The Collaborative International Dictionary of English v.0.48:

Stumper \Stump"er\, n.
   1. One who stumps.
      [1913 Webster]

   2. A boastful person. [Slang]
      [1913 Webster]

   3. A puzzling or incredible story. [Slang, U.S.]
      [1913 Webster]

WordNet (r) 3.0 (2006):

stumper
    n 1: a particularly difficult or baffling question or problem
         [syn: poser, stumper, toughie, sticker]

Moby Thesaurus II by Grady Ward, 1.0:

33 Moby Thesaurus words for "stumper":
   Chinese puzzle, baffling problem, brain twister, campaigner,
   crossword puzzle, crux, electioneer, enigma, enigmatic question,
   floorer, jigsaw puzzle, knot, knotty point, mind-boggler, mystery,
   nut to crack, perplexed question, perplexity, poser, problem,
   puzzle, puzzlement, puzzler, question, question mark,
   sixty-four dollar question, sticker, stump orator, stump speaker,
   tough proposition, vexed question, whistle-stopper, why