Она решила проблему другим путём.

Questions & Answers about Она решила проблему другим путём.

Why does путь end in -ём here?
The noun путь (way/path) is an anomalous masculine noun. In most cases, it declines like a feminine noun ending in a soft sign (taking ). However, in the instrumental case used here, it takes a standard masculine ending -ём, becoming путём.
Why are другой and путь in the instrumental case here?
The instrumental case is used to express the means or method by which an action is done. Just as you might say you write by means of a pen (ручкой), she solved the problem by means of a different way (другим путём).
Can путь be used for both physical paths and abstract methods?
Yes! While путь often translates to a physical route or track, it is very commonly used metaphorically to mean a way, method, or approach to doing something, exactly like the word way in English.
Why use the perfective verb решила instead of the imperfective решала?
The perfective решила emphasizes the successful result of the action. She did not just spend time trying to solve it (which would be решала); she successfully found the solution and finished the task.

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