Is there a word or phrase (preferably one that functions as verb) to describe what you're doing when you solve a problem mainly by trying this and that until you finally hit upon the solution when you're supposed to solve it methodically? I'm looking for a word/phrase that has a more self-deprecating tone that accentuates a lack of due method than "solved by trial and error," which to me sounds quite neutral (and in some, especially mathematical, instances of problem-solving, quite a valid approach).
As an example, when you're given a puzzle that is to be solved logically but you solve it not through brainwork but by exhausting every move possible until everything clicks into place, what might you say to disabuse someone who subsequently unduly praises you? "I _____ this puzzle. (So it's not much of an achievement, as I was supposed to solve it methodically, which I didn't do.)"