Here are some synonyms for the phrase "didst the top your head," which means to think of something quickly without prior knowledge or research. Some possible options include "off the cuff," "on the spot," "impromptu," "instinctively," "spontaneously," "extemporaneously," "without preparation," and "offhand." These phrases all suggest a sense of improvisation or quick thinking, rather than relying on preexisting knowledge or careful planning. Whether you're coming up with a solution to a problem or simply answering a question, these synonyms imply a certain degree of creativity and spontaneity that can be both exciting and challenging.