zugestehen
to concede
To acknowledge something as true or correct; to admit it, often after initial hesitation or disagreement.
Ich muss zugestehen, dass deine Lösung besser ist als meine.
I have to concede that your solution is better than mine.

to concede / grant
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to concede
To acknowledge something as true or correct; to admit it, often after initial hesitation or disagreement.
Ich muss zugestehen, dass deine Lösung besser ist als meine.
I have to concede that your solution is better than mine.

'Zugestehen' (to concede / grant) is a separable verb. The prefix 'zu' comes at the end of the main clause, while in subordinate clauses and infinitives it remains attached to the verb.
Er gestand seinen Fehler erst nach langer Diskussion zu.
He conceded his mistake only after a long discussion.
The verb 'zugestehen' (to concede / grant) is almost always used with a person in the dative. The structure is: someone (subject) grants/concedes something (accusative) to someone (dative).
Die Firma gestand den Mitarbeitern eine Gehaltserhöhung zu.
The company granted the employees a pay raise.
In the meaning 'anerkennen' (to acknowledge), what is conceded is often a fact, a mistake, or an opinion. This is frequently expressed with a 'dass' clause or an abstract noun.
Am Ende musste sie zugestehen, dass sie sich geirrt hatte.
In the end, she had to concede that she had been mistaken.
In the meaning 'gewähren' (to grant), what is granted is often a right, an advantage, or permission. Typical nouns here are 'ein Recht' (a right), 'ein Rabatt' (a discount), 'eine Frist' (a deadline/extension), or 'ein Privileg' (a privilege).
Das Gericht gestand dem Angeklagten das Recht auf einen neuen Anwalt zu.
The court granted the defendant the right to a new lawyer.
to allow
'erlauben' and 'zugestehen' can both mean that someone is allowed to get or do something. 'erlauben' is the normal word when someone gives clear permission: parents, teachers, or bosses allow something. 'zugestehen' often sounds more formal and more often means granting someone a right, an advantage, or an extension, sometimes after discussion. In addition, 'zugestehen' can also mean acknowledging something as true. Learners may confuse the words because both have to do with approval or agreement. In everyday language, 'erlauben' is usually simpler and more natural; 'zugestehen' fits better with rights, negotiations, or concessions.

Die Firma gesteht den Mitarbeitenden wegen des Umzugs eine längere Frist zu.
Because of the move, the company grants the employees a longer deadline.
Nach dem Gespräch hat der Chef mir einen freien Tag erlaubt.
After the conversation, the boss allowed me to take a day off.