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When it's a good consultant, yes. I have advised many companies on how to solve a problem which the company was not able to solve by itself. In fact it is my speciality.*
Successful corporates tend to be good at solving common or familiar problems, but can have trouble with situations which the company has not faced before.
* If your company, or somebody you know, is struggling with a really tricky problem please get in touch. I'd be glad to help.