
die Auflösung
dissolution
The formal ending or breakup of a group, an organization, or a contract.
Die Band gab nach zehn gemeinsamen Jahren ihre Auflösung bekannt.
After ten years together, the band announced its dissolution.
dissolution / solution / resolution
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dissolution
The formal ending or breakup of a group, an organization, or a contract.
Die Band gab nach zehn gemeinsamen Jahren ihre Auflösung bekannt.
After ten years together, the band announced its dissolution.

solution
The solution to a riddle, a problem, or an unclear situation. The answer or explanation that creates clarity.
Die Auflösung des Kriminalfalls überraschte selbst die erfahrenen Ermittler.
The solution to the criminal case surprised even the experienced investigators.

resolution
The image sharpness or level of detail of a digital image, a monitor, or a camera, usually measured in pixels.
Für den Druck benötigen wir das Logo in einer sehr hohen Auflösung.
For printing, we need the logo in a very high resolution.

dissolution
The chemical or physical process in which a solid substance disperses and dissolves in a liquid.
Die vollständige Auflösung der Tablette im Wasser dauert etwa eine Minute.
The complete dissolution of the tablet in the water takes about one minute.
'Auflösung' derives from the separable verb 'auflösen' (to dissolve; to resolve; to disband). It consists of 'auf-' and 'lösen' (to loosen/solve). Here, the prefix 'auf-' reinforces the idea of complete loosening or resolving—whether it is the end of a group, the solution to a riddle, or the disintegration of a substance.
Die Polizei arbeitet an der Auflösung des Falls.
The police are working on solving the case.
You can recognize this meaning in the context of organizations and social groups. Typical words in this context are 'Vertrag' (contract), 'Verein' (club/association), 'Firma' (company), 'Band' (band), or 'Parlament' (parliament).
Nach langen Diskussionen kam es zur Auflösung des Vereins.
After long discussions, the association was dissolved.
When it is about the answer to a question or a problem, you often find 'Auflösung' together with words such as 'Rätsel' (riddle), 'Fall' (case), 'Geheimnis' (secret/mystery), or 'Widerspruch' (contradiction).
Am Ende des Buches finden Sie die Auflösung des Rätsels.
At the end of the book, you will find the solution to the riddle.
In the technical field, 'Auflösung' refers to image quality. Signal words here are 'Pixel' (pixel), 'Bildschirm' (screen), 'Kamera' (camera), 'Foto' (photo), or 'Video' (video).
Mein neuer Monitor hat eine sehr gute Auflösung.
My new monitor has a very good resolution.
In a technical context, quality is often described with the adjectives 'hoch' (high) or 'niedrig' (low). You say that a device 'eine hohe Auflösung hat' (has a high resolution) or that you 'die Auflösung einstellt' (set the resolution).
Das Bild ist unscharf, weil es eine zu niedrige Auflösung hat.
The image is blurry because it has too low a resolution.
This meaning is used in a scientific or everyday context of mixing. It appears with words such as 'Tablette' (tablet), 'Pulver' (powder), 'Salz' (salt), 'Zucker' (sugar), and a liquid such as 'Wasser' (water).
Die Auflösung des Zuckers im Tee geht schneller, wenn man umrührt.
The dissolution of the sugar in the tea is faster if you stir it.
solution
Lösung is primarily the answer you are looking for to a riddle or a case. Auflösung additionally clarifies the connections and shows how the riddle is explained. Lösung fits a brief answer, while Auflösung is more appropriate for the final revelation together with an explanation.

In der Auflösung wird erklärt, welche Spuren den Gärtner verraten haben.
The explanation reveals which clues gave the gardener away.
Die Lösung des Rätsels lautet: Der Gärtner war der Täter.
The solution to the riddle is: The gardener was the culprit.