When the pears are green

In the dim twilight, Jiang Qingye and Song Xing stood beside the chicken coop and rabbit hutch at home and kept counting the number of chickens and rabbits. The two were trying to guess how many rabbits and chickens could have thirty-five heads and ninety-four legs.

"Hahaha...this is so funny." Song Li lay on Jiang Qingzhou's back and laughed, and the note in her hand kept shaking.

"Miss!"

"sister in law!"

Song Xing and Jiang Qingye complained about Song Li at the same time. Song Li's sudden laughter completely disrupted their thoughts, and they forgot how many rabbits and chickens they had just calculated.

Song Li laughed for a long time before she stopped. She reached out to wipe away the tears from her laughter, then sat on the stool that Jiang Qingzhou had brought over.

"Come here quickly, you two. Since it's an arithmetic problem, there must be a way to solve it. Let's think about it together, and maybe we can figure it out." After Song Li finished speaking, he waved to Song Xing and Jiang Qingye.

The four of them sat together. Song Li read the question again, then asked Jiang Qingye with a smile: "Qingye, you go first. The question says there are 35 animals in total. If all 35 are rabbits, how many legs should they have?"

Jiang Qingye began to draw two squares on the ground with his fingers. Three and five were written on the top of the squares and four was written on the right side of the square. Then he drew diagonal lines in the two squares and wrote the results of multiplying three and four and the results of multiplying five and four in the triangles respectively. Finally, he added the numbers in the same diagonal row, and the result was one hundred and forty.

"This method is great!" Song Li clapped her hands in praise. She used to think that the ancients didn't know how to do complicated multiplication, but now it seems that even a four-digit number can be multiplied by a four-digit number using this method.

Jiang Qingye excitedly told Song Li that this method was called floor brocade, which Yang Yu had just taught him in the afternoon.

Song Li then asked Song Xing: "Xiao Xing, Qingye has just calculated that if they were all rabbits, there would be 140 legs, but the question says there would be 94 legs, so how many extra legs are there?"

Song Xing thought for a moment and replied to Song Li: "One hundred and forty minus one hundred still leaves forty, plus the extra six, that's forty-six. Big sister, there are forty-six extra legs."

Song Li happily touched Song Xing's head. She gave Song Xing a thumbs up and said, "Xiao Xing is also great. Was this also taught by Master Yang?"

"It's Master Li." Song Xing corrected Song Li with a smile.

"No matter who taught you, it's good as long as you can learn it. Then whose are the extra forty-six legs? Who should answer this time? Let Qingzhou!" Song Li smiled and pushed Jiang Qingzhou who was sitting next to her.

Jiang Qingzhou smiled and said to Song Li, "Isn't this their topic? I'd better not get involved."

"Go ahead, go ahead!" Song Li shook Jiang Qingzhou's arm. The young man was sensitive. Although this was a question that Yang Yu left for Song Xing and Jiang Qingye, she also wanted Jiang Qingzhou to participate. She didn't want Jiang Qingzhou to feel that he was excluded from the three.

Jiang Qingye and Song Xing also stood up. Song Xing shook Jiang Qingzhou's other arm, and Jiang Qingye pushed Jiang Qingzhou's back. The three of them begged Jiang Qingzhou to answer quickly.

"I'll tell you, I'll tell you." The three of them stopped what they were doing when they heard Jiang Qingzhou say this. They stared at Jiang Qingzhou, expecting him to continue.

Jiang Qingzhou stroked the back of Song Li's hand with his index finger, and answered the question with a smile: "A rabbit has four legs, a chicken has two legs, so the extra one is naturally the chicken's leg."

"Why is it a chicken leg and not a rabbit leg?" Song Xing felt a little confused.

Jiang Qingye patted Song Xing on the shoulder and explained to him with a smile: "Because the question says there are chickens and rabbits, let's assume that they are all rabbits. The extra ones are naturally chicken legs. Each rabbit has two more legs than each chicken. I understand. Half of the forty-six is ​​the number of chickens."

"Qingye is great, then why don't you count the number of chickens!" Song Li looked at Jiang Qingye expectantly. She wanted to know how the ancients calculated division.

Jiang Qingye went to the kitchen and found a long branch. He first broke the wooden stick into a dozen pieces, then used two small branches to arrange them into a "丅" shape, and then used four small branches to arrange them horizontally.

"Sister, brother-in-law, this represents forty-six. Master Yang taught us to use the counting stick method to calculate division." Song Xing hurriedly explained to Song Li and Jiang Qingzhou who were confused.

Song Li then understood how Jiang Qingye calculated. In fact, it was not much different from the division method used in later generations, except that Arabic numerals were used in later generations, while branches were used here instead.

"There are twenty-three chickens." Jiang Qingye looked up at Song Li, Jiang Qingzhou and Song Xing happily.

Jiang Qingzhou smiled and touched Jiang Qingye's head. The two brothers' eyes met and they both laughed happily.

When the laughter stopped, Song Li asked Song Xing again: "Since Qingye has calculated that there are 23 chickens, then Xiaoxing can calculate how many rabbits there are."

"Twelve rabbits." Song Xing calculated in his mind and quickly gave the answer.

After hearing Song Xing's answer, Song Li happily said to them, "You two are awesome!"

"Sister-in-law, can we also assume that they are all chickens, and then subtract ninety-four from seventy, and half of the resulting number is the number of rabbits." Another algorithm emerged in Jiang Qingye's mind.

Song Li did not answer immediately. She asked Jiang Qingye and Song Xing to calculate together to see if the answers were the same.

It was already dark in the yard. Jiang Qingzhou went to the kitchen, lit the oil lamp, took it out, and placed it on a stool in the yard. The wind was not strong, and the wick swayed constantly with the wind.

Song Li and Jiang Qingzhou didn't say anything. They stood aside and watched the two children writing and drawing on the ground.

"The answer is the same as before." Song Xing and Jiang Qingye raised their heads at the same time and looked at Song Li and Jiang Qingzhou with excitement.

Song Li praised the two of them again, and then continued to answer the question of when the two mice met.

Song Li first asked Jiang Qingzhou to draw a long horizontal line on the ground, and then divide it into five equal sections.

"This line represents the thickness of the wall, and each section represents one foot. Xiaoxing is bigger than Qingye, so Xiaoxing plays the rat and Qingye plays the mouse. Xiaoxing stands on the east side, Qingye stands on the west side, and Qingzhou reads the questions." Song Li assigned roles to the three people and stood aside watching them.

Jiang Qingzhou followed Song Li's instructions and recited a sentence: "The big rat wears one foot a day, and the small rat also wears one foot a day."

Jiang Qingye and Song Xing walked forward for a distance respectively. Song Li pointed to the distance they walked behind them and told them that this was the thickness of the wall that the big mouse passed through on the first day.

"The size of a rat is doubled every day, and the size of a mouse is half of that every day." After Jiang Qingzhou finished reading, Jiang Qingye and Song Xing were stunned for a moment, and they looked at Song Li for help.

Song Li ignored it and asked the two of them to discuss what this sentence meant first.

Jiang Qingye walked over to Song Xing, and the two of them discussed in a low voice. Finally, he told Song Li the result of the discussion: "Sister-in-law, the big rat will wear two feet on the second day, and the small rat will wear half a foot."

Song Li nodded. She asked Jiang Qingye to return to his original position, and then asked the two of them to continue moving forward.

"Xiaoxing, answer this question. How much is left between you and Qingye now?" Song Li asked, standing between the two of them.

Song Xing glanced at Jiang Qingye in front of him and replied with a smile: "Sister, there is still half a foot left."

"That's right. Then on which day did Qingye say that the big and small mice will be able to meet?" Song Li asked.

Jiang Qingye jumped directly to Song Xing and answered loudly: "Of course it's the third day."

"That's great. I'll stew eggs for you tomorrow. Go back to sleep." Song Li urged the two to go back and rest. The village had become quiet, and the sound of crickets chirping could be heard from the corner of the yard from time to time.

The chirping of crickets was so clear that even after Song Li returned to her room, she could still hear it.

"Qingzhou, I will send Xiaoxing back tomorrow. If I can't come back tomorrow, I will definitely come back the day after tomorrow. Don't worry." Song Li rested her head on Jiang Qingzhou's arm, and she whispered in Jiang Qingzhou's ear.

Jiang Qingzhou's hand paused for a moment, then he looked at Song Li with reluctance.

Song Li smiled and reached out to rub Jiang Qingzhou's ears, and the two of them laughed and joked again.