How to break into a math book

Before the game officially started, Su Gechi explained the ins and outs of the matter to Tu Hua.

After the exit of the [Life and Death] level was closed, Su Gechi could not get out. The level created by the virus not only restricted the challengers, but also blocked the NPCs that originally belonged to this game.

But Su Gechi found that although he was trapped in the level, he could transfer to the level where he participated in through the network line, and as long as he still encountered Tu Hua in the level, he could accompany Tu Hua as a prop come out together.

In the end, the two really wanted to go together, and met unexpectedly in the [Mathematics Friendship Contest].

It took a while for Tu Hua to realize that he plunged headlong into Su Gechi's arms under his excitement, and quickly distanced himself from him. Fortunately, everyone didn't seem to notice anything unusual, except for the five people in the opposite team who were aggrieved. out of sight.

Su Gechi said: "Don't worry about this level, the virus has not invaded, and you will pass the level safely."

Another boy from the other team seemed to be dissatisfied with the "boyfriend is the referee" game rule: "You know them, so you must guarantee them pass the level, isn't it too unfair?"

Su Gechi smiled and opened his arms to him: "I won't do anything that violates the principle of fairness. If you think it's unfair for me to hug him just now, I can hug you too."

Boy: "...Forget it."

The game starts on time.

第一轮，涂化队和对方队伍必须各派出一个人进行单独对抗,对抗胜利者可以查看那个28位数中的任意3-5位数字，而失败者将会被直接淘汰。总共有五轮对抗机会,每个队员只能被派出来一次,只要有人回答出来这个28位数被396整除的概率即可结束游戏,答对的队伍直接通关,没有答上来的队伍将会被淘汰。

The title given by the confrontation system in the first round was [card game].

It is impossible to judge the content of the confrontation just from the title of the title. Tu Hua doesn't know the level of the opponent's team. Logically speaking, Tian Ji's horse racing principle should be used for this kind of round-robin competition. The five people don't seem to be teammates like them, they seem to be temporarily combined after entering the game.

In this way, their understanding of each other and the cohesion of the team must not be as good as Tu Hua's team, which made Tu Hua feel relieved.

Because there are many boys in the team, Tu Hua originally wanted to send a boy, so that he could have an advantage if he encounters any physical confrontation. Unexpectedly, Sun Wei took the initiative to ask Ying: "I will come first this round."

On the opposite side, they saw a girl coming out from Tu Hua's side, and they also sent a tall girl out.This girl was about the same height as Tu Hua, and she stood in front of Sun Wei with a strong aura.

However, Sun Wei completely turned a blind eye and still had that indifferent expression on his face.

Su Gechi looked at the two with a smile on his face: "Are you ready?"

Hearing a "bang", as if by magic, the basketball court instantly turned into a bustling high-end casino. Su Gechi was wearing a black suit, dressed like a casino waiter, and there was a green card in front of him. There are 4 stacks of cards on the table.

This scene is simulated very realistically, there are other NPCs on other tables around, and melodious music is played in the whole hall, looking around, the people on the field are either rich or expensive, as if they really came to Macau Same.

Su Gechi held a long strip of cards in his hand, pointed to the four stacks of cards in front of the two, and began to introduce the rules: "Here are four stacks of cards, each with seven cards, and the first seven cards have all points. It is 4, the points of the second pile are all 4, the third pile is 7, and the fourth pile is 1 points. Now you need to take turns to draw cards from these 2 piles. When the sum of the points of all the cards you take out is At 3, the last player to draw a card wins."

In fact, this is a very simple game. Two challengers take turns to take cards, and the game ends when the sum of all the cards they hold reaches 27 points. That is to say, if you want to win, you must ensure that you can get Make the points become 27 points of cards at the end.

And here there are only four kinds of cards in total, the points are 1, 2, 3, and 4. It seems that there are many ways to form 27, but in fact, you only need to get the decisive 2.

27 is composed of 252. For the four numbers 1, 2, 3, and 4, if you want to use two cards to form 7, you only need a combination of 3 and 4, but if you want to form 5, it is very easy.That is to say, as long as the person who takes the card first takes a 2, no matter what card the second person takes, when the first person takes it again, it is enough to form a multiple of 5.

Because there is no number greater than 5 among these four cards, if you want to form a 5, you must take the card twice, so as long as the first hand takes the card with a point of 2, no matter how the second hand takes it, it will not be able to come back.

So this is actually just a game where the outcome is determined by who comes first. Of course... all challengers must think of this.

Tu Hua looked at the two people on the stage, Sun Wei's expression was still calm, this game was somewhat similar to the game of ten sons they played with the Pharaoh in the pyramid, so Tu Hua was sure that Sun Wei must know the solution.

But that's not necessarily the case with the tall girl on the opposite side.Although she has an overwhelming advantage in height and momentum, her expression seems to be confused, her fingers are stippling on the table, as if she is calculating something.

However, this does not mean that they can take it lightly. Sure enough, Sun Wei asked aloud: "How do you decide the order of taking the cards?"

Su Gechi took a dice from the corner of the table and placed it in the center of the table: "Throw the dice to decide, the one with the highest score gets the card first."

Without any hesitation, Sun Wei grabbed the dice and threw it out—four o'clock.

The points are not too big, but as long as the girl opposite is not too lucky, she still has a chance to win.Sun Wei looked up at the tall girl, and stretched out his hand to signal, "It's your turn."

The girl seemed annoyed because she hadn't figured out a countermeasure yet, and she seemed a little irritable.She casually grabbed the dice and threw it out. Perhaps because of her strength, the dice actually spun several times on the table, before it finally settled down.

Ended up at six o'clock.

The members of the Tuhua team immediately died down, and even Sun Wei, who had always been calm, showed a gloomy cloud on his face.The opponent got the upper hand, that is to say, if the opponent can find the way to solve the problem, Sun Wei will lose this game.

But the tall girl didn't seem to be happy about getting the upper hand, her brows were still furrowed.

She thought for a long time, and then took a 4-point card from the 4 piles of cards and placed it between the two of them.Sun Wei glanced at her incredulously, and then took a 3-point card.

Although he didn't get the upper hand, he was lucky to meet an opponent who didn't understand the rules.Several people watching the game from the opposite team seemed to be dissatisfied with this girl, but she didn't expect that she couldn't even think of the most basic order of the game.

The sighing voice of her teammates made the girl even more stressed. She looked at Su Gechi with a sad face: "Am I going to lose?"

Su Gechi didn't answer her, but broadcast the points of the cards they both took out now: "Each of you took out a card, and the sum of the points now is 7 points, which is 27 points away from 20, please continue the game .”

The tall girl sighed, and took out a 1 this time.Sun Wei followed her and took a 4.

This poor girl didn't realize until now that it was originally her first hand, but because of a mistake, Sun Wei became the first hand, and the person who got 7 points in the end was Sun Wei, which means that no matter what card she takes next, Sun Wei will Take out a card that can make 5 points with her, and the remaining 20 points are finally achieved by Sun Wei anyway.

她终于绝望了，剩下的三轮随便应付着分别拿了2、3、1三张牌，而孙维则拿了与之对应的3、2、4三张。

In the end, it was Sun Wei's last 27-point card that made all the drawn cards into 4 points.

The game is over and Sun Wei wins.

The girl admitted that her skills were not as good as others, and that she hurt her teammates, so she turned around and bowed to her teammates, before turning into pixels and disappearing.

The level scene is back on the basketball court.

Su Gechi pointed to the 28 cards beside him, and said to Sun Wei: "This round, you can choose to turn over 5 cards."

只有答出这个28位数被396这个数字整除的概率他们才能最终通关。按照三个学霸最初的科普，想要这个数字被396整除，就要它分别能被4、9、11整除。

被4整除需要数字末尾两位数能被4整除，被11整除需要数字的奇数位之和减去偶数位之和的数能被11整除，而被9整除只需要这个28位数所有数位之和能够被9整除就行。

The conditions for divisibility by 4 and divisibility by 11 must wait until the number of digits is determined, but divisibility by 9 does not require these complicated steps.

The numbers filled in under these 28 cards are on the next screen, that is to say, as long as these 28 numbers are added, if their sum can be divisible by 9, it proves that the 28-digit number can be divisible by 9.

Tu Hua tried to add it, and found that the sum of these 28 natural numbers is exactly equal to 135, and 135 happens to be divisible by 9.

This problem seems to be another way.

This question seems to ask them to calculate a clueless probability, and gives 10 completely uncertain numbers, that is to say, to calculate the probability that these 10 digits can be divisible in countless combinations.

So if there are no unique conditions for this question, this probability may only be calculated by a computer.

According to the law proposed by the academic masters, this number happens to be divisible by 9. Does it mean that this number is actually divisible by 396 no matter how the uncertain ten digits are combined?

Tu Hua articulated his astonishing idea, and sure enough, he got approval.But it would be too hasty to judge that the probability of being divisible is 100% based on this alone, so they decided to verify it again.

Now that we have been able to prove that this number is divisible by 9, we only need to verify whether it is divisible by 4 and 11.That is to say, they only need to check the last two digits of the number to judge whether it can be divisible by 4; and to check all the numbers with odd digits, the remaining digits are even digits, so that they can judge whether the number can be divided by 11 or not. [-] divisible evenly.

After all, they only need to look at the 15-digit number and get a maximum of three rounds of victory to draw a conclusion.

So Sun Wei chose the last two digits, and the numbers in the first, third and fifth digits.

Su Gechi flipped the card over, and saw that the last two digits were 76, and the first, third, and fifth digits were 5, 3, and 3 respectively.

76除以4恰巧等于19，这就证明这个28位数正巧能够被4整除！

Tu Hua was secretly happy, the answer was one step closer to his guess.

Soon there will be a second round of confrontation, and Su Gechi announced the name of the confrontation game - [Year, Year, Year, Year, Year].

The person sent by the Tuhua team to join the battle was Shen Siyi, and the other side also sent a boy.The boy was wearing glasses, with a gentle appearance, he also looked like a top student.

Like the previous round, the game scene changed again, this time they came to the brightly lit ancient Chang'an streets.The surroundings are full of NPCs in ancient costumes. It seems that lanterns are being held on the quaint streets, and Su Gechi is also dressed as a scholar, standing under a lantern riddle stand, watching everyone.

He pointed to a pair of couplets hanging next to the palace lantern and said: "The flowers are similar every year, but people are different every year. Each word in these two sentences represents a number, and the same Chinese character represents the same number. It just so happens that these numbers can form two formulas: year x year = similar flowers, year ÷ year = person ÷ difference, please judge what number each word represents, and the one who answers correctly wins."

Shen Siyi and the other student bully were already deep in thought, but Tu Hua couldn't get into the topic for a long time.

Because Su Gechi's appearance as an NPC is too distracting.

He was wearing a plain white robe, holding a folding fan in his hand, and his long black hair was tied with a white jade hairpin, exposing his smooth forehead.There are only eight big characters in Tu Hua's head at this time: the face is like a crown of jade, and the country is beautiful.

Su Gechi seemed to notice his gaze and smiled at him.

Tu Hua suddenly felt blood rushing up, but his eyes were still reluctant to move away from him.If Su Gechi was really born in ancient times, he must be a well-known handsome man, right?It is estimated that all the girls in a radius of a hundred miles are rushing to marry him...

Thinking of this, Tu Hua suddenly felt a little disheartened. In real life, Su Gechi is also a handsome guy. He looks good, has a successful career, and is still very young. Even if he doesn’t have a girlfriend, he wants to be with him. There will certainly not be fewer people.

As for myself... I can only have a relationship with him that is nothing but a game, or a childish relationship with math problems.

Tu Hua suddenly felt that life was a bit sad.

Although he was wandering all the time, Shen Siyi who was sent out to answer the questions was not inferior at all.

[The flowers are similar every year, but people are different every year] Each character in this sentence represents a number, and the same Chinese character represents the same number, that is to say, there are "year" and "year". Words are repeated.

The equation given in the topic is a multiplication and a division, and the calculations are based on the two numbers "year" and "year": year × age = similar flowers, age ÷ year = person ÷ difference.

First of all, it can be concluded that "Year × Sui Sui" is the multiplication of two digits with the same single digit and tens digit, and the three digits of "similar flowers" with different ten and hundreds digits are obtained; "Year ÷ year" is the division of these two two-digit numbers, and finally a number less than 1 is obtained, because the one-digit number of "person" divided by the two-digit number "different" must be less than 1.

Next, use the ten natural numbers from 0 to 9 to apply and exclude.

First of all, neither "year" nor "year" can be 0 or 1. If it is equal to 0, then the multiplication result is also 0, and the three-digit number will not appear; if it is equal to 1, then in "year × age" "In this multiplication, the number 11 will definitely appear. When the two-digit number with the same digit as the tens digit is multiplied by 11, you will inevitably get a three-digit number with the repetition of the digit and the digit of the hundreds. This does not conform to the "similar flowers" three word situation.

Next, assume that one of the numbers in "year" and "year" is 2.If "year" is equal to 2, then "year" cannot be repeated with it, so the minimum value of "year" is 3.

22×33=726，也就是说“花相似”三个字代表726，这样“相”字的2就与“年”的2重复了，所以“岁”不能等于3。

而22×44=968，22÷44=5÷10，恰巧与题目条件相符。

Shen Si Yi used almost less than 20 seconds to think about the result. He raised his hand first and said to Su Gechi: "I know the answer."

His opponent was still in a dazed state, watching him dumbfounded and saying the answer: "Year=4, age=2, flower=9, appearance=6, appearance=8, person=5, not=1, same=0."

So Tu Hua admired Su Gechi's ancient costume for less than a minute, and the scene returned to the basketball court.

The boy on the opposite side was directly eliminated. Although his teammates regretted it, they had nothing to say.It's not that their players are too weak, but that their opponents are too strong.

Shen Siyi looked relaxed, looked at Su Gechi and said, "How many cards can I turn over?"

Su Gechi shrugged: "Originally, you could only turn over 4 cards this round, but you answer the question too fast, and you can be rewarded for turning over one more card."

于是沈思易顺着上一**家的思路，翻了接下来的几个奇数位的牌，第7位到第15位的奇数位上的数字分别是：8、2、9、6、5。

The opponent seemed to have discovered the pattern of their flop, and there was a lot of discussion on the sidelines.Tu Hua was a little worried. The opposing team seemed to have some masters, and they would not be ignorant of the rules of divisibility, so even if they hadn't won the duel, they could still tell from Tu Hua's flop that the number was 396. probability of divisibility.

If you don't start early, it is very likely to make wedding dresses for others.

"I don't think they have thought of the divisibility law." Tang Bo analyzed, "After the first two rounds, they have seen that their team's winning percentage is very low, and the possibility of them winning the next match is very small. If they have made The same guess as you, in order to reduce casualties in the team, they will definitely say 100% of the answer."

"Because this is not a desperate move, the answer has been confirmed by two-thirds. But they still hold back, which proves that they don't actually know what the answer is."

Tang Bo's analysis is very reasonable, but it doesn't mean that Tu Hua and the others can tell the answer to their guess right now.They have to play another round of confrontation to determine the answer.

In this round, Tu Hua decided to play in person, and the boy on the opposite side was the boy who questioned Su Gechi in the first place.

The name of this round of competition is [Fendouzi], and Tu Hua couldn't help thinking of the prison Fendou game he met in the virus checkpoint, and his back was a little cold sweat.

But this game is obviously much simpler.

The game scene has not changed this time. They are still on the basketball court, but there is an extra table in front of Su Gechi, with 4 cloth pockets on the table and 9 beans beside it.

Su Gechi explained: "This game is very simple. Whoever figured out a way to put 9 beans into the four pockets first, and ensure that the number of beans in each pocket is an odd number, can win."

It is simply impossible to divide 9 beans into four parts and ensure that the number of beans in each part is an odd number.Not only did Tu Hua feel confused, but the boy next to him was also confused.

9 beans are divided into 4 piles, there must be an even number among them, even if he divides into three piles, put 3 beans in the first three pockets, and put nothing in the last pocket, it is still wrong, because 0 is also even.

Tu Hua stared at the 9 soybeans on the table, feeling very upset.Why are you so perverted every time you encounter a topic related to beans?

Seeing that the two of them couldn't think of an answer for a long time, Su Gechi comforted him: "Think carefully, don't panic."

Tu Hua tried his best to calm himself down. This kind of question is obviously the most suitable for him. It seems unsolvable, but in fact there will definitely be an exquisite answer.

Tu Hua analyzed the rules Su Gechi said word by word, his eyes kept searching the table.Apart from the 9 beans, the only information on the table is the 4 cloth pockets.

Put the beans in each of the 4 cloth pockets...cloth pockets!

So the trick is not to divide the 9 beans into 4 piles at all, the focus is on these four cloth pockets!

Tu Huafan came to his senses, raised his head excitedly and said to Su Gechi, "I know the answer!"