Chapter Forty-Nine: The Story of the Hundred Chickens Problem
In the past two days, the streets of Nanyang have been full of people, waving their sleeves into rain.
The competition is set up in the square in front of Huazhou Academy, and on both sides of the ring is a dazzling couplet, which I heard is the handwriting of Miss Deng Yu: "Heaven and earth, the real heroes on the stage on winning and losing; Coming from south to north, it is the talented subordinates who see the real chapter. "People are not better than martial arts, or they are about literary talents, but this young lady of the Deng family wants both, and she wants to marry a hero who can write and martial arts.
The good position in front of the ring has long been occupied by various families, and some families still set up a table in front of the stage, with tea stove preserves, drinking tea while watching the excitement, and those who want to participate in the competition also bring their own relatives and friends to cheer for themselves.
These sons of these families in Nanyang, usually pursue Deng Yu is a clear and secret fight, but they also abide by the rules and never tear their faces, but this is a clear fight to recruit relatives, and it is these sons of the world who are the most energetic to fight, this field has not started to earn a field in the front, and the quarrels are non-stop, this said that the son of your family will only have a few oil poems, and he can't even pull a one-stone bow, the son who said that your family only knows how to dance with guns and sticks, and he can't even know how to count, and he has to ask the master to write a love letter. It was just that there was no fighting.
But this time the Deng family is really a little ruthless, sign up for the competition, the registration fee will be ten times, but if the two future fourth and sixth uncles are not satisfied, they will not let you compare, and let you perform a martial arts and recite a few crooked poems to verify that you are indeed a civil and military talent. Deng Jiaguan called this the first test, the first time you passed, you can go to the ring and Miss Deng to make a move, if you can touch Miss Deng Yu's hands and feet or any key place, no matter success or failure, there is still something to earn. Some people who are usually familiar with Deng Yu can't beat it, in case Deng Yu sees her glorious image compared to Pan An, maybe she will release the water and choose herself. These sons of the world are bursting with confidence and full of confidence.
Let's just say that this Deng Yu, even if the Deng family's family background is also broken, not to mention that this Deng Yu is a beautiful girl with a family background, appearance, literary talent, and martial arts?
Gao Chong, Qian Jichen took Dazhu, Ding Li and others with Qian Jichen, and the group came to this Huazhou Square, and heard the shouts and cheers of the cheerleaders from a distance. Nearly 10,000 people have gathered here, and the square is surrounded by all kinds of vendors, there are those who sell food, fruits, jade ornaments, small handicrafts, and those who sell rouge gouache, cloth, hats, shoes, and clothes are like a material exchange conference, which is very lively.
There are a lot of people in the square, but Gao Pet's line of people is still more conspicuous, except for a few people from the Qian family, Gao Pet's subordinates are wearing pants and belts, and they are very eye-catching.
Deng Yuren is already beautiful, and today she is dressed in a tight-fitting red suit, slim and elegant, and her body is full of youthful atmosphere, so it is no wonder that the young people in Nanyang are a little crazy today.
Deng Yuan, the fourth elder of the Deng family who was in charge of registration in front of the stage, also saw Gao Pet and his party coming, he thought that Gao Pet and they were also here to compete and recruit relatives, so he squeezed through the crowd and came to Gao Pet:
"This son, Deng Yuan in the Xia Deng family, the word is like the wind, the fourth in the family, responsible for the primary registration of the little sister competition to recruit relatives, if you want to participate in the competition, you can come with me."
"In Xiatongling, I am highly favored, passing through Nanyang, not to recruit relatives, Brother Deng has worked." High favor in return.
"It's not Deng Yuan bragging, no matter what the talent looks like, the little sister is the best choice, this Nanyang inside and out, no one else, admiration and saying that the matchmaker has broken through the threshold, but the little sister's vision is too high, my Deng family has no choice but to come up with this strategy to choose a good son-in-law, why not try it?"
"This Nanyang has been outstanding since ancient times, if you want to talk about talents, there is no place in the world that can compare to Nanyang, your ancestors Deng Yu, Zhuge Kongming, and Fan Jumo are not among the arrogant people, I believe that Deng Xiaomei will definitely be able to choose a good son-in-law." Gao Pet is just watching the excitement, and he has another important task on his body, so he has no intention or time to make a lot of trouble in Nanyang.
At this time, several high-ranking guard recruits muttered below: "If my young master participates in the competition, he will not be a martial artist. Gao Zhong and Deng Yuan both heard this sentence, and Gao Zhong couldn't help but stare at the two pro-soldiers, which meant to say: You have a lot of things.
"Since Brother Gao is talented, why don't you try it, one is also to help my Deng family make a show, but it is not necessarily whether you can be this son-in-law or not, and the other is to kill the arrogance of these so-called talents in our Nanyang, so that they can calm down and do learning and martial arts." Deng Yuan changed his tactics this time, just let Gao Zhong play on stage, and when you come to the stage, it's not up to you to decide whether to be a son-in-law or not.
At this time, Qian Jichen, who was on the side, also came to join in the fun. Although he has a daughter, the old man and the little girl are very fond of this high pet, and they want to marry this family, and the more they look at it, the more satisfied they are. But in this atmosphere at the scene, I don't care about my own daughter. Say:
"Gao Gongzi, it's okay for the past two days, go up and have fun, and kill this girl's arrogance, this world is still a man's world, and it also makes my man raise his eyebrows in Nanyang." Speaking of high pets, there is some heartbeat. At this time, the third competition has begun, first is the literary competition, if you win, you can compare martial arts. The Deng family still gave in and let the opponent choose between the first literary competition and the martial arts competition.
Participating in this third competition is Shen Changfeng, a son of Nanyang, he is crazy about this Deng Yu, and he has exhausted all means to chase Deng Yu, and his Nanyang competitors have suffered his secret losses many times.
The Shen family has four brothers, wind and rain, thunder and lightning, Changfeng is the boss, this boss is competing on the stage, this Shen Changyu, Shen Changlei, Shen Changdian and his family are cheering for Shen Changfeng. A few years ago, the Shen family was underestimated and marginalized by the Nanyang family, but the Shen family helped Dajin fight the Great Song Dynasty because his father was now an official in Liu Yu's mansion, and in the past six months, especially after the city was occupied by Li Cheng, it has become increasingly arrogant.
This Shen Changfeng not only wants to marry Deng Yu home as his wife, but also wants to use this time to make some limelight and let the Shen family grow their faces in Nanyang. Because he believed that he had some literary talents, Shen Changfeng chose Wenbi first, otherwise Wubi accidentally kicked the girl of the Deng family, and his face couldn't be hung up, and he also hoped that this Wenbi would suppress Deng Yu's arrogance.
"Okay, Shen Gongzi, the first question is a riddle, you listen: 'I wear my own armor, rampant in the countryside, the autumn wind rises in August, and the city is full of golden armor.'" Hit a dish. ”
It's hard to get Shen Changfeng, thinking about that Changfeng, cooking wine and fighting poems on weekdays, in the countryside and restaurants, I haven't eaten anything, and the son of a family has never seen anything. So by the way: "Braised crab." ”
"I'm sorry, Shen Gongzi, although this is not far from the topic, it is not the correct solution, but there are still opportunities below."
"What is not a crab? Can you tell me below? "Shen Gongzi has some, I wanted to make a difference, but I didn't expect that it would be a failure at the beginning.
"Shen Gongzi, can you see the source of the last two sentences?"
"I don't know."
Huang Chao at the end of the Tang Dynasty was a great hero with all-round talents in civil and military affairs, and the poet Lin Kuan at the end of the Tang Dynasty had a poem: "Mo Yan immediately won the world, and heroes have interpreted poetry since ancient times." That's true. Huang Chao, the leader of the peasant uprising at the end of the Tang Dynasty, was such a hero who immediately fought the world and wrote ambitious "poems". In addition to being proficient in martial arts, Huang Chao also loves to read and can write poetry. When he first participated in the scientific examination, he was not the first, but he wrote a poem called "Budi Chrysanthemum Poem", listen to it:
'Wait until autumn comes on September 8, after my flowers bloom, a hundred flowers will be killed, and the incense array will penetrate Chang'an, and the city will be full of golden armor. This riddle should have the word chrysanthemum, so it is a chrysanthemum crab. ”
Deng Yu only admired heroes like Huang Chao and Cao Cao, so it was normal to be familiar with Huang Chao, but Shen Changfeng was different, and Huang Chao was disdainful as a thief at that time.
This dish is very poetic, and it is of course common to be favored by future generations, but it is rare to come up with this dish in the Southern Song Dynasty. There is no such dish on the market, since today, this chrysanthemum crab is popular in Nanyang, and then to the entire Great Song Dynasty.
Let's say that the literary comparison in the ring is not as good as the examination room of the imperial examination, but your reaction and knowledge are tested. Deng Yu has been interested in calculation since childhood, and almost all of the ten arithmetic scriptures in ancient China are available at home, such as the Tibetan book "Zhou Ji Sutra", "Nine Chapters of Arithmetic", "Island Sutra", "Zhangqiu Jian Sutra", "Xiahouyang Sutra", "Five Classics of Arithmetic", "Records of Mathematics", "Five Cao Sutras", "Ancient Arithmetic", and "Fixation". From this collection of the "Ten Books of Reckoning", it also reflects the unusualness of the Deng family from another aspect. So Deng Yu's question to Shen Changfeng is arithmetic.
"Shen Gongzi, you are also a disciple of my Nanyang family, I will give you another chance, I don't know if you have studied mathematics during this time, I don't embarrass you, the second question in this essay exam is an arithmetic problem."
"Miss Deng doesn't have to care, my son has also learned arithmetic, and general questions are still difficult for my son," Since this Changfeng likes this Deng Yu, he has done a lot of homework on this Miss Deng family, and knows that Deng Yu loves arithmetic, so he has been studying.
"Shen Gongzi listened, there is an old man, he has a hundred yuan, to sell hens, roosters and chickens, the price of a rooster is four cents; The price of a hen is two cents; There are three chickens. Where you buy 100 chickens for 100 dollars, ask the chickens, mothers, and catfishes? ”
This full question is recorded in the famous "Hundred Chickens Problem" in the "Zhang Qiu Jian Suanjing", which was written in ancient China about the 5th and 6th centuries, which is the 38th question under the original scroll and the last question in the whole book.
This is a ternary indefinite equation problem with multiple answers, which is quite difficult.
The original question and answer in the book are as follows: "Today there is a chicken Weng, which is worth money; The hen is one, and it is worth three; Three chickens are worth one. Where you buy 100 chickens for 100 dollars, ask the chickens, mothers, and catfishes? Answer: Chicken Weng four, worth twenty; Eighteen hens, worth fifty-four; Seventy-eight chickens are worth twenty-six. He replied: Eight chickens, worth forty; The hen is eleven, worth thirty-three, and the chicken is eighty-one, worth twenty-seven. And he replied: Twelve chickens, worth sixty; Hen four, worth twelve; The chicken is eighty-four and worth twenty-eight. ”
Zhen Luan and Li Chunfeng, the famous proofreaders of ancient Chinese arithmetic, did not give a solution when they commented on the book, and only Xie Chawei, an arithmetic scholar from about the 6th century, wrote an incorrect solution. In the Qing Dynasty, there were more and more people who studied the technique of 100 chickens, and in 1815, Luo Tengfeng used the 'Great Yan Qiu Yi Technique' to solve the problem of 100 chickens.
In 1874, Ding Zhuozhong created a simple arithmetic solution. Around this time, Shi Yu Yu (c. 1870) popularized the Baiji Wen's work "Baiji Shuyan", and since then the Baiji problem and Baiji Shushu have been widely known.
There are many forms of expression for the problem of 100 chickens, such as 100 monks eating 100 steamed buns, 100 dollars buying 100 birds, etc. There were similar problems in Yang Hui's arithmetic book in the Song Dynasty, and similar problems were circulated in the Near East countries in the Middle Ages.
For example, both the Indian arithmetic book and the work of the Arabic scholar Abu Kamil have the problem of buying a hundred birds for a hundred dollars, and the title is almost identical to that of the Zhang Qiu Jian Sutra. However, in ancient times, these sutras often focused on the results and rarely explained the process, so it was more difficult to learn on your own. Even if the problem is the same but the data is different, it would be a tragedy to rely on rote memorization if you don't know the calculation process and the solution.
Deng Yu changed the price here by two prices, so the answer is different. Although Deng Yu came up with the question, she didn't figure out the calculation of this question, and it took a long time to come up with the number answer. She meant to be embarrassed by Shen Changfeng.
Hearing this question, Shen Changfeng fainted suddenly, this Shen Changfeng is also erudite, and faintly remembered that he had seen this hundred chicken question in "Zhang Qiu Jian's Sutra", and remembered that there were several answers, but at that time, I didn't know how to solve it, if I used the exhaustive method, it was very timeless. But what is the solution? Standing on this stage for two days or three days? Weirdo family has a problem? Therefore, Shen Changfeng shook his head impatiently, and he still failed.
At this time, someone came up to send Shen Changfeng off the stage, but this Deng Yu walked to Taichung and said to everyone:
"Just now, the Shen family's son's challenge failed, does anyone have an answer to this hundred chickens problem and will solve it?"
Deng Yu stopped, swept the audience, and stopped at Gao Chong's body, and saw Gao Chong writing something on paper with a strange pen.
"If anyone can give the answer and provide the algorithm, there is a prize! Only the answer will be awarded 10 taels of silver, and the algorithm will be awarded 10 taels of gold. ”
At this time, Gao Zhong had already finished counting, and he also knew that it was impossible to have a complete algorithm in this Great Song Dynasty, and only he, a traverser, would have this benefit. He handed over the finished solution process and answers to Deng Yuan and Deng Laosi, who had been on the side, and said to Deng Yuan: "In order to encourage the scientific spirit of your young lady, you can hand this over to your young lady, if you don't understand, I am still here for the past two days, you can come and ask me, I will live in Fu Ji." ”