Put on your thinking cap to solve this puzzle.
thinking cap
idiomA metaphorical state of focused thinking or concentration, invoked to encourage problem-solving.
Origin
disputed originProbably by analogy with considering cap, which is attested from the early 17th century.
We need a better marketing strategy, so put on your thinking caps and share your ideas.
The committee donned their thinking caps to address the complex logistical challenges that threatened the success of the upcoming international conference.
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blue-sky thinking
A form of thinking that is not grounded or in touch with the realities of the present, and can thus benefit from creative imagination.
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bust a cap
To fire a weapon; to shoot with a gun.
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cap in hand
In a humble and respectful manner.
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cap it all off
To finish or complete something; to add a finishing touch.
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cap over the windmill
In a bizarre or eccentric manner.
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considering cap
An imaginary hat worn to aid careful thought or deliberation.
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feather in one's cap
An accomplishment; particularly one that is flaunted or boasted of.
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set one's cap at
To choose a man as a potential husband (for a girl).