ungelöst
unresolved
Refers to a problem, puzzle, or question for which no answer or solution has yet been found.
Der Kriminalfall aus dem Jahr 1995 ist bis heute ungelöst.
The criminal case from 1995 remains unresolved to this day.

unresolved / undissolved
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unresolved
Refers to a problem, puzzle, or question for which no answer or solution has yet been found.
Der Kriminalfall aus dem Jahr 1995 ist bis heute ungelöst.
The criminal case from 1995 remains unresolved to this day.

The word consists of the prefix 'un-' (not) and 'gelöst' (solved/dissolved), the past participle of 'lösen' (to solve/dissolve). So it literally means 'not solved' or 'not dissolved'. This fits both a problem that has not been solved and a substance that has not dissolved in a liquid.
Viele mathematische Probleme der Antike sind heute noch ungelöst.
Many mathematical problems from antiquity are still unresolved today.
'Ungelöst' (unresolved/undissolved) belongs to the word family of 'lösen' (to solve/dissolve) and 'die Lösung' (the solution). The verb 'lösen' can mean both 'ein Problem lösen' (to solve a problem) and 'Pulver in Wasser lösen' (to dissolve powder in water), which directly explains the two meanings of 'ungelöst'.
Für dieses Rätsel gibt es keine einfache Lösung.
There is no simple solution to this puzzle.
You can tell from the context whether a problem or a substance is meant. If people are talking about abstract things like a case, a puzzle, or a conflict, the first meaning is intended. In a chemical or physical context, it refers to a substance that has not dissolved.
Der Konflikt zwischen den beiden Ländern blieb ungelöst.
The conflict between the two countries remained unresolved.
In the meaning of 'not clarified', 'ungelöst' (unresolved) is very often combined with nouns such as 'Fall' (case), 'Problem' (problem), 'Rätsel' (puzzle/mystery), or 'Frage' (question).
Die Frage nach dem Sinn des Lebens ist für viele Menschen ungelöst.
The question of the meaning of life remains unresolved for many people.
This meaning of 'ungelöst' (undissolved) is used almost exclusively in the technical language of chemistry or physics to describe the state of a substance in a liquid.
Die Analyse zeigte ungelöste Partikel in der Flüssigkeit.
The analysis showed undissolved particles in the liquid.
open
'offen' and 'ungelöst' can both say that there is not yet a clear answer or solution. 'offen' is more general and fits questions, decisions, or items on a list. 'ungelöst' is used more for problems, puzzles, cases, or difficult questions for which a solution is being actively sought. The words can be confused because both refer to something that is not yet finished. As a practical rule: a decision is often 'offen', while a problem or puzzle is more likely to be 'ungelöst'.

Wegen eines Fehlers im System bleibt das Problem vorerst ungelöst.
Because of an error in the system, the problem remains unresolved for now.
Der Termin für die Untersuchung ist noch offen.
The date for the examination is still open.