Human brain vs computer

I am looking for a problem that can not be solved by computer but can be solved by human while computer can verify if the answer is correct or not. In fact what is the question in my head is that is there a way to clearly show the smartness in human brain compared to huge computation power of the processors.

This is indeed, an open problem. The Church-Turing thesis, in its most popular conception, states that anything that can be computed by a human with a pen and paper can be computed by a Turing Machine. We have not yet been able to prove or disprove this thesis, therefore no one can tell you such a problem.

StackExchange Computer Science Q#116443, answer score: 2