(take exception to; "She challenged his claims")
(issue a challenge to; "Fischer challenged Spassky to a match")
(ask for identification; "The illegal immigrant was challenged by the border guard")
(raise a formal objection in a court of law)
(requiring full use of your abilities or resources; "ambitious schedule"; "performed the most challenging task without a mistake")
(stimulating interest or thought; "a challenging hypothesis"; "a thought-provoking book")
(disturbingly provocative; "an intriguing smile")