Xueba, I beg you to go and escort him quickly!

"Title: A positive integer is said to be "rising" if it has at least two digits in its decimal representation, and each digit is smaller than the digit to its right. How many such "rising" positive integers are there? "

Confused on the spot.

Those bosses, or the graduate students and Ph.D.s brought in by the boss, were all confused.

"Wait! Wait! Did it start right away?"

Xu Heng, "Yes, I answered it in the shortest time, and I joined the group! One question, one opportunity."

The group leader watched the whole process.

There are more than thirty people here!

Xu Heng, "I will come up with five questions, the five questions are over, and the quota for joining the group today is over."

"@All Members, hurry up, opportunity waits for no one!"

"@All Members, don't think about looking up answers online, it's impossible."

Xu Heng's words are sure!

The owner of the group naturally knows what Xu Heng's words mean, Xu Heng has solved the Olympiad questions before!

He made the questions, and he had the answers. Even if this group of people looked it up online, they couldn't find it after digging through it!

Unless it is true!

But the thinking of high school Mathematical Olympiad, if you do not study mathematics when you are admitted to university, even if you are a graduate student or a Ph.D., your heart will tremble.

No matter how good your grades are, you have thrown away mathematics for several years, or even ten years, how do you answer?

The college entrance examination questions may still have traces to follow, but the Olympiad competition questions will only make one head and two big.

Moreover, the question types of the Olympiad competition have changed a lot!

Maybe it was like this last year, but next year there will be a change in thinking, and different question types will appear, so it is a test of a person's true strength.

After seeing Xu Heng's first question, many people fell silent.

Xu Heng, "@All Members, the opportunity is here for you! Hurry up! Many people in our group can answer this question within 5 minutes! It's very simple!"

Simple? !

puff-

Many bosses looked at this question with blank faces, as if looking at a bible, what the hell?

"Can't you find it? Can't you find the answer online? What about similar question types?"

Both secretaries had their hands full.

"Boss, I really can't find out!"

Boss, "Are you sure you graduated from a graduate school? Did you falsify your academic qualifications? You can't do this question! I even lowered the difficulty! You said you are a high school student!"

"I'm furious!"

"Oh! Boss, don't be angry..."

Can the boss not be angry?

I earned millions and tens of millions, but ended up capsized here!

"Depend on!"

The veins on his forehead were throbbing, and he was gnashing his teeth.

What a shame!

With his appearance, the other bosses are not much better.

a building.

boss office.

"Call Secretary Hu to the office!"

"Yes! Boss!"

When Secretary Hu, who was wearing a OL professional narrow skirt and had a curvaceous figure, walked into the boss's office, she looked a little flustered.

"Boss...it's not good now...it used to be after working overtime at night...but now, my husband is still working overtime outside...this..."

The boss gave Secretary Hu a blank look.

"What are you thinking! I remember you graduated from the mathematics department of the university, right?"

Secretary Hu was stunned for a moment, the mysterious blush on his face was gone.

The boss immediately handed over the phone, "Solve this question for me!"

Secretary Hu, "???"

"Ah?! This... Boss, this... just let me go! I forgot, boss, please, don't torture me, I was wrong, I was wrong... You said Wherever it is..."

The boss had a black line on his face, "Get out! Get out!"

He was bored to death.

Looking at the question on the phone, I felt uncomfortable.

Depend on!

Never thought it was so difficult to get close to someone!

In my own capacity, as soon as I stop there, many people will strike up a conversation. It's good now!

Do the math!

Also calculate these things!

The key is that I don't know how to do it yet!

"Hehe! I deal with numbers all day long, but I didn't expect to fall into numbers in the end!"

The boss smiled wryly, "It's too embarrassing for him!"

"Leave the group!"

Both the group owner and Xu Heng can receive group message notifications that everyone has left the group.

The group leader immediately sent a message to Xu Heng's trumpet, "Xu Heng is great, absolutely!"

But someone still answered the question.

"The numbers in the positive integers that meet the conditions are all different non-zero numbers, that is, the binary or more than binary subsets of the set S={1, 2, 3, ..., 9}."

"Conversely, for each subset of binary or more than binary, arrange its numbers from small to large, and get a positive integer that meets the conditions. There are 29=512 subsets of S, of which there is only one There are 9 subsets of elements, an empty set."

"Therefore, there are 512-10=502 positive integers that meet the conditions!"

Xu Heng, "@集主, pull into the group."

"Second question: if the first digit of a six-digit number is 5, is it always possible to add six more numbers behind it, so that the resulting twelve-digit number is exactly a perfect square number?"

Nima...!

The corners of the bosses' eyes twitched, they were all dumbfounded!

"Where did this topic come from?"

"I can't find it on the Internet! It's really evil!"

"What and what is this?"

These bosses are proficient in "sophistication of the world", and they have long forgotten about learning.

Even if they were high-achieving students, they couldn't solve these high school problems.

"What the hell? It's a math problem again! Such a simple problem? How can it be so simple? Why can't I do it at all!"

"hiss……!"

In the group, someone has already wailed, "This question is too difficult! Are you sure it is a high school Olympiad question?"

Xu Heng, "Yes."

The group owner, "I think it's too difficult, maybe your level is not enough."

Everyone, "Group leader, you should be a high school student, right? You will?"

The group leader, "It's a very simple question! This question obviously doesn't work!"

"105 six-digit numbers with 5 as the first digit can be derived from 105 twelve-digit perfect square numbers. That is, there are 105 natural numbers n to satisfy."

“5×10（11次方）≤n2＜6×10（11次方）亦即7×10（5次方）＜n＜8×10（5次方）”

“由于7×105（5次方）与8×10（5次方）之间不存在10（5次方）个整数，故上式不可能成立。”

"That's right! It's that simple! Are you sure you are high school students?"

He was directly looked down upon!

Some bosses gritted their teeth, and through the screen, their voices squeezed out from between their teeth, "I am also the boss of three companies, and I was looked down upon!"

"Stinky boy! The future is long! Once you enter the society, you will know that it is useless to know these things!"

angry!

Withdraw from the group!

This method doesn't work, so I have to find another way.

This wave of ridicule caused many people to withdraw from the group.

The group leader said, "Eh... I accidentally calculated the answer to this question. It's really too simple. They don't know how to do it so simple. I'm worried for them."

Xu Heng didn't say much, "The third question is a proof question."

"Prove: If the integer coefficient quadratic equation ax2+bx+c=0 (a≠0) has rational roots, then at least one of a, b, and c is an even number."

When Xu Heng came up with a question, he came at his fingertips!

One question, after another.

The group owner knows how Xu Heng came up with these questions.

He took a deep breath and looked at the third question of the review group. He also took out a pen and paper and began to write and draw.

If the first two questions were too simple, then this question stumped the group leader and aroused his interest.

Even the group owner, who participated in this year's Mathematical Olympiad, started writing and drawing, let alone the bosses.

Inside the office.

And the boss yelled loudly, "Solve this problem! Promotion! Salary increase!"

But the group of graduate students in front of him looked bewildered.

Boss, "%￥#￥%..."

"Forget it! I won't struggle! I won't humiliate myself! Quit the group! Quit the group on my own initiative!"

A few more left!

Until the review group, there are only a few people left...  

The corners of Xu Heng's mouth were drawn, and he smiled.

Just about to switch the tuba, the group owner sent a message, "That... Mr. Xu Heng, this proof question..."

Xu Heng, "?"

Group owner, "I'm curious about the proof process."

Xu Heng, "..."

Group leader, "Please tell me!"

Xu Heng, "Assume that the rational root p/q, p, q are coprime integers, and substitute into the original equation to get a(p/q)2+b*(p/q)+c=0, so as to get ap2+bpq+ c2=0."

The group leader, "Hmm..."

Xu Heng continued, "If p and q are both odd numbers, then 0=ap2+bpq+c2 is always equal to a+b+c (mod2), so there is at least one even number among a, b, and c."

"If one of p and q is even, the other is odd. If p is odd and q is even, then 0=ap2+bpq+c2 is always equal to a (mod2), that is, a is even."

"do you understand?"