Using just a tiny hint as a starting thread, I found the right answer.
Literal
Slight hint [object-を] thread-opening [to-にして], correct answer [object-を] found.
糸口 ('thread opening, the end of a thread') is a metaphor for a clue or starting point — the place where you grab the thread and start unraveling. わずかな ('slight, meager') emphasizes how little the hint was. 糸口にする ('to use as a starting point') takes the metaphor and makes it a verb phrase. The sentence celebrates clever problem-solving.