Chapter 32 Jingguo's most difficult permutation and combination problem



Did Baili Tang want to tell him through this childish tiger-eating chess game that if he couldn't even beat him with this kind of chess, then he should stop opposing him?

Not to mention that Chao Hong had such an idea, Lord Zhang, General Meng and others all had the same idea.

"Winning a game is just a coincidence." Chao Man'er pouted.

"Are you dissatisfied?" Baili Tang asked her. He was answered with another cold snort, "Xiao Lian, play a game with her!"

"Xiao Lian obeys!"

Okay! Then I will defeat this little maid first, and then defeat everyone else! Chao Man'er thought!

The ideal is like Baili Tang’s waist, but the reality is Liang Qiuyu’s slim waist!

After just over thirty rounds of the first game, Chao Man'er lost.

Unconvinced, she played another round, but unfortunately lost again.

Girls are naturally shy, let alone in front of so many people!

Soon, Chao Man'er lost all hope.

No matter whether she or Xiaolian plays first, there is only one result - loss!

"You must have cheated!" Chao Man'er was so angry that she tore up the paper!

Everyone was stunned by what they saw.

Chao Hong was thinking, is this my precious daughter? She lost the game of chess, and her character as well. You've completely disgraced me as a father!

Liang Qiuyu and the others didn't say anything. Xiaolian, who won the game, was neither arrogant nor impatient, and stood aside in a well-behaved manner.

"Hahaha. You seem unconvinced. How about I give you a few questions?"

"Come on!" Chao Man'er was an impatient person.

"Let's make a bet. You and Xiaolian have to answer this question together. No one else can help you. If you beat Xiaolian, I can agree to a reasonable condition. If you lose, go back with your father and study this tiger chess game carefully. Don't come to my palace, lest we all meet and get upset!"

Baili Tang doesn't like Chao Hong and his daughter, they are very annoying.

Then don't blame me for not talking about it in front of relatives.

No matter what the question was, Man'er would definitely lose. How could Man'er compare to the clever little girl like Bingxue? Chao Hong knew this better than anyone else. He knew his daughter too well. He usually asked her to study more, but she never listened.

So Chao Hong said, "Sure. I can join Man'er's group. Meng Fang can join her group."

"Why me?" Meng Fang didn't want to join in. His Majesty would ask those difficult questions later, and how would he answer them? Chao Hong was sure he was a military commander!

"General Meng, what are you afraid of?" Lord Zhang patted General Meng on the shoulder!

"Master Zhang is a top scholar, well-educated and talented. You will not let an illiterate fool off..."

"It's happily decided like this." Baili Tang said, "It's agreed that no one can give any hints to anyone except the person answering the question. Anyone who breaks the rules will be punished with a hundred lashes!"

Eunuch Yang: Since that day, Your Majesty has always mentioned punishment. For safety's sake, I'd better keep quiet.

Lord Wang: Your Majesty, why hasn’t your board arrived yet? I just want to “carry out the execution” as soon as possible so that I don’t have to live in fear and anxiety all day long!

Liang Qiuyu said with a smile, "Your Majesty, please tell me the question!"

"This question is too difficult. I'm afraid some people will say I'm deliberately making things difficult for them! It's a headache!"

"Speak!" Chao Man'er looked so cute when she was angry.

Baili Tang: "This is a big question, I will break it down into six smaller questions: Now there are 8 different balls, put into 4 identical boxes, each box contains at least 1 ball, how many ways can you put them?"

After hearing the first question, Chao Man'er laughed: "It's so simple, are you trying to insult my and my father's intelligence?"

Insulting someone's intelligence? Isn't that Baili Tang's golden line?

Baili Tang didn't bother to pay attention to her and continued to ask questions:

"8 different balls are put into 4 different boxes, with at least 1 ball in each box. How many ways are there to put them?

How many ways are there to put 8 identical balls into 4 identical boxes?

How many ways are there to put 8 identical balls into 4 different boxes?

How many ways are there to put 8 different balls into 4 identical boxes?

8 different balls are put into 4 different boxes. How many ways are there to put them?

This set of permutation and combination questions, consisting of 6 small questions, was exactly the same as the national examination questions from a certain year in Yu Tang's previous life. It was said that it stumped a large number of candidates at that time (mainly because it took too long to calculate carefully, which was not worth the effort), especially the liberal arts students.

The ancients also studied permutations and combinations. The earliest ones included the Eight Trigrams and Sixty-Four Hexagrams in the Book of Changes.

In the Song Dynasty, Shen Kuo's Mengxi Bitan recorded a series of questions:

In any two-way game, using four pieces, there can be eighty-one games.

If there are three square lines and nine pieces are used, there can be 19,683 games.

If there are four squares and sixteen pieces are used, there can be 43,467,21 possible games.

With five square lines and twenty-five pieces, there are eighty-four billion seven hundred and twenty-eight billion eight hundred and sixty-nine thousand four hundred and forty-three games.

"Mengxi Bitan" introduces algorithms such as powers, permutations and combinations.

Not every "ancient person" knew this kind of advanced mathematics. Chao Man'er could be ruled out first. Her father probably didn't understand it either. As for Meng Fang and Xiao Lian, it was uncertain.

Baili Tang felt that the only person who had a chance of solving the problem was Zhang Dongzheng.

But just now, there was a playful smile on Lord Zhang's face, but now he was very serious - he couldn't laugh anymore.

These 6 questions are too difficult!!

Only Chao Man'er said: "Simple, simple! It's so simple, Eunuch Yang, prepare the box and ball for me!"

Eunuch Yang looked at Baili Tang and would only do as he was told after Baili Tang nodded.

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