Word or phrase that means to solve a problem mainly via trial and error

Question

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.)"

Answer 1

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:

Noun

2. (computer science) A method of computation wherein the computer is let to try all permutations of a problem until one is found that provides a solution, in contrast to the implementation of a more intelligent algorithm.

Verb

1. (transitive) To solve (a computational problem) by brute force methods.

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.)

Answer 2

If you want complete absence of methodology, one could find the solution by throwing everything against the wall and seeing what sticks (although brute force is more applicable to your puzzle example -- where there is a kind of methodology at work: a dumb brute force method as opposed to a smarter method that brings logic to bear.)

Answer 3

stumble through something TFD

to get through a sequence of something awkwardly and falteringly.

I stumbled through the completion of the puzzle.

Answer 4

Empirically

As in ‘ I solved the problem empirically’ - it means ‘by trial and error’ or experimentation.

Definition, The Free Dictionary:

Relying on or derived from observation or experiment: empirical results that supported the hypothesis.

https://www.thefreedictionary.com/empirically

A doctor said this to me once - that we could ‘treat the problem empirically’. I didn’t know what he meant at first, but he meant - ‘take the medicine anyway, even though we’re not completely sure what the problem is, then we’ll see what happens, and decide next steps according to the results.’

Answer 5

'by dint of ...' is a term that means what you mean, somewhat. 'By dint of her efforts she finally achieved her goal'.

Answer 6

The idiom “by the grace of god” may fit.

While this has religious reference, it is often used idiomatically. It implies that the success occurred not by purpose, but by happenstance or luck.

“I solved that problem by the grace of God. I don’t know how it works and I couldn’t do it again if I tried.”

“I passed that test by the grace of God. I guessed on all the multiple choice questions.”

Answer 7

Consider fluke:

Achieve (something) by luck rather than skill.
_{Oxford Living Dictionaries}

Answer 8

Even more pointed, you could say “they succeeded, despite their best efforts”.

This usually implies that everything actively done by the actor was wrong, but they somehow arrived at the correct answer.

“He won the election, despite his best efforts.”

“I didn’t study at all. I passed that test, despite my best efforts”

Answer 9

heuristic: involving or serving as an aid to learning, discovery, or problem-solving by experimental and especially trial-and-error methods. https://www.merriam-webster.com/dictionary/heuristic

Answer 10

From a rather limited domain of usage into the mainstream:
Voodoo programming (WP)

Voodoo programming refers to the practice of getting a program to produce desired output by using guesses, trial-and-error, cookbooks, copy-pasting from online resources, or similar techniques without truly understanding the underlying problem. (emphasis mine)

could be a possible candidate.

"I solved this puzzle by voodoo programming!"

Note the "solved" because you have still technically solved the puzzle.

Use case:

There has been much trial and error with many, many different amps as well as guitar effects. Dissatisfaction led me to start modifying amps to get the tones I was looking for. Eventually I started designing my own circuits and Voodoo Amps was born. (emphasis mine)

Answer 11

by hook or by crook is a nice one