WordNet (r) 3.0 (2006):

puzzle over
    v 1: try to solve

Moby Thesaurus II by Grady Ward, 1.0:

18 Moby Thesaurus words for "puzzle over":
   agonize over, apply the mind, be at sea, be uncertain, beat about,
   doubt, feel unsure, flounder, grope, hammer at, hammer away at,
   puzzle, question, stew over, think hard, thrash about, wonder,
   wonder whether