The legendary "revelation" of the divided horse
Xiaoming is a smart and cute child, the only thing he lacks is that he is a bit sloppy in his studies, and every exam is due to carelessness and misses the pass. It wasn't until one time, in order to act as a clever chivalrous man, that he gave someone a small sheep in vain to wake up.
Speaking of a Sunday in autumn, the sun was shining and breezy, and Xiaoming, as usual, drove the sheep to the hillside behind his home with his neighbor Li Lan, who was a year younger than him. Xiao Ming found that Li Lan was a bit abnormal, and the laughter and laughter of the past were not only gone, but his innocent face was full of sorrow and heavy hearts. An inquirer knows that it was --
Li Lan's grandfather died a few days ago, leaving behind the inheritance of 17 sheep, and when he was dying, he said to Li Lan's father, the second uncle and the third uncle: "Son, I am dying, although my father was industrious and thrifty before he died, he did not leave any valuable property for you, only the 17 sheep you three brothers to share." The eldest daughter is about to go to junior high school, need to spend money, more points, just divide 1/2 of it, the second child is still small, there is no shortage of money for the time being, it is divided into 1/3 bar, the old three are young and promising, there will be good development in the future, it will be divided into 1/6 bar. These sheep are excellent breeds, and you must not slaughter them easily..." Before he could finish speaking, he lost his breath.
Today, Li Lan's father and two uncles finished their grandfather's affairs, and when they began to divide the sheep, they found that their grandfather's will could not be executed at all. Because 1/2, 1/3, 1/6 of the 17 sheep are simply inexhaustible without slaughter.
After listening to Li Lan's story, Xiaoming was also helpless, looking at the group of 17 sheep in Li Lan's family, thinking that if there were 18 sheep, it would be easy to deal with. He turned his gaze to the little sheep in his house, and suddenly his eyes lit up, remembering a legendary story of splitting horses-
Legend has it that a long time ago, an old farmer left 19 horses for his three sons before his death, and made a will: the old man scored 1/2, the old second score 1/4, and the old third point 1/5. Afterwards, the three sons of the old farmer thought hard and could not find a plan for dividing the horses (according to the local customs at that time, they regarded horses as gods and could not be slaughtered); they consulted many learned people, and everyone thought and thought, and finally always shook their heads and said that they could not help; the neighbors suggested that they asked the official to judge, and the official also thought about it, and finally withdrew from the church on the grounds that it was inconvenient to ask questions about family affairs. Until a few days later, a chivalrous man who rode by heard about this incident, volunteered to "send" his mount to the home of the three brothers, let the horses make up 20 horses, and then according to the old farmer's will: the boss scored 1/2, took 10 horses, the old two points 1/4, took away 5 horses, the old three points 1/5, took away 4 horses, and finally there was 1 horse left, and the chivalrous man rode away by himself. Afterwards, while praising this chivalrous man's chivalrous courage, people praised his ingenuity and wisdom, which has been passed down to this day.
Thinking of this, Xiaoming happily rolled on the grass and comforted Li Lan with great certainty: "You can rest assured, this problem is very easy to solve, I will 'send' this sheep of my own family to you, and will it be solved after making up 18?" Li Lan was suspicious, looking at Xiaoming's indifferent and serious look, she thanked herself and drove the 18 sheep home.
Xiao Ming was lying on the green and hairy hillside, looking up at the blue sky and white clouds, waiting very comfortably for the cute little sheep that Li Lan had brought from home.
After a moment, Li Lan returned empty-handed, and Xiaoming jumped up and asked, "What about my sheep?" ”
"Divided!" Li Lan replied excitedly.
"How could it be?" Xiao Ming asked doubtfully, "Isn't there still one left?" ”
"How can that be?" Li Lan slowly and logically calculated to Xiao Ming: "You think, 18 sheep, my father divided 1/2, got 9, the second uncle divided 1/3, got 6, the third uncle divided 1/6, got 3, isn't it just 18?" ”
Bob couldn't figure it out. The same question, why do similar approaches have very different results?
Originally, according to the old farmer's will, the three brothers divided 19 horses according to 1/2, 1/4 and 1/5 respectively, the eldest could get 9.5 horses, the second could get 4.75 horses, the old third could get 3.8 horses, the three people got a total of 9.5 + 4.75 + 3.8 = 18.05, there were 0.95 horses left, 0.95 horses and then 1/2, 1/4 and 1/5 points. The boss can get 0.475, the second can get 0.2375, the third can get 0.19, at this time the boss can get a total of 9.975 horses, the second can get a total of 4.9875 horses, the old three can get a total of 3.99 horses, there are 0.0475 horses left, and they have to continue to score, and endless. The chivalrous act of righteousness takes advantage of this, cleverly turning infinite problems into finite problems by "borrowing one".