catch-22
catch-22 {n.}, {informal}
From Joseph Heller's novel "Catch-22", set in World War II.
1. A regulation or situation that is self-contradictory or that conflicts with another regulation. In Heller's book it referred to the regulation that flight crews must report for duty unless excused for reasons of insanity, but that any one claiming such an excuse must, by definition, be sane.
Government rules require workers to expose any wrongdoing in their office, but the Catch-22 prevents them from their doing so, because they are not allowed to disclose any information about their work.
2. A paradoxical situation.
The Catch-22 of job-hunting was that the factory wanted to hire only workers who had experience making computers but the only way to get the experience was by working at the computer factory.
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Source: A Dictionary of American Idioms