unsolved
adj.describing a mystery, crime, or problem that has not been explained or fixed yet.
adj.referring to a problem, mystery, or crime for which no solution or explanation has been found. Often used to describe cold cases or mathematical paradoxes.
“The mystery of the missing keys remains unsolved.”
“Police are still looking for new evidence in the unsolved robbery that took place last winter.”
“Despite decades of rigorous investigation and the application of modern forensic technology, the identity of the culprit in the 1974 case remains one of the city's most famous unsolved mysteries.”
Typically used attributively before a noun or predicatively after a linking verb like 'remain' or 'stay'.
Usage unsolved problem
“Keeping it out of the rover's moving parts is still an unsolved problem .”
“Both were investigating the then unsolved murders of two schoolgirls, Karen Hadaway and Nicola Fellows, in Brighton’s Wild Park in 1986.”
From un- + solved.
Etymology adapted from Wiktionary, available under CC BY-SA 4.0.