Chapter 248: Night Pearl of the East Sea
The last country to compete was Dongling Kingdom.
Emperor Jingxi asked, "I wonder what the envoy of Dongling wants to compete with us Dayuan?"
"Your Majesty, let's have a math contest. We'll give a question, and as long as the people of Dayuan can answer it within two incense sticks, Dayuan wins. Otherwise, our Dongling country wins."
"Okay, then I wonder what the prize that Dongling Country has put forward is?"
Dongling Kingdom originally wanted to gamble bigger, but after the other three countries failed in succession, Dongling Kingdom decided to change its previous demands.
"Your Majesty, we know that Your Majesty has been looking for the long-lost "Fishing Alone on a Cold River". Our monarch is fortunate to have obtained the original copy of "Fishing Alone on a Cold River". If Dayuan wins, we will present this painting to Your Majesty. In addition, we will give Dongling's largest East China Sea Night Pearl to the person who answers the question. But if Dayuan loses, we Dongling ask Your Majesty to exempt us from paying tribute this year."
Emperor Jingxi had always wanted the original copy of "Fishing Alone on a Cold River". He learned that the painting was in the hands of the Kingdom of Dongling and took it out as a bet.
Emperor Jingxi nodded and agreed on the spot, "Okay. I agree to the envoy's request. Please ask the envoy to give the questions."
The Dongling envoy took out a chessboard and said, "Next we will ask a question. Please listen carefully. This is a chessboard with 64 squares. We put one grain of rice on the first square, two grains of rice on the second square, four grains of rice on the third square, eight grains of rice on the fourth square, and so on. The number of grains of rice in each square will double that of the previous square. How many grains of rice should be placed on the 8st square?"
When the people of Dayuan heard this topic for the first time, they all exclaimed that it was too simple.
One of the officials couldn't help but ask, "Envoy from Dongling, are you sure this is the topic for the competition? This topic is too simple."
The envoy from Dongling State smiled meaningfully. He thought to himself, you will find out whether this question is simple or not soon.
The Dongling Kingdom envoy nodded to the official and said, "Yes, this is the question we set. As long as everyone can figure it out within two incense sticks of time, Dayuan Kingdom will win."
Qianhuan didn't expect that the question posed by Dongling Kingdom was actually the difficult problem that mathematician Archimedes had posed to the king. This is the story of doubling rice grains, and it is also the principle of mathematical multiplication.
This question sounds simple, but it is actually very difficult to calculate.
Especially for the ancients who had never learned multiplication, it was even more difficult.
Of course Qianhuan could solve this problem, but she didn't plan to take the lead for the time being. If no one could solve it after a stick of incense, then she would decide to take action.
The princes of Dayuan Kingdom, the ladies and gentlemen of noble families, and the civil officials were all very confident that they could figure out the answer.
The eunuch officially lit the first incense stick, and everyone immediately started doing mental arithmetic, everyone wanted to be the first to figure out the answer.
At the beginning everyone was full of confidence, but after half an incense stick of time, sweat began to appear on everyone's forehead.
They calculated in their minds for a long time, but still couldn't figure out how many grains of rice there were.
Finally, everyone asked the servants to bring abacus, and the whole hall was filled with the sound of "crackling" of abacus.
But in the end, when the first stick of incense had burned out, no one stood up to answer the question.
The eunuch went up and lit the second stick of incense.
Emperor Jingxi wanted the painting "Fishing Alone on a Cold River" very much, but he saw that no one in the audience was answering the question.
He asked anxiously, "Haven't you figured it out yet?"
Everyone shook their heads, and one official said with emotion, "Your Majesty, this question looks easy on the surface, but it is actually very difficult to calculate."
Qianhuan really wants the East China Sea Night Pearl.
She instructed Chiying behind her, "Chiying, please get me a piece of paper and a pen."
"Yes, Miss Qianhuan."
The prince looked at her and asked, "Can Huan'er solve this problem?"
"Well, I can figure that out."
Chi Ying had already handed the paper and pen to Qian Huan, and she began to calculate on the paper.
In fact, this question is a power of 2 problem in modern times.
Put 1 grain of rice on the first chessboard square, which is 2 to the power of 0;
Put 2 grains of rice on the second chessboard square, which is 2 to the power of 1;
Put 4 grains of rice on the third chessboard square, which is 2 to the power of 2;
……
By analogy, the 2st square on the chessboard is 20 to the power of .
There were no calculators in ancient times, so Qianhuan used multiplication to calculate on paper herself.
Qianhuan figured out the answer after a while, and saw that the second incense stick had burned more than half way.
Emperor Jingxi urged, "Everyone hurry up and count, the second incense stick is almost burned out."
The people below had sweat on their foreheads. They didn't expect that a problem that looked so easy would actually be so difficult to calculate.
At this time, Qianhuan came out and said, "Your Majesty, I have figured out the answer."
Everyone else had a look of disbelief on their faces. The official who was the best at arithmetic said, "County Lady Jingrou, you are kidding. Of all the subjects I am best at, arithmetic is the best. I haven't figured it out yet, so you have already figured it out? You are not making up an answer, are you?"
"Whether the answer is nonsense or not, the Dongling Kingdom envoy will know after taking a look."
Having said that, Qianhuan handed the answer she had written on a piece of paper to the envoy from the Dongling Kingdom.
When the envoy from Dongling State saw the numbers written on the chart and compared them with the answers from his own country, he found that not a single number was wrong.
The Dongling Kingdom envoy was surprised. "How is it possible? Even if the best arithmetic master in Dongling Kingdom were to calculate this question, it would take most of the day to get the correct answer. The county lady actually figured it out in such a short time. It's incredible. Please tell me, how did you figure it out in such a short time?"
Qianhuan thought, humph, why should she tell Donglingguo her arithmetic method? Besides, even if she said she used multiplication, they wouldn't understand.
"Emissary from Dongling, I am so sorry that I cannot tell you how I calculated it. But I have given the correct answer. Please fulfill your promise and present the "Fishing Alone on a Cold River" to your majesty. Also, please give the East China Sea Night Pearl to this county lady."
Emperor Jingxi also said, "Yes, envoy of Dongling Kingdom, I am willing to accept the defeat and please fulfill your promise."
The Dongling envoy said, "Your Majesty, we are convinced of our defeat, and we will fulfill our promise."
The envoy from Dongling State asked his attendant to bring up the painting "Fishing Alone on a Cold River", and the eunuch took it and presented it to the emperor's desk.
Emperor Jingxi opened it and nodded happily, saying, "Yes, it is indeed an authentic work."
Emperor Jingxi couldn't let it go. He looked at it several times before reluctantly giving it to the chief eunuch, "Li Dequan, keep it for me and make sure to take good care of it."
"Yes, Your Majesty, I will keep it well for you."
Afterwards, the envoy from Dongling State took out an exquisitely carved wooden box.
He held it out with both hands and handed it to Qianhuan respectfully, "County Lady, this box contains the Night-Shining Pearl of the East China Sea."
Qianhuan took it and opened it, only to see a fist-sized luminous pearl in the box. The pearl was emerald green all over and had a faint luster.
Qianhuan was very satisfied with this night-shining pearl. She thought happily: With this night-shining pearl, she no longer needs to light an oil lamp when she gets up at night.