Guo Jing gently lowered Huang Rong on a chair. Under the lamp light they saw that lady’s countenance to be thin and pallid, as if she did not have any blood; they felt compassionate toward her. Guo Jing was about to open his mouth asking for some water but seeing that lady so engrossed in whatever she was doing, he was afraid to interrupt her train of thought; hence he refrained from making any noise.
After sitting down for a moment, Huang Rong’s spirit was slightly revived. She saw the bamboo strips on the ground to be approximately four ‘cun’s [about 13cm or 5inches] long and two ‘fen’s
[about 7mm or ½ inch] wide; they were bamboo strips usually used for calculation. Again she looked closer, those computation were based on ‘shang, shi, fa, jie’ [business/commerce, reality, law, lending (money)] method of calculation with four decimal point. Right now she was calculating the square root of 55,225; with the ‘shang’ position had shown the result to be 230. But that lady was still struggling with the third digit.
Huang Rong quipped, “Five! Two hundred and thirty five!”
That old lady was startled, she raised her head, her eyes were gleaming, looking at Huang Rong with a penetrating gaze, and then immediately lowered her head to continue her calculation. When she raised her head, Guo and Huang, two people saw her face; it was simple and beautiful. They believed she was not even forty years of age yet. Perhaps the hair on her temples had turned grey because she had too much in her mind.
After computing for while, the lady figured out the answer was indeed ‘five’; she raised her head to look at Huang Rong again. She looked confounded, but also angry, as if she was going to say, “You are but a young girl; you have made a lucky guess, what’s so strange about that? Just don’t mess with my business here.” She wrote down ‘235’ five characters [er bai san shi wu] on a piece of paper, then proceed to the next problem.
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This time she was looking for the cube root of 34,012,224. She started by putting down the ‘shang’
and ‘shi’ and ‘fang’ [square], followed by ‘lian’ [inexpensive], ‘yu’ [corner] and ‘xia’ [lower], six strips; and found the first digit to be ‘three’.
Huang Rong softly said, “Three hundred and twenty four.”
That lady uttered an ‘Hmm’ sound, how could she believe her? She continued calculating for a long time, and after a time needed to drink a cup of tea later, the result came out, it was indeed ‘324’.
That lady straightened up her back and stood up; it appeared that her forehead was full of wrinkles, but her cheeks were full, her face looked round. The upper half of her face look old, the lower half looked young, looked like both parts differed by as much as twenty years. Her eyes stared at Huang Rong, suddenly she pointed toward the inner room and said, “Come with me.” She took an oil lamp and walked in.
Guo Jing propped Huang Rong up and followed her inside. The inner room’s wall was round; the floor was covered with fine sand. On the sand were written many weird symbols, vertical and horizontal lines and circles; also some characters such as ‘tai’ [great], ‘tian yuan’ [first/primary sky], ‘di yuan’ [first/primary earth], ‘ren yuan’ [first/primary human], and ‘wu yuan’ [first/primary object].
Guo Jing had no idea what they were; he was afraid to mess these symbols up, so he stopped at the door and did not dare to step into the room.
Since her childhood Huang Rong had been trained by her father in all kinds of mathematics. She looked at the symbols on the ground and immediately recognized it was an advance technique in mathematics called the ‘tian yuan zhi shu’ [sky primary technique]. Even though it looked complicated, it should not be too difficult to solve as long as one understood the principle.
[Author’s note: It very much resembles the modern day algebra. Our country since the ancient times had developed this calculation technique, with ‘tian’, ‘di’, ‘ren’ and ‘wu’ as four unknown variables; much like the X, Y, X and W variables in western algebra]
Huang Rong pulled the bamboo stick from her waist; leaning on Guo Jing she started writing on the sand. In a short while all seven, eight mathematics problems on the sand were solved. That lady had painstakingly tried to solve those problems in months; seeing the solutions, she could not help but feeling deeply confounded. She was silent for half a day then suddenly asked, “Who are you?”
Huang Rong showed a faint smile and replied, “What’s so special about ‘tian yuan si [four] yuan zhi shu’? The mathematics book has nineteen primaries, after the ‘ren’ there are ‘xian’ [immortal],
‘ming’ [bright], ‘xiao’ [firmament], ‘han’ [from Han dynasty], ‘lei’ [rampart], ‘ceng’ [layer], ‘gao’
[high], ‘shang’ [top/above], and ‘tian’ [sky]. Before the ‘ren’ are ‘di’ [earth/ground], ‘xia’
[below/under], ‘di’ [low], ‘jian’ [subtract], ‘luo’ [drop], ‘shi’ [die], ‘quan’ [fountain], ‘an’
[hidden/secret], and ‘gui’ [sly/crafty]. Once you mastered the nineteenth primary, all problems will look easy!”
That lady looked dejected, her body trembled; she dropped to the ground, holding her head in her hands as she was lost, deep in thought. A moment later she raised her head and with a delighted face asked, “Your mathematics skill is a hundred times better than mine, but let me ask you this: you Eagle Shooting Hero
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have a three by three array of number one thru nine, no matter how you add it up, vertically, horizontally or diagonally, the sum of any three numbers has to be fifteen. How do you arrange it?”
Huang Rong thought, “My father established the Peach Blossom Island based on the five ways variation; what’s so mysterious about it? The ‘jiu gong’ [nine palace or halls] is the foundation of the Peach Blossom Island diagram; how could I not know about it?” Therefore, with a calm voice she recited, “The ‘jiu gong’ diagram is constructed like the pattern on the turtle shell [Translator’s note: do a google search with keyword ‘Lo Shu Square’]; four and two are the shoulders, eight and six are the feet. Three on the left and seven on the right; put on nine and tread on one, while five occupies the center.” While reciting this she made a diagram of the ‘jiu gong’ on the sand.
That lady’s countenance turned ashen, she sighed, “I thought I developed this secret formula.
Turned out there is a song about it handed down for generations.”
Huang Rong smiled, “Not only ‘jiu gong’, even four by four array, or five by five, down to the hundred by hundred array, are not too difficult,” she said, “Take four by four array for example; we have 16 numbers in four rows. First we determine the four corner pairs; one and sixteen made a pair, so are four and thirteen. Then we determine the four pairs inside; six and eleven make a pair, so are seven and ten. This way the sums of all horizontal, vertical, and diagonal rows are all 34.”
That lady made the diagram on the sand and sure enough, it was as Huang Rong had said. Huang Rong continued, “Each hall of that nine halls diagram can be transformed into ‘ba gua’ [eight-diagram]. Eight by nine equal to 72 numbers. These numbers: 1 to 72 loop around the ‘jiu gong’
like wreaths. Each loop consists of eight numbers; each four-loop forms another bigger loop, there are four corner loops altogether, which make the total number of loops to be 13. The sum of the numbers in each loop is 292. This diagram variation recorded in the Luo Shu [luo – name of a river, shu – book] is divinely wonderful; no wonder you are not aware of it.” While explaining it, Huang Rong also drew the 72 numbers of the eight diagrams of the nine halls on the sand.
The lady was dumbfounded, she faltered and asked, “Miss, who are you?” But before Huang Rong could answer her, she felt a shot of pain on her chest; her face paled, and anxiously she took a vial from her pocket and swallowed a green pill from the vial. After half a day her face relaxed, she sighed and said, “It’s finished, it’s finished!” Two drops of tears rolled down her cheeks.
Guo Jing and Huang Rong looked at each other; they thought this lady’s behavior was so weird.
That lady had not spoken anything when suddenly there was an intermittent call from the outside. It was the Iron Palm Clan pursuers. “Are they friends or enemies?” the lady asked.
“They are enemies pursuing us,” Guo Jing said.
“Iron Palm Clan?” the lady asked.
“Yes,” Guo Jing replied.
The lady inclined her ear to listen for a while and then said, “Qiu Bangzhu [Clan Leader Qiu]
personally leads his clan to pursue. Who are you actually?” When asking this her voice was stern.
Guo Jing moved forward one step, stood up in front of Huang Rong, and with poise in his voice he said, “We are the Nine-fingered Divine Beggar Hong Bangzhu’s disciples. My martial sister is
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injured by the Iron Palm Clan’s Qiu Qianren. We took refuge here. If Senior has a close relation to the Iron Palm Clan and is unwilling to give us shelter; then we will take our leave.” Having said this he raised his cupped fist and then turned around to help Huang Rong stood up.