feat / trick
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trick / stunt
A particularly skillful, often surprising or difficult action that is usually performed for entertainment, for example in a circus or at a magic show.
Der Akrobat vollführte ein atemberaubendes Kunststück auf dem Hochseil.
The acrobat performed a breathtaking stunt on the high wire.
The word is made up of 'Kunst' (art/skill) and 'Stück' (piece). So it describes a 'piece' that is so difficult or impressive that it requires great skill or 'Kunst' (art/skill).
Es war ein Kunststück, alle Möbel allein in den dritten Stock zu tragen.
It was a feat to carry all the furniture up to the third floor by myself.
When referring to a performance, 'Kunststück' (trick/stunt) is often used with the verbs 'vorführen' (to perform/demonstrate), 'vollführen' (to perform), or 'zeigen' (to show).
Der Zauberer führte ein verblüffendes Kunststück mit den Karten vor.
The magician performed an astonishing card trick.
To describe a difficult achievement, the fixed structure 'Es ist ein Kunststück, ... zu ...' (It is a feat to ...) is often used. This emphasizes the difficulty of the task.
Es ist ein echtes Kunststück, bei dem Lärm konzentriert zu bleiben.
It is a real feat to stay focused with that noise.
The first meaning usually refers to a physical performance put on display (circus, sports, magic). The second meaning appreciatively describes successfully handling any difficult task, often an abstract one (organization, negotiation).
Der Hund kann einige lustige Kunststücke.
The dog can do a few funny tricks.
number
'Nummer' and 'Kunststück' can both occur in a performance, for example in a circus or a show. 'Nummer' means a whole act or program item. That can be a song, a dance, a joke, or also a 'Kunststück' (trick / stunt). 'Kunststück', on the other hand, means a particularly skillful or difficult action that someone performs. The words can be confused because a 'Kunststück' is often part of a 'Nummer'. If you mean the program item, use 'Nummer'. If you mean the special feat or trick, use 'Kunststück'.
Der Artist zeigte ein gefährliches Kunststück auf dem Seil.
The performer did a dangerous stunt on the tightrope.
Nach der Pause kam eine lustige Nummer mit zwei Clowns.
After the break, there was a funny act with two clowns.