die Andeutung
hint
An indirect clue or hidden remark that suggests something without saying it directly.
Er machte nur vage Andeutungen über seine Zukunftspläne.
He made only vague hints about his plans for the future.

hint / trace
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hint
An indirect clue or hidden remark that suggests something without saying it directly.
Er machte nur vage Andeutungen über seine Zukunftspläne.
He made only vague hints about his plans for the future.

'Die Andeutung' (hint) is the noun formed from the verb 'andeuten' (to hint at). 'Andeuten' means to say or show something indirectly. If you know the verb, you will also understand the noun.
Er deutete an, dass er bald kündigen möchte.
He hinted that he would like to resign soon.
The typical verb used with 'Andeutung' (hint) is 'machen' (to make). You 'macht eine Andeutung' (make a hint). It is often described more specifically with adjectives such as 'vage' (vague), 'leise' (subtle), or 'vorsichtig' (cautious).
Sie machte nur eine vage Andeutung, dass sie Probleme hat.
She made only a vague hint that she was having problems.
In the meaning 'schwache Spur' (faint trace), 'Andeutung' is almost always used with the preposition 'von' (of). The structure is: 'eine Andeutung von + noun' (a trace of + noun).
Der Himmel zeigte nur eine Andeutung von Morgenrot.
The sky showed only a trace of dawn red.
hint / notice
'der Hinweis' and 'die Andeutung' can both draw attention to something. However, a 'Hinweis' is usually more direct and helpful: it says or shows relatively clearly what you should pay attention to. An 'Andeutung' is indirect. You do not say something openly, but only let it be understood. That is why an 'Andeutung' can also feel uncertain or hidden. Learners may confuse the words because an 'Andeutung' can be a kind of 'Hinweis'. The difference is: a 'Hinweis' gives clear help, while an 'Andeutung' often has to be understood between the lines.

Mit einer kurzen Andeutung machte sie klar, dass sie morgen nicht kommen kann.
With a brief hint, she made it clear that she cannot come tomorrow.
Frau Fischer gab uns im Restaurant den Hinweis, dass die Küche gleich schließt.
At the restaurant, Ms. Fischer told us that the kitchen was about to close.