solve
The German word 'lösen' is used in a similar way to the English word 'solve'. It is used to describe the process of finding a solution to a problem, puzzle, or equation. For example, one might say 'Ich kann das Problem nicht lösen' (I can't solve this problem) or 'Das Rätsel zu lösen war sehr schwierig' (Solving the puzzle was very difficult).
I can't solve this puzzle.
This sentence applies the verb 'lösen' in the context of puzzle-solving. The verb 'kann' means 'can', followed by 'nicht' showing the inability to perform an action.
He has to solve the problem.
This is a straightforward example where 'lösen' is used to mean 'solve' a problem. The verb 'muss' (must) denotes the urgency or requirement of action.
They could solve the mystery.
In this context, 'lösen' functions as 'to solve', specifically referring to a mystery or enigma. The use of 'könnten' (could) suggests a hypothetical situation.