das Puzzle
puzzle
A patience game in which a picture cut into many small pieces has to be put back together.
An regnerischen Tagen legen wir gerne ein Puzzle mit 1000 Teilen.
On rainy days, we like to do a 1,000-piece puzzle.

puzzle
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puzzle
A patience game in which a picture cut into many small pieces has to be put back together.
An regnerischen Tagen legen wir gerne ein Puzzle mit 1000 Teilen.
On rainy days, we like to do a 1,000-piece puzzle.

When putting together a picture from small pieces, German uses the fixed expression 'ein Puzzle legen' (to do a puzzle). The verb 'legen' (to lay/place) is typical here.
Am Wochenende haben wir den ganzen Nachmittag ein Puzzle gelegt.
At the weekend, we spent the whole afternoon doing a puzzle.
The individual elements of a puzzle are called 'die Teile' (pieces). People often refer to the number, for example 'ein Puzzle mit 500 Teilen' (a 500-piece puzzle) or 'das letzte Teil suchen' (to look for the last piece).
Mir fehlt nur noch ein Teil, dann ist das Puzzle fertig.
I'm only missing one piece, then the puzzle is finished.
In the figurative sense, 'Puzzle' describes a complex problem or mystery. Here, it is about fitting information or clues together like puzzle pieces to form a complete picture.
Für die Polizei war der Fall ein schwieriges Puzzle.
For the police, the case was a difficult puzzle.
Especially in the figurative meaning, the verbs 'zusammensetzen' (to put together) or 'zusammenfügen' (to fit together) are often used. You put the 'Teile' (pieces) or 'Hinweise' (clues) together into a whole.
Der Detektiv fügte die verschiedenen Spuren zu einem Puzzle zusammen.
The detective fitted the various clues together into a puzzle.
problem
'das Problem' and 'das Puzzle' can both mean a difficult task. 'das Problem' is general: something is difficult and needs a solution. 'das Puzzle' is used figuratively when a solution has to be put together from many individual pieces of information or parts. It often sounds mysterious and emphasizes the many small pieces. Learners may confuse the words because a puzzle can also be a problem. For normal difficulties, it is better to say 'Problem'; for a complex search for connections, 'Puzzle' works well.

Nach der Arbeit wurde die Planung der Reise für ihn zu einem schwierigen Puzzle.
After work, planning the trip became a difficult puzzle for him.
Am Abend hat sie das Problem mit dem Antrag endlich verstanden.
In the evening, she finally understood the problem with the application.