Aseemingly arbitrary flash "out of the blue," through which the solution to a problem suddenly becomes apparent to you, but you do not consciously know how you "figured it out," is called priming brainstorming mental set insight

The answer would be insight. In psychology, this only happens when a solution or answer to a problem grants itself rapidly and deprived of warning. It is the sudden finding of the correct answer following improper attempts founded on trial and error.

answer; sociological imagination;

answer; interpreting someone's past consistent with present deviance;