While I produced a formal proof for all possible solution (using techniques I learned at university), others "solved" it much quicker with a a mix of brute force and random generators.

Google or whoever set the challenge made sure that "calculators are allowed", for a reason I suppose. That's my fixation with Optimisation as a social goal (Re: Curious about Perl's strengths in 2018).

I am also a self-taught programmer. Never had any formal training bar some Pascal. And at the same age as you (14), I got into my first "birthday paradox" gaffe by trying to fit 3**13 combinations of football matches into my ZX-Spectrum's 48K(bytes), too cocky by my previous success in creating an iterator for listing them. "Out of Memory" it said and I thought I reached the Edge of the Universe. But it was a lesson since.

I am not sure what's best: to make the mistakes as early or as late in life. Next time I am around I will make them as late and document the outcome. But I am not sure 42 will still be the answer...