
die Nuss
nut
A fruit with a hard shell and an edible kernel.
Für den Kuchen brauchen wir gemahlene Nüsse.
For the cake, we need ground nuts.
nut
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nut
A fruit with a hard shell and an edible kernel.
Für den Kuchen brauchen wir gemahlene Nüsse.
For the cake, we need ground nuts.

a tough nut
A difficult task, a complicated problem, or a person who is hard to convince.
Diese Matheaufgabe ist eine wirklich harte Nuss.
This math problem is a really tough nut.

socket
In tool technology, an attachment for a wrench (e.g., a ratchet) that fits over the head of a screw or a nut.
Gib mir mal die 13er-Nuss für die Radmuttern.
Pass me the 13 mm socket for the wheel nuts.

noggin / head
(colloquial) A person's head.
Pass auf, dass du dir nicht die Nuss an der tiefen Decke stößt.
Watch out that you don't bang your noggin on the low ceiling.
As a fruit, 'Nuss' (nut) is often connected with the verb 'knacken' (to crack). Common descriptive adjectives are 'gemahlen' (ground), 'gehackt' (chopped), or 'geröstet' (roasted).
Am Abend knacken wir oft Nüsse vor dem Fernseher.
In the evening, we often crack nuts in front of the TV.
The idiom 'eine harte Nuss (zu knacken)' (a tough nut to crack) describes a difficult problem or a person who is hard to deal with. The verb is usually 'sein' (to be) or 'darstellen' (to represent/pose).
Dieses Rätsel ist eine wirklich harte Nuss.
This puzzle is a really tough nut.
When 'Nuss' (socket) is used in the context of tools, cars, or repairs, it refers to the attachment for a wrench. Often a number comes before it, indicating the size.
Kannst du mir die 10er-Nuss reichen?
Can you pass me the 10 mm socket?
The use of 'Nuss' (noggin/head) for the head is purely colloquial. It is used in informal conversations among friends or family.
Achtung, der Türrahmen ist niedrig, stoß dir nicht die Nuss!
Careful, the doorframe is low; don't bang your noggin!
In the colloquial meaning 'Kopf' (head), there are fixed expressions such as 'jemandem eins auf die Nuss geben' (to hit someone on the head) or 'eins auf die Nuss bekommen' (to get hit on the head).
Wenn du nicht aufhörst, bekommst du gleich eins auf die Nuss!
If you don't stop, you're about to get one on the noggin!
head
Kopf is the neutral term for the upper part of the body. Nuss can also mean the head in colloquial speech, but it sounds joking or coarse and therefore does not fit every situation. For a factual statement, Kopf is the safe choice.

„Setz einen Helm auf, damit deine Nuss geschützt ist“, scherzte sein Freund.
“Put on a helmet so that your noggin is protected,” his friend joked.
Setz einen Helm auf, damit dein Kopf geschützt ist.
Put on a helmet so that your head is protected.