TL;DR: Khổng Minh Thần Toán is a divination card book circulated in Vietnam with 384 cards, each matching one of 64 hexagrams combined with one of six moving lines. Each card holds a Hán Việt verse, a Vietnamese translation, a commentary by Thông Huyền Lão Nhân, and a ready-made reading. The casting method uses three number groups divided by 8, 8, and 6 according to Tiên Thiên numbers to find the upper trigram, lower trigram, and moving line, then looks up the matching card, sharing its calculation core with Mai Hoa Dịch Số. The name linked to Gia Cát Lượng is folk tradition and some libraries record it as legend, while official histories of him mention no divination book; his image as an all-knowing strategist comes largely from the 14th-century novel Tam Quốc diễn nghĩa.
What is the Khổng Minh Thần Toán?
The Khổng Minh Thần Toán is a divination book used to look up interpretations when casting a hexagram, widely circulated in Vietnam with 384 cards. The number 384 is not arbitrary: it equals 64 hexagrams multiplied by 6 moving lines, meaning each hexagram in the Bát Quái (the Eight Trigrams) has six possible moving lines, and each such combination of hexagram and line is assigned its own card. The querent casts and obtains a combination, then looks up exactly that card to read the verse, the translation, the commentary and the interpretation.
The structure of a card in the currently circulating edition usually has four parts. The first part is the card number and the hexagram name together with a classification such as Thượng Thượng (highest grade), Trung Trung (middle grade) or Hạ Hạ (lowest grade), along with the moving line. The second part is the verse in Chinese characters with Hán Việt romanisation. The third part is the translation of the verse's meaning into Vietnamese. The fourth part is the commentary by Thông Huyền Lão Nhân and the detailed interpretation for the querent. For example, on the card numbered 336, corresponding to the hexagram Sơn Trạch Tổn with the Sixth line moving, the Hán Việt verse speaks of a small boat that has crossed wind and waves and now docks safely, and the interpretation section ranks this card as good, holding that all matters will flow smoothly, that lost objects will be found, that plans should be pursued, and that business will be profitable. Compare card 342, corresponding to the hexagram Bát Thuần Khôn with the Sixth line moving, where the verse instead speaks of bad fortune, calamity and prayers that receive no support, and the interpretation ranks it as not good and advises the querent to halt every pursuit and wait out the inauspicious period.
What is notable is that the cards in the book do not merely describe good or bad fortune in general terms but are tied to each specific kind of matter. For the same card, the book may set out separate meanings for seeking wealth, for travelling far, for litigation, for marriage. This manner of presentation makes the Khổng Minh Thần Toán closer to an applied lookup table than to a purely philosophical work.
How to set up a Khổng Minh Thần Toán hexagram using three groups of numbers
The method of setting up a hexagram in the edition circulating in Vietnam uses three groups of numbers that the querent chooses or thinks up. The first group is divided by 8, and the remainder is taken as the Upper hexagram. The second group is divided by 8, and the remainder is taken as the Lower hexagram. The third group is divided by 6, and the remainder is taken as the moving line. The remainder is matched against the Tiên Thiên Bát Quái (Earlier Heaven Eight Trigrams) sequence, in which Càn is 1, Đoài is 2, Ly is 3, Chấn is 4, Tốn is 5, Khảm is 6, Cấn is 7, Khôn is 8. For the moving line, dividing by 6 gives a remainder running from 1 to 6, and when the division comes out even, 6 is taken.
The Khổng Minh Thần Toán book gives the example of the three number groups 75, 47 and 58. The first group, 75, divided by 8 leaves a remainder of 3, corresponding to the hexagram Ly as the Upper hexagram. The second group, 47, divided by 8 leaves a remainder of 7, corresponding to the hexagram Cấn as the Lower hexagram. The third group, 58, divided by 6 leaves a remainder of 4, corresponding to the fourth moving line. Combining the Upper hexagram Ly with the Lower hexagram Cấn gives the hexagram Hỏa Sơn Lữ, with the fourth line moving, and one then consults the table to find the corresponding card. It should be noted that in the book the printed example states the sixth moving line in its description line, but the calculated result is again line 4; this is a printing or editing error in the circulating edition, and the reader should trust the calculation.
This mechanism resembles the number method of Mai Hoa Dịch Số in that both use division with remainders to derive hexagrams and lines, and both rely on the Tiên Thiên Bát Quái numbers. Therefore a core hexagram-casting engine following Mai Hoa, such as the LapQueMaiHoa engine, can be used to calculate the Upper hexagram, the Lower hexagram and the moving line for the Khổng Minh Thần Toán, after which one need only consult the table of 384 cards to obtain the result. The difference lies in the fact that Mai Hoa also uses external correspondences, time and objects to interpret more deeply, whereas the Khổng Minh Thần Toán mainly stops at looking up the card.
| Step | Action | Calculation | Example result |
|---|---|---|---|
| 1 | Take the first number group | Divide by 8, take the remainder, match to the Tiên Thiên numbers | 75 divided by 8 leaves 3, corresponding to Ly |
| 2 | Take the second number group | Divide by 8, take the remainder, match to the Tiên Thiên numbers | 47 divided by 8 leaves 7, corresponding to Cấn |
| 3 | Take the third number group | Divide by 6, take the remainder, a remainder of 0 counts as 6 | 58 divided by 6 leaves 4, fourth moving line |
| 4 | Combine the Upper and Lower hexagrams | Ly above, Cấn below | Hexagram Hỏa Sơn Lữ |
| 5 | Consult the table of 384 cards | Find the exact hexagram and moving line | Card Hỏa Sơn Lữ with the fourth line moving |
| 6 | Read the card | Verse, translation, commentary, interpretation | Interpretation according to the card's content |
Where do the edition circulating in Vietnam and the edition Moore describes differ?
They differ in how the hexagram is set up. The edition circulating in Vietnam sets up the hexagram by the 8, 8, 6 division over three groups of digits, exactly as the Khổng Minh Thần Toán book states in its opening section. The edition that Steve Moore (2012) describes in his book review Lost (and Found) in Translation: The Shenshu Attributed to Zhuge Liang instead sets up the hexagram by the total number of strokes of three Chinese characters. These are two editions that differ in their method of setting up the hexagram, so when consulting one should know which edition one is using.
Why does the book bear Gia Cát Lượng's name?
The official histories about Gia Cát Lượng do not mention any divination book. The main historical source about him is the biography in the Tam quốc chí (Records of the Three Kingdoms), volume 35 (Thục thư 5), the Gia Cát Lượng truyện, compiled by Trần Thọ in the third century, later annotated by Bùi Tùng Chi in the fifth century by adding many other sources, such as the Tấn thư, volume 82, the Trần Thọ truyện by Phòng Huyền Linh and the seventh-century court historians. These sources record that he served as chancellor of the state of Thục Hán, helped Lưu Bị establish the state, acted as regent for Lưu Thiền, campaigned to pacify the southwest and led several northern expeditions, and died in 234 at Ngũ Trượng Nguyên. No passage says he composed a divination book or established a system of hexagrams for posterity.
The image of Gia Cát Lượng as a master calculator who knew everything in advance comes mostly from the novel Tam Quốc diễn nghĩa (Romance of the Three Kingdoms), which appeared in the fourteenth century, more than a thousand years after his death, according to Encyclopaedia Britannica, entry Zhuge Liang. This novel builds the character Khổng Minh into almost a saint, able to predict wind, predict fate, arrange battle formations and perform rites to summon wind. From that literary figure, popular tradition gradually attributed to him many books and many methods of calculation, among them the Khổng Minh Thần Toán.
The book's name being attached to Gia Cát Lượng is popular tradition and something some libraries record according to legend, while the official histories about him do not mention any divination book, according to the Tam quốc chí, volume 35 (Thục thư 5), the Gia Cát Lượng truyện by Trần Thọ. No original text from the Three Kingdoms period confirms that he was the author, and the content of the book itself reflects a manner of presentation, a method of casting and a classification of good and bad fortune that took shape much later.
This does not diminish the book's usefulness for someone consulting a hexagram. It only puts the name in its proper place: the name Khổng Minh Thần Toán is a way of naming by the prestige of a historical figure, not evidence of authorship.
Three things often confused: the line texts of the Chu Dịch, the Khổng Minh Thần Toán cards and Tiểu Lục Nhâm
These three systems all use hexagrams and lines but differ in their unit of consultation and their method of setting up the hexagram, so beginners easily confuse them.
The line texts of the Chu Dịch are ancient wording attached directly to each line of the 64 hexagrams in the Kinh Dịch, dating from before Confucius and transmitted through many generations. A person casting by the Chu Dịch reads the hexagram text and the moving line text, then interprets according to the hexagram image, the responding line and the line position. This is the root layer; every later system that uses hexagrams takes the 64 hexagrams from here.
The Khổng Minh Thần Toán cards are a layer overlaid on those 64 hexagrams. Each hexagram has six cards corresponding to six moving lines, 384 cards in total. Each card has its own verse, its own translation and its own commentary, and does not use the line texts of the Chu Dịch as its main content. The querent need only arrive at the correct hexagram and line to look up a ready-made card with an interpretation, without having to interpret it himself.
Tiểu Lục Nhâm is a method of finger counting that is entirely different in mechanism. This method uses six palaces in the order Đại An, Lưu Niên, Tốc Hỷ, Xích Khẩu, Tiểu Cát, Không Vong, and sets up the reading by counting through month, day and hour on the joints of the fingers. The circulating Khổng Minh Thần Toán itself has a passage recounting that Lý Thuần Phong of the Tang dynasty took the idea from this book to establish the six-palace finger-counting method, but that is the book's own account, with no historical source to corroborate it. This is a simplified branch that does not use the 64 hexagrams and has no 384 cards.
| Criterion | Line texts of the Chu Dịch | Khổng Minh Thần Toán | Tiểu Lục Nhâm |
|---|---|---|---|
| Unit of consultation | 64 hexagrams, 384 lines, reading the hexagram text and line texts | 384 cards, each card corresponding to one hexagram with one moving line | 6 fixed palaces |
| Method of setting up | Coin tossing, yarrow stalks or number methods | Three number groups divided by 8, 8, 6 | Counting month, day and hour on the finger joints |
| Source of interpretation | Ancient wording in the Kinh Dịch | Verse, translation, commentary, ready-made interpretation | Meaning of the six palaces and orally transmitted interpretation |
| Traditionally attributed to | King Wen, the Duke of Zhou, Confucius | Gia Cát Lượng according to tradition | Lý Thuần Phong of the Tang dynasty according to tradition |
| Level of detail | Short, requires an interpreter | Long, with a ready-made interpretation | Short, depends on the person counting |
How should one read a Khổng Minh Thần Toán card correctly?
The editions of the Khổng Minh Thần Toán circulating in Vietnam classify cards by grades such as Thượng Thượng, Trung Trung, Hạ Hạ. This classification is helpful for beginners because it gives a quick view of the card's general tendency, but it is also the place most prone to misunderstanding. A card ranked Hạ Hạ does not mean that everything will fail, but is usually a reminder to slow down, to hold oneself steady, to wait for the time. A card ranked Thượng Thượng also does not mean that everything will come about on its own, but that conditions are more favourable and the querent must still do his own part of the work.
The editions are also not entirely consistent with one another in their classification and in the content of the commentary. Some editions emphasise the Hán Việt verse, some expand the interpretation section by each kind of matter, some add the commentary of Thông Huyền Lão Nhân with its own manner of exposition. The reader should know which edition he is using, because for the same hexagram with the same line moving, two editions may give different commentaries on the degree of favourability.
One point to note about the name Thông Huyền Lão Nhân. This is an appellation commonly seen in the Khổng Minh Thần Toán editions in Vietnam, used to refer to the writer of the explanatory section. The materials that can be consulted do not give the specific identity of this figure, so he should not be assigned to any historical person. This is a compilation pen name, not a figure with a determinate biography.
The most reasonable way to use it is to treat the card as a framework of suggestions for one's own reflection, not a fixed verdict. If the card says to avoid petty people, then what needs doing is to review one's current relationships and see where there is misunderstanding or unhealthy competition. If the card says to travel far, then what needs doing is to see whether one is stuck in an old place and what options exist for changing one's environment. The value of the book lies in the fact that it forces a person to stop and look at what he is doing from another angle.
Should one trust the result of a hexagram absolutely?
One should not. The books in this line do not themselves place themselves in the position of deciding on people's behalf. The Tử Vi ghi chép số 01 (Tử Vi record no. 01) has a passage recalling the sayings "Nhân định thắng thiên" (human determination conquers heaven) and "Đức năng thắng số" (virtue can overcome fate), meaning that human determination can overcome heaven and that merit can overcome destiny, and it takes Gia Cát Lượng himself as an example: he knew the realm would divide into three, yet still went up Kỳ Sơn six times and in the end did not succeed. The detail of going up Kỳ Sơn six times is according to the Tam quốc diễn nghĩa (lục xuất Kỳ Sơn, the six campaigns from Kỳ Sơn), a novel, not the official history Tam quốc chí. This is a view that many authors in the Eastern line recall: the hexagram indicates tendencies and conditions, not a certain outcome.
For matters involving finance, health or law, a hexagram cannot replace professional advice. The querent still needs a doctor, a lawyer or a financial expert depending on the matter. Placing the hexagram in its proper role, as a tool for self-questioning, will avoid both extremes: complete dismissal and absolute belief.
Practical summary
For a beginner, the sequence for grasping the Khổng Minh Thần Toán comes down to three tasks. Master the Tiên Thiên Bát Quái number sequence and the method of division with remainders by 8 and by 6. Master how to combine the Upper hexagram with the Lower hexagram to arrive at the hexagram name. And know how to look up the correct card by hexagram together with moving line in the table of 384 cards of the edition one is using. These three tasks are enough to set up a hexagram and look up a card, while the deeper interpretation depends on affinity and on how familiar one is with the Kinh Dịch.
