The Collaborative International Dictionary of English v.0.48:

Challenge \Chal"lenge\, v. t. [imp. & p. p. Challenged; p. pr.
   & vb. n. Challenging.] [OE. chalengen to accuse, claim, OF.
   chalengier, chalongier, to claim, accuse, dispute, fr. L.
   calumniar to attack with false accusations. See Challenge,
   n., and cf. Calumniate.]
   1. To call to a contest of any kind; to call to answer; to
      defy.
      [1913 Webster]

            I challenge any man to make any pretense to power by
            right of fatherhood.                  --Locke.
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   2. To call, invite, or summon to answer for an offense by
      personal combat.
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            By this I challenge him to single fight. --Shak.
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   3. To claim as due; to demand as a right.
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            Challenge better terms.               --Addison.
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   4. To censure; to blame. [Obs.]
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            He complained of the emperors . . . and challenged
            them for that he had no greater revenues . . . from
            them.                                 --Holland.
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   5. (Mil.) To question or demand the countersign from (one who
      attempts to pass the lines); as, the sentinel challenged
      us, with "Who comes there?"
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   6. To take exception to; question; as, to challenge the
      accuracy of a statement or of a quotation.
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   7. (Law) To object to or take exception to, as to a juror, or
      member of a court.
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   8. To object to the reception of the vote of, as on the
      ground that the person in not qualified as a voter. [U.
      S.]
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   To challenge to the array, favor, polls. See under
      Challenge, n.
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The Collaborative International Dictionary of English v.0.48:

challenging \challenging\ adj.
   1. requiring full use of one's abilities or resources; as,
      challenging task.

   Syn: ambitious, demanding.
        [WordNet 1.5]

   2. disposed to or engaged in defiance of established
      authority.

   Syn: insubordinate, resistant, resistive.
        [WordNet 1.5]

WordNet (r) 3.0 (2006):

challenging
    adj 1: requiring full use of your abilities or resources;
           "ambitious schedule"; "performed the most challenging
           task without a mistake" [syn: ambitious, challenging]
    2: stimulating interest or thought; "a challenging hypothesis";
       "a thought-provoking book" [syn: challenging, thought-
       provoking]
    3: disturbingly provocative; "an intriguing smile" [syn:
       challenging, intriguing]

Moby Thesaurus II by Grady Ward, 1.0:

39 Moby Thesaurus words for "challenging":
   alluring, arrogant, audacious, bold, brash, brassy, brazen,
   bumptious, cheeky, cocky, contemptuous, daring, defiant, defying,
   derisive, disdainful, disregardful, encouraging, energizing,
   exciting, galvanic, galvanizing, greatly daring, impertinent,
   impudent, insolent, inviting, pert, piquant, prompting,
   provocative, provoking, regardless of consequences, rousing, saucy,
   stimulant, stimulating, stimulative, stirring