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Let's suppose in a meeting, a couple of co-workes are discussiong about an issue and are going to find out a solution to it! One of them brings up a solution. The other person who's playing the leading role at the meeting raises sole objections to that solution and says:

  • Can you think of any other way?

Would it indicate the same message naturally and idiomatically to say:

  • Can you come up with any othe way?
  • Does any other way crosse your mind?
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Yes, come up with is a substitute for think of in this context. It won't work in every case, and the reverse won't always work, but here it does.

There's a slight difference. If you want people to hold something in mind - "think of a number, any number" - then you want think. Also, come up tends to imply that people are being novel or creative, or having to engage their critical faculties; think can include just remembering something.

Cross your mind is a different matter. It implies that it is involuntary, like a memory occurring to your or an idea striking you without you being an active participant. It could work, depending on what impression you want to give.

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