Synonyms for Solve (same or very similar meaning)
WordNet sense 1 (settle, as of a debt):
clear
WordNet sense 2 (find the solution):
resolve, resolve
WordNet sense 3 (find the solution to (a problem or question) or understand the meaning of):
lick, work, work out, figure out, puzzle out
From the ODE community, based on WordNet
add/edit