“Go to the back of that round hut, from there walk straight to the light three steps, then turn diagonally to the left four steps, then straight three steps and diagonally to the right four steps. By carefully walking straight and diagonally like this, you won’t make a wrong step,” Huang Rong said.
Guo Jing followed her instruction to the letter; and sure enough, every time he stepped his foot down, he would step on a submerged wooden stake. Only those wooden stakes were not firm, some of them wobbled and some were planted on an angle; if his lightness kungfu was not good, they would fall into the marsh. He focused all his attention to walk three steps diagonally and four steps straight; and after walking a total of 119 steps they arrived at the front of the square hut.
The hut was actually without a door. Huang Rong whispered, “From here you jump forward, make sure you land on the left side.”
Carrying Huang Rong on his back Guo Jing jumped forward and landed on the left side, he could not help but feel amazed, “Everything is exactly as Rong’er has anticipated.”
There was a courtyard inside the wall, which was divided into two parts: on the left was solid ground, while on the right was a pond. Guo Jing crossed the courtyard and entered the main hall. Outside the hall was a moon gate without any door on it. “Go straight ahead,” Huang Rong said, “There is nothing strange from here on.”
Guo Jing nodded. With a loud and clear voice he said, “The passing visitors took the liberty to enter the house; I beg the esteemed host to forgive our boldness.” He waited for a moment then proceeded to enter the hall.
Inside the hall there was a long table; on it were seven oil lamps, arranged in the Big Dipper formation. On the ground squatted a grey-haired lady, her clothes were made from coarse fabric. Her attention was focused on the countless bamboo strip scattered on the ground; so deep was her concentration that even when she heard people came in, she did not raise her head to look.
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.
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!”