How to break into a math book

Tu Hua couldn't help but fell into deep thought. This question seems to have many known conditions, but in fact there is no most critical condition.If the monkeys told him how many fruits were left in the end, he might be able to deduce an accurate number, but according to the current distribution method, there are countless possible results.

Because the monkey only told him that the pile of fruits was eaten by five monkeys, and then divided equally, without specifying the specific number in a certain link, that is to say, there was a lack of an accurate limiting condition.

Tu Hua decided to sort out the clues first, and then try to find a way to confirm the limiting conditions of this pile of fruits.

He was not good at mental arithmetic, so he picked up a wooden stick and squatted on the ground to write down his thoughts.

First of all, the number of this pile of fruits can be divided into 5 parts and one more, which means that if there are 4 more fruits, this pile of fruits can happen to be divided equally.So assume that the number of fruits after giving 4 more fruits is A.

那么第一个猴子过来时把果子均分成5份,拿走了一份之后,剩余的果子数量为A×4/5；第二个猴子再次均分，并且拿走了一部分之后，剩余的果子数应该为A×4/5×4/5；同理，第三个猴子拿走了属于自己的那份果子之后，剩余的果子数量是A×4/5×4/5×4/5；第四只猴子取走之后剩下的果子为A×4/5×4/5×4/5×4/5；最后一只猴子取走之后剩余A×4/5×4/5×4/5×4/5×4/5。

所以依据上面的推算，所有猴子都拿完之后，果子的剩余数量是A×（4/5）^5,也就是A×1024/3125。

But since the monkeys did not give any limiting conditions, there are countless ways to round the number A of this pile of fruits. Of course, the smallest one is exactly 3125.

And if the distribution is based on the total number of 3125, after the fifth monkey takes his share, the number of remaining fruits is 1024, and these 1024 fruits are the remaining four shares after being divided into five, so The number of fruits taken by the fifth monkey happened to be 1024÷4=256.

Tu Hua wrote down this number. He must find a way to confirm the number of a certain batch of fruits to the monkey group, otherwise he will never be able to calculate how many fruits there are in total.

Tu Hua looked at the monkey leader: "Is the last tribal leader who took the fruit here?"

The old monkey brought a stronger monkey from the group of monkeys: "That's him."

Tu Hua asked, "How many monkeys are there in your tribe?"

Finally, the leader of the monkey group who took the fruit said: "There are more than 50 monkeys in our tribe, and everyone has already distributed the fruit."

"So how many did they get?"

The monkey scratched its ears and cheeks for a while, and finally remembered: "Each monkey got 4 fruits, and some of them were not enough, so I distributed those fruits to the children."

There are more than 50 monkeys in total, and each of them gets 4 fruits, and some of them are not enough... This obviously fits the number 256!

For the rounding of the number result of A×1024/3125, A equal to 3125 is the smallest answer, that is to say, the number of fruits obtained by the fifth monkey is 256, which is the smallest integer result. If the number is larger, it is obvious It doesn't fit the description of the fifth monkey who took the fruit to his tribe.

So according to various known conditions and reasoning, A=3125 is the correct answer.

But at first when making the assumption, Tu Hua set the condition to add 4 more fruits to this pile of fruits to ensure that they can be divided equally, that is to say, the real number of fruits should be 3125 minus 4 , that is 3121.

"I know the answer." Tu Hua looked at the digital code in the old monkey's hand, "The total number of fruits in this pile is 3121."

The old monkey pondered for a while, then called the five monkey leaders over, and confirmed to them one by one according to the results of Tu Hua's analysis, it was indeed correct.

The group of monkeys immediately cheered. Monkeys are animals that pay great attention to the hierarchy and yearn for fairness. After learning the real result, they all expressed their willingness to return the fruits they got and redistribute them.

Everyone is happy.The old monkey happily handed the digital password to Tu Hua: "Thank you!"

There was a note stuffed in the glass bottle, and Tu Hua quickly opened the bottle to see what was written on the note.But the moment he unfolded the note, he fell into a cloud of fog again. The number on this note was simply garbled: [236889007589086].

Tu Hua looked at the string of numbers longer than the phone number with a splitting headache: "What does this number... mean?"

Su Gechi smiled meaningfully, and did not intend to reveal any details.

Tu Hua stuffed the note into his pocket dejectedly, ready to find the next password.After all, there are a total of five such passwords. Maybe when the five passwords are collected, the mystery of them can be seen?

While comforting himself like this, Tu Hua walked into the depths of the forest.

But after wandering around the island for a long time, he walked almost all the places where there might be clues, and found no abnormal information.So Tu Hua was going to take the garbled code to meet up with his teammates to see if the others had found all the information.

When he returned to the beach, Shen Siyi, Sun Wei and Wang Boyu had already arrived and were discussing something together.Tu Hua quickly handed over the digital code he found: "I only found one."

Shen Siyi took the note in his hand and frowned, "Sure enough, it's similar to ours."

Sun Wei continued: "We found three pieces of information in total, but they were all strange numbers."

She opened the three pieces of paper, and saw three strings of numbers written on them: [1066] [8098] [66889006].In addition to the [236889007589086] obtained by Tuhua, these four strings of numbers are more like a phone number.

Tu Hua was puzzled: "So the last piece of information... didn't we find it?"

"No, I found it." Wang Boyu stood by the sea, fished out a drift bottle from the sea water, and handed it to Tu Hua, "It should be this one."

Tu Hua opened the note in the drifting bottle, and as a result, the prompt message became even more mysterious.

这上面并不是数字，而是一道奇怪的题目：【10=5020=15030=215040=21450那么50=】

Shen Siyi also leaned over to take a look, and he was also at a loss for having many ideas: "What the hell is this?"

Sun Wei frowned and said, "Could the answer to this question be a reminder to us?"

Tu Hua squatted down and copied the title on the beach: "I feel that this should be an assignment. The 10, 20, 30, and 40 in front of the equal sign are just equivalent to xyz unknowns."

Shen Siyi also nodded: "What Tu Hua said makes sense. This should be a kind of assignment, but there are certain laws between the assigned values, and there are also laws about the assigned numbers."

“10、20、30、40、50这些被赋值的数字以10为单位递增，”涂化分析道，“而被赋值的数呢？难道和数列中某些规律一样，存在倍数或者指数的关系？”

Sun Wei murmured: "Multiples and exponents... don't seem to have an obvious relationship. I think these numbers have one thing in common. They all have 0 at the end and can be divisible by 10 and 5."

Shen Siyi said: "And their digits are increasing, the first one is two digits, the second is three digits, the third is four digits, and the fourth is five digits, which proves that 50 The number represented should be a six-digit number."

Sun Wei agreed: "Yes, and the last digit of this six-digit number should be 0."

Tu Hua recorded everyone's conclusions on the beach, and wrote a 0 at the end of the six-digit number: "And the first four assigned numbers all contain the number 5, so will this six-digit number be 5 also appeared?"

Shen Siyi also squatted down, and wrote a 0 in front of the 5 written by Tu Hua: "According to the law of the first four numbers, 5 does appear in the place in front of 0."

涂化继续观察那几个数字，发现10被赋值为50，后面三个数字分别变成了150、2150和21450，后一位的数字必然包含前面的数字，并且会再添上一位。2150就是150前面一位加了个2，21450就是在2150中间加了个4，这是不是意味着这个第六位数字就是在21450的基础上另外添加一个数字出来？

Just when Tu Hua almost thought that he had found the meaning, Wang Boyu, who had been watching the busy scholars, suddenly asked strangely: "What are you doing? According to the assignment method of this question, isn't 50 equal to 10?"

Sun Wei looked up at him: "How do you know?"

Wang Boyu shrugged his shoulders with an innocent look: "The title itself said, [10=50], both sides of the equal sign are the same and can be converted to each other, so isn't the 50 he asked exactly equal to 10?"

The three people who did the math for a long time: ...

Wang Boyu scratched his head innocently: "What's wrong? Isn't it right?"

The three looked at each other, and Tu Hua was the first to break the embarrassment: "It seems that every time... Comrade Wang Boyu helped us break the situation."

Shen Siyi also nodded in agreement, and saluted the nose of his plane: "Yes, yes, yes, after all, you can see far from standing tall."

Sun Wei frowned: "Although the answer is far-fetched, it seems to be like this. Both sides of the equal sign are completely equal, and 50 is indeed equal to 10. But what is the significance of setting this question?"

Tu Hua glanced at Su Gechi, who was gloating at the side, he had known for a long time that Su Gechi liked to engage in this kind of low-IQ reversal, deliberately tricking people into it, and said helplessly: "It's the same as last time, I guess Let's get out of the math."

Looking at mathematics in mathematics, it is obviously something that belongs to mathematics, but it often has a surprising side. Su Gechi really likes this kind of reversal.

Tu Hua stood up, kicked over all the shame calculus that the three of them had just written on the beach, and then wrote a big "10": "So this last message is 10, right?"

孙维把剩下的四条信息依次摆在地上：【10】【1066】【8098】【66889006】【236889007589086】，这五串复杂的数字到底想说明什么？

According to the original rules of the checkpoint, they need to judge a sequence based on these five digital codes. Do these five digital information contain any rules and conditions for the sequence?