grid so that it satisfies certain constraints as well as the Latin square condition, that is, each row and column contains all of the numbers in {1, 2,...,n}. Our algorithm based on the framework automatically yields puzzle instances whose difficulties to solve can be adjusted by means of puzzle inference rules built into the algorithm. Taking up BlockSum puzzle for example, we performed experiments to demonstrate that, as is expected, human solvers tend to solve puzzle instances correctly that are produced with easy inference rules, whereas they tend to fail to solve those produced with sophisticated rules