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.)"
Best Answer
The phrase brute force covers some of that, though it is not random, but instead slightly more methodical. It is like trial and error, but generally enumerating all possible solutions and then trying them one by one. For example, you want to solve an equation with two positive integer variables: you start with both set to zero, and then try out if the equation works. If not, you increment one, and repeat. Until you have found a combination that works. Or, in the words of the question: "by exhausting every move possible until everything clicks into place"
While it has a 'method', it is somewhat self-deprecating, as I solved the equation through brute force implies that you didn't do it in the mathematically best way. If has the connotations of dumb repetitive trial and error.
Most dictionaries only list "brute force" as a noun relating to strength (e.g. Merriam-Webster, dictionary.com), but Wiktionary has entries relating to the sense we want:
Therefore you could say: "I brute-forced my way through this puzzle".
(NB Wiktionary is not generally accepted as a respected dictionary, but it is often more up to date with neologisms than more respected dictionaries. Words/phrases that don't appear in respected dictionaries are less likely to be widely understood.)
(I do acknowledge the replies to my original comment, which is why I did not first post this as an answer. But re-reading the question I believe it could match the OP's intended meaning.)