thinking cap

a state of mind marked by reflection or concentration: If we put on our thinking caps, we may come up with the answer.

1870–75 Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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Example sentences
So put on your thinking cap, fire up your video camera, and come up with a
  great experiment.
Put on your thinking cap and make a wise decision that will have a positive
  long-range effect on your piggy bank.
If you want to do something in your own special way, put on your creative
  thinking cap.
Put on your thinking cap, engage your brain and plug into your imagination.
Idioms & Phrases
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