brains / little head
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brains
Refers figuratively to intelligence, reason, or cleverness. It is often used in the expression 'Köpfchen haben' (to have brains).
Um dieses Rätsel zu lösen, braucht man ein gutes Köpfchen.
To solve this puzzle, you need brains.
'Köpfchen' (little head / brains) is the diminutive form of 'der Kopf' (the head). The ending '-chen' makes the noun neuter ('das') and expresses that something is small or cute. All nouns with '-chen' are neuter.
Die Katze rieb ihr Köpfchen an meinem Bein.
The cat rubbed its little head against my leg.
In the figurative sense, the most common use is the fixed expression 'Köpfchen haben' (to have brains). It means that someone is intelligent or clever and can make connections quickly.
Sie hat wirklich Köpfchen, sie hat die Aufgabe als Erste gelöst.
She really has brains; she was the first to solve the task.
The figurative meaning 'Verstand' (intelligence / reason) is often used without an article, as in 'Köpfchen benutzen' (to use one's brains). When it refers to a real, small head, there is usually an article or possessive pronoun before it, for example 'das Köpfchen des Vogels' (the bird's little head).
Für dieses Spiel braucht man vor allem Köpfchen.
For this game, you mainly need brains.
head
'der Kopf' and 'das Köpfchen' can both refer to the body part or to the mind. 'Kopf' is the normal, neutral word. It is used in everyday language for the body part and also figuratively for thinking or the mind. 'Köpfchen' is the diminutive form and often sounds affectionate or playful. For a small head, for example a baby's, 'Köpfchen' fits. In the expression 'Köpfchen haben' (to have brains), it means cleverness. Learners may confuse the words because both have to do with the head and thinking. As a practical rule: use 'Kopf' for normal situations, and use 'Köpfchen' for something small or affectionate, or for the fixed expression 'Köpfchen haben'.
Bei diesem Rätsel braucht man wirklich Köpfchen.
You really need brains for this puzzle.
Nach dem langen Tag tut mir der Kopf weh.
After the long day, my head hurts.