adjective

insoluble

Impossible or extremely difficult to solve.

The mystery seems insoluble because none of the witnesses agree.

Etymology

Latin solvere means to loosen or resolve. With the negative prefix, insoluble names something that cannot be resolved, including a problem resistant to solution.

More examples

We need more information before declaring the problem insoluble.
The disagreement feels insoluble, but both sides keep talking.
What looks like an insoluble puzzle becomes easy with one clue.

Forms

insoluble

insolubility noun — The state of being impossible to solve.

Similar words

unsolvable: Directly states that no solution can be found.
intractable: Emphasizes resistance to management or improvement, not necessarily solution.