challenge has 3 distinct synonyms spread across 2 of its 9 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
a demanding or stimulating situation
“they reacted irrationally to the challenge of Russian power”
a call to engage in a contest or fight
questioning a statement and demanding an explanation
“his challenge of the assumption that Japan is still our enemy”
a formal objection to the selection of a particular person as a juror
a demand by a sentry for a password or identification
ask for identification
“The illegal immigrant was challenged by the border guard”
Synonyms, antonyms and the broader and narrower relations for challenge come from Princeton University’s WordNet. Full sources and licences.