How to break into a math book

Hundred chickens and hundreds of money problem!

Tu Hua and his teammates looked at each other, stepped forward and asked, "What problems did you encounter?"

The middle-aged man was holding a copper coin in his hand, and he frowned helplessly: "I'm the cook of Xu's mansion, my master gave me a hundred dollars to come to the market to buy chickens, and said that I must buy enough chickens. But this mother-in-law's chickens vary in size and price, and both of us were stumped by the price."

Shen Siyi asked the old woman: "Grandma, how do you sell this chicken?"

The old woman counted with her withered fingers: "My rooster costs 5 yuan, the hen costs 3 yuan, and the chickens cost 1 yuan. The chickens are enough for him to buy, but I don't know how to distribute them."

At this moment, the system prompt sounded suddenly, and the task rules of [Go to the streets of Ming Dynasty] were promulgated:

[Submission: Go to the streets of the Ming Dynasty for a walk]

[Rules: Find Xu Guangqi and help him uncover the round string seven-star array to pass the level.There is only one chance to decrypt, if the challenge fails, the whole group will be eliminated. 】

Tu Hua originally thought that the task of this level would be related to the Hundred Chickens and Hundred Coins, but who knew that the mission rules didn't even mention chickens.In this way, this street arithmetic problem obviously has nothing to do with Xu Guangqi, a scholar who compiled "The Big Test".

Just when they thought they had triggered the wrong mission, the middle-aged man who bought the chicken suddenly said: "Look at your attire... Could it be that you are here to visit our master?"

Wang Boyu asked strangely: "Who is your master?"

When mentioning his master, the middle-aged man was full of pride, raised his head and said loudly: "My master is Mr. Xu Guangqi! If you can help me solve the problem of buying chickens, I will introduce you! "

It turns out that they have already entered the mission plot!Everything went smoothly. It seems that if you want to find Xu Guangqi, you must first solve the problem of buying chickens.

A hundred chickens and a hundred coins was a difficult problem in ancient times, but for today's highly developed mathematics discipline, it is just a primary school Olympiad problem.Tu Hua quickly came up with the answer.

Using equations to solve problems is the most intuitive way. As long as x is the number of roosters, y is the number of hens, and z is the number of chicks, a set of indeterminate equations can be obtained.

Because the total number of chickens to be bought is 100, the first equation should be xyz=100, that is, the sum of the number of roosters, hens and chicks is 100.

The sum of the prices of all chickens is 100 yuan, a rooster is 5 yuan, then the total amount of money spent on buying a rooster is 5x, a hen is 3 yuan, the total amount of money spent on buying a hen is 3y, and a chick is 1 yuan Three, then one is one-third of the money, so the amount of money spent on buying chicks should be 1/3z.All the money spent by all roosters, hens, and chicks is 5x3y1/3z=100.

The title is simple, but the problem is that this is an indeterminate equation, which means it has three different answers. 100 money to buy 100 chickens, according to the solution of the equation, there are a total of three matching options.

The first type: 4 roosters, 18 hens, and 78 chicks; the second type: 8 roosters, 11 hens, and 81 chicks; the third type: 12 roosters, 4 hens, and 84 chicks [-] chickens.

Which of these three solutions is what middle-aged men need, they don't know.

But this is different from a math problem that requires a unique answer. This chicken buying incident has a scene, so the answer must be chosen according to the actual situation.

Tu Hua thought for a while, and said to the middle-aged man: "I don't know why Mr. Xu asked you to buy chickens? If you want to eat meat, I suggest you choose the third plan, 12 roosters, 4 hens, and 84 chickens." 4, because this kind of plan has more roosters and is suitable for eating meat; if you want to lay eggs, it is recommended that you choose the first plan, 18 roosters, 78 hens, and [-] chicks, because this plan has the most hens; If you want both meat and eggs, choose the second compromise."

The middle-aged man slapped his forehead, and suddenly realized: "When you said that, I remembered. A few days ago, the housekeeper said that the house lost a few hens, and the eggs are not enough recently. It seems that I should buy more hen!"

As he said that, the middle-aged man handed the money to the old woman, and took another cage to fill the hundred chickens he needed: "Thank you so much! I'll take you back to see the master!"

The Xu Mansion was not far from the market. Tu Hua and Wang Boyu helped the middle-aged man carry the chicken coop and walked for about 5 minutes to the gate of the Xu Mansion.

Xu Guangqi's mansion is not considered luxurious. It can be seen that he should be a person who is addicted to academic research and has no interest in eating, drinking and enjoying himself.Bypassing the carved screen wall at the entrance, the huge circular formation in the yard comes into view.

I saw an old man with gray hair pacing on the round platform with his hands behind his back, as if he was thinking about something.

The middle-aged man called out to the old man respectfully: "Master, someone is here to pay respects."

Xu Guangqi turned his head and showed a kind smile: "You are finally here."

As soon as he finished speaking, the circular formation platform began to vibrate violently, and the white marble patterns were staggered and reorganized to form a circular seven-star formation.The reason why it is called the Seven-Star Array is that six five-pointed stars are evenly scattered on the circumference of the array, and a stone platform with a five-star pattern rises from the center of the circle.

These seven star-shaped stone platforms are of different colors. From left to right, the position of Xu Guangqi's station is red, yellow, blue, pink, light yellow and light blue, and the one in the center of the circle is white.Because the six star-shaped stone platforms on the circumference are evenly distributed, the distance between each adjacent star is the same. The red star is symmetrical to the pink star through the center of the circle, and the red, white, and pink stone platforms are on the same straight line. Similarly, yellow, white, and light yellow are also in a straight line, and the blue and light blue stone platforms also correspond to each other through the white stone platform.

So what is the function of this [Circular String Seven Star Array]?

Just listen to Xu Guangqi said: "This round string seven-star array is actually a number maze. Each star-shaped stone platform represents a number. If you can accurately name the number represented by the seven stars, you will be rewarded when the seven stars are condensed."

Xu Guangqi took out a dice the size of a Rubik's cube from his cuff and threw it in front of them: "The center of the white circle is the starting point. You need to roll the dice in the order of white, red, yellow, blue, pink, light yellow, and light blue. The dice are You take a few steps at what time, and each of the five people throws once to make a round, and there are three rounds of chances in total."

"After each round, when there are people standing on the three stone platforms in the same straight line, one or more hints representing the number of this star will be randomly given out of the three stone platforms to help you solve the problem."

The rules are relatively complicated, and Tu Hua thought for a long time before he understood the extended meaning of this rule.First of all, all five of them will start from the white stone platform at the center of the circle, and the five of them will roll the dice in turn. When the dice comes out, they will walk to the corresponding stone platform according to the number of steps.If there are people standing on the three stone platforms on the same straight line, these three stone platforms will randomly give out prompts for filling in numbers. There may be only one prompt or multiple prompts.

They only have three rounds of chance. After three rounds, even if they don't get a hint, they must fill in the numbers represented by the seven stone platforms.

From this point of view, the seven-star array is a bit like a circular chessboard, since it is impossible for three of the six points on the circumference to lie on a straight line, which means that they want three points to appear in a straight line, Someone must stand on the stone platform at the center of the circle.

But according to the number of steps of rolling the dice, if they start from the center of the circle, it will never be possible to form a straight line at the end of the first round.Because the maximum number of dice is six points, and this is a seven-star formation, they can take up to six steps. According to the order of six steps, they can only reach the light blue stone platform on the circle, and they have to take another step to return to the starting point in the center of the circle.

This means that the system seems to have given them three rounds of chances, but only the last two rounds can actually be prompted.

Tu Hua was the first to pick up the dice and cast a number of 3.In order, he started from the white stone platform in the center of the circle, walked three steps, passed the red and yellow respectively, and came to the blue stone platform to stand still.

The second dice thrower was Sun Wei. She rolled a 2 and walked to the yellow stone platform.

Among the next few people, Wang Boyu and Tang Bo both rolled 6 and walked to the light blue stone platform one step away from the starting point of the center of the circle. Shen Siyi rolled 5 and stood on the light yellow stone platform.

At the end of the first round, no one has reached the center of the circle, that is to say, no three points are in a straight line.They lose their chance to get tips in the first round.

There seemed to be a tacit understanding, and none of the five of them spoke, and the second round soon took place.

At the end of the second round, five people were lucky to stand on two straight lines.Wang Boyu just took a step and stood at the center of the circle. Tang Bo stood at the yellow position, and Tu Hua stood at the light yellow position. The three of them stood on the straight line of yellow, white and light yellow; while Sun Wei, Wang Boyu and The three of Shen Siyi formed a straight line again, that is, blue, white, and light blue.

After the five people stood still, Wang Boyu at the center of the circle jumped excitedly: "Two! We have two straight lines! Does this mean that we can get at least two hints?!"

Just as he jumped up, the white five-pointed star under his feet slowly formed an opening, and an exquisite wooden brocade box rose from the stone platform.He almost stepped on the box, picked it up quickly and opened it, only to see a piece of white paper in the box, on which there was a line of small characters written with a brush: "Looking at the seventh floor of the towering tower, the red lights are doubling, with a total of 380 lights. Excuse me." How many lamps are there?"

"Is this the hint to fill in the numbers on the white stone platform?" Wang Boyu said with a mournful face, "How come there are classical Chinese texts in the math game that was agreed upon?"

Tu Hua has a good grade in Chinese, and he especially likes classical Chinese poems. This doggerel with hidden mathematical mysteries is actually not difficult, the translation is simple, and the difficulty of the topic itself is not high.

The general meaning of this poem is: There is a seven-story tower with a total of 381 lights on the tower. The number of lights on each floor is double that of the upper floor, so how many lights are there on the top floor.

If the guess is correct, the answer to this question should be the number represented by the white stone platform where Wang Boyu is currently.So as long as they know the answer to this question, they can be the first to obtain the number of the center of the seven-star array.