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unsolvability has 1 distinct synonym spread across 1 of its 1 sense. 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. Its one recorded opposite is solvability.
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.
the property (of a problem or difficulty) that makes it impossible to solve
Synonyms, antonyms and the broader and narrower relations for unsolvability come from Princeton University’s WordNet. Full sources and licences.