It could be “recognition” which is a more meaningful word for what is often called intuition or experience. You draw on the many patterns embedded in your mind

It could be “recognition” which is a more meaningful word for what is often called intuition or experience. You draw on the many patterns embedded in your mind from your growing experience to “recognise” the solution, and thus can’t completely explain how you recognised the solution. Analogous to the way that you recognise the face of a friend without being able to explain any set of logical steps you followed to perform that recognition. You brain matched input to a pattern.