Like most things in programming, there is no "only way" to solve something, and certainly no one language (or DSL) to solve anything. You could solve it programmatically in C writing your own backtracker or state enumerator and a function (or block of code if you are like an old coworker that liked 10k SLOC C functions).

miniKanren, Prolog, and others let you write the rules more concisely (almost always) and clearly (most of the time, not everyone will write clear code and clarity is subjective) than that, though.