unsolvably

Without possible solution

In a manner that cannot be solved or resolved.

A problem may be unsolvably complex, or two positions unsolvably opposed.

The word appears most often in mathematics and logic, where certain problems are proven unsolvably difficult—no algorithm can ever crack them: The equation remained unsolvably tangled.

mystery

enigmatic

Puzzling and obscure

incomprehensible · indecipherable · unanswerable · unfathomable · puzzling · mystifying · baffling · confounding · perplexing · riddling

complexity

intricate

Elaborately detailed, many parts

knotty · tangled · complicated · multifaceted · impenetrable · inscrutable · opaque · abstruse · arcane · esoteric

impossibility

unresolvable

Impossible to settle

insurmountable · insuperable · unattainable · unachievable · unworkable · unfeasible · unrealizable · irremediable · incurable · irreparable

Opposites
solvability

unsolvablytractably

In manageable manner

manageably · easily · readily · simply · straightforwardly

Family

unsolvable

Familiarity
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Used worldwide · Timeless · Abstract · Everyday, not technical · Rated G