I normally hate overused catchphrases in English, like "paradigm shift" and "out of the box thinking". But I was recently chatting (in Chinese) with a friend about an earlier situation in which someone had used "out of the box thinking". (The phrase was used by my daughter's teacher). I was at a loss to translate the idiom. Is there some appropriate 成语? A 成语 would be especially nice because the idiom in English is anecdotally thought to derive from a story of management consultants. In addition, like many 成语, the meaning is really non-obvious from the words alone.
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别出心裁 also known as 别出新裁 is one 成语 that fits the bill:
"别出" means out of the box
I think 天马行空 is the one.
but use it carefully,天马行空 does not always commendatory
"Thinking outside the box" can be translated to 奇思妙想, which is a 成语 and also a noun.
Your idea is great! That is really thinking outside the box. 你这主意太棒了！可真是奇思妙想。
"Think outside the box" can be translated to 打破常规，开动思想, or 打破常规思维, which both are common expressions, but not 成语.
You need to think outside the box to sovle this problem. 要解决这个问题，你得打破常规，开动思想。 要解决这个问题，你需要打破常规思维。
It is interesting that there are a lot 4-character non-成语 common expressions in Chinese, for example: 大步前进，树叶茂密，小河流水，奋勇向前，又大又圆，越越来好，etc. I think 4-character expressions sound more poetic and more pleasant to the ear.