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.

'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.
answer
'die Antwort' and 'die Auflösung' can both give a solution or explanation. 'die Antwort' is very general: to a question, a message, or also to a problem. 'die Auflösung' is used more when something was previously unclear, suspenseful, or puzzling and clarity emerges at the end. In a normal conversation, 'Antwort' sounds more natural. For a riddle, a crime story, or an unclear situation, 'Auflösung' is more precise.

Nach dem Spiel liest du die Auflösung des Rätsels vor.
After the game, you read out the solution to the riddle.
Für die Familie ist die Antwort auf die Reisefrage noch offen.
For the family, the answer to the travel question is still open.