Yes, I'll explain right here !
The "principal graduate" (狀元, trạng nguyên) or "first doctoral candidate" is the title given to the scholar who achieved the highest score on highest level of the Imperial Examination. In fact, during more than a thousand years of East Asian imperial examination, there have not been many exams that applied this degree. Why so ? As a rule, each exam selects only one principal graduate and this person will almost certainly become the prime minister within a few years. However, the evaluation standards are extremely difficult, even more difficult than today's Doctor degree. It requires not only abilities and qualities but also personal history within three generations of his family. Therefore, the principal graduate appears in life only as a myth about education and morality. When it is mentioned in a literary context, we just need to understand that the character is very talented and behaves with integrity. In this story, the principal graduate degree plays a role as the result of the character's rigorous process of moral and educational training. Strange events just positively support that.
Besides, I can also help you understand that : "Poinsettia exam" (科舉) is an informal name for the imperial examination. This exam is held every 3-4 years, if the country is in chaos, we will have to wait even ten years or more. Contestants must go through three rounds like EURO and World Cup : Province, Capital and Court. Candidates are given a small travel fee by the government, and they must bring tents and beds (these items are woven from bamboo, small in size and can be folded and worn over the shoulder) to the exam venue. In the past, this was a very difficult journey, but in return, the candidates were respected by the whole society (because the majority of people were illiterate), they were exempted from paying taxes, joining the army and doing social work. However, the exam is very strict, any cheating by both examiners, candidates and guards can lead them to the guillotine. In addition, the words and meanings in the test are not allowed to refer to all royal figures, anyone who violates (accidentally or intentionally) can spend many years in prison. Because of these strict regulations, most students only hope to pass the first exam to have the opportunity to teach or become a pharmacist. There were even ridiculous cases where many candidates took the exam for decades and still could not pass. As for the final exam, the emperor directly sets the questions and supervises the exam, because this round usually only has a few dozen persons passing. The list of successful candidates will be announced on several boards placed at the royal palace gate. Of course, the highest passer will have their name listed on the golden board (I'm sorry that this detail caused you to misunderstand : Board, not Table). The golden board later is an allegory for success today, actually, in the past it was just a wooden board painted yellow. According to the law, yellow and golden are the emperor's exclusive colors, anyone else using them will be considered a violation, so being named on the golden board is a huge honor for Asian students of all time.
About the hidden meaning of the story, as I understand it, the turtle symbolizes longevity, and anyone who lives long will accumulate many valuable experiences, therefore the pearl is a symbol of wisdom. The scholar is given a gem as well as a precious book to pass the exam. Speaking of this, I think of stories "The Sleeping Beauty" and "The Devil with the Three Golden Hairs". Obviously, the maiden is very young and has little life experience, so she needs to be "opened her mouth" by a very experienced man. This is a problem of physiological psychology education. :D