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Insoluble (Adjective)

Admitting of no solution or explanation; "an insoluble doubt".

All adjective clusters.

The mathematician struggled with the insoluble problem for months before finally giving up.
The detective faced an insoluble mystery that left him questioning his own abilities.
The philosopher's argument centered around an insoluble paradox that challenged traditional morality.
The team of scientists were stumped by the insoluble question of how the ancient civilization had disappeared.
The couple's marital problems had become an insoluble issue that seemed impossible to resolve.