Have (one's) thinking cap on phrase
The term thinking cap denotes an imaginary cap humorously said to be worn in order to facilitate thinking.
To be using or be prepared to use one's intellectual capacity to the greatest extent.
I can see you guys all have your thinking cap on, so let's get started with the first question.
The moment John stayed silent and closed his eyes, I knew he had his thinking cap on.
This phrase is usually used in simple present tense.
This phrase dates from 1821.