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

After all, this is the final question!

If you say two solutions to answer, can you answer with two solutions?

impossible!

They can't believe it!

This is the International Olympiad!

How could it be such a joke!

But Xu Heng remained expressionless and continued to answer the second question.

The following proves that for any...

According to the analysis of (1) (the first solution) in the first question, as long as [formula], B does not have a winning strategy, then when N is larger, it is obvious that there will be no winning strategy.

……

The meaning of mi here is for an integer i from 0 to n, after B asks a certain question, if A's answer for i is inconsistent with the set of times asked.

Since the meaning of mi is very important in order to understand this proof, I will explain it in detail: it can be understood in this way, mi is the assumption that x=i, then after A finishes answering a certain question asked by B, the number of consecutive wrong answers by A ; We know that A cannot answer wrong k+1 times in a row, so if for a certain i, mi≥k+1...

……

According to the previous analysis, B can't win anyway.The whole problem is proved.

Finish!

Xu Heng wrote another (2) second solution:

Note that p and q are real numbers satisfying 2qp, choose a positive integer k0 such that...

……

此时Pj+1=Dj+1,记y是根据(1)得到的序列;相应地,记z是甲回答“否”,Pj+1=DCj+1,根据(1)（第二种解法）得到的序列。于是……

According to the nature of the selected k0, we get min{T(y), T(z)}q2qk+pk2qk.

All answers are complete.

Xu Heng originally closed the test paper and was about to hand it in.

After all, Xu Heng wrote a full six pages for this last big question!

Two solutions!

Two questions!

Two complete sets of ideas.

The examiners were completely dumbfounded!

Their scalps are numb!

Although they couldn't understand it, Xu Heng's obvious two (1) and two (2) made them realize clearly that this must be the answer from two different ways of thinking.

Not only that!

There are two ways to solve the first question!

The second question, there are two kinds!

Simply inhuman!

They originally thought that if Xu Heng could answer the last final question, it would be enough to defy the sky!

But they underestimated Xu Heng's strength too much!

For the first question, Xu Heng gave two ways to solve the problem!

They were dumbfounded!

The frog in the well finally realized how powerful Xu Heng is!

But their shock is not over yet, or...their three views have been shocked to the top by Xu Heng!

Just in this case!

Xu Heng answered the second question!

When he solved the second question, he wrote the second (2)!

Rumbling--

!!!

Like a bolt from the blue!

Crack - boom boom boom -

Slashed the three examiners from head to toe!

They can be regarded as being shocked by Xu Heng!

The shock of this side has not had time to digest!

There's another wave coming!

What is this called?

Why wave after wave!

More than that!

It's more ferocious than the last wave!

This is simply a stormy sea!

Completely break the defense! ! ! ——

The three examiners almost collapsed to the ground!

They glanced at each other, and suddenly supported each other, their teeth clenched.

Looking at each other, it seems to say: Hey! MAN!hang on!Be sure to hold on!

Looking at Xu Heng again, their eyes widened.

Just like in a song: "Eyes stare like brass bells..."

Even buy Karma!Even buy Karma!Even buy Karma!

Shet!Shet! !Shet! ! !

Not human, this guy is definitely not human!

None of them wanted to admit that Xu Heng was really that strong!

Just when Xu Heng was about to put down his pen, close the test paper and leave.

Suddenly he stopped!

Three examiners, "!!!"

Xu Heng turned the test paper to the third question.

The three examiners were suspicious at the time, "Could it be that the answer is wrong?"

One operation is as fierce as a tiger, but the result is a dog by mistake?

???

The three examiners suddenly felt relieved.

They looked at each other, after all, this was the final question!

wrong!

It must be wrong!

But...Xu Heng didn't look at his own problem-solving process at all, but at the problem!

They ignored it!

Just when they were a little complacent, Xu Heng picked up the pen again.

He didn't alter any of the process, but at the end, he wrote another (1)...

This is the third one!

Geek!

Click! !

Geek! ! !

As soon as Xu Heng picked up his pen, he wrote down the third way of solving the problem!

At the same time, he murmured in his heart, "In fact, this decoration is to prove that a number that cannot be x can be found out of any 2 (k+1 power) numbers, that is, continuous k+1 is negated, and it is easy to prove..."

According to this idea, Xu Heng solved the first question for the third time.

After that, Xu Heng continued to answer the second question without stopping.

(2)!

This is the third time he has written it!

For any y, as long as y is not given a negative answer in K+1 consecutive inquiries, B cannot deduce that y is x or not...

Splendidly.

The third way to solve the problem!

All written!

This time, Xu Heng put down his pen and closed the test paper again...

This time!

The three examiners held their breath and didn't dare to move!

They are afraid!

I'm really scared!

They were afraid that the second Xu Heng closed the test paper, he would open the test paper again and write out a new method of solving the problem!

"hiss……!"

They were staring at Xu Heng!

Just look at Xu Heng!

At this moment, they forgot that they were examiners, where they were, and what they were going to do. They only remembered that they were going to stare at Xu Heng!

As Xu Heng closed the test paper, he slowly placed it on the examination table...

suddenly!

Xu Heng was stunned for a moment, then glanced at the test paper meaningfully.

Geek! ! !

The three of them subconsciously froze, they almost hugged each other!

And Xu Heng got up with a strange expression, he... chose to hand in the paper.

he's gone!

Just like that, he walked out of the examination room lightly!

This time, Xu Heng still took less than an hour.

As for the three examiners!

They were completely in no mood to think about whether to hand in the paper for an hour or not. They were completely overwhelmed by Xu Heng's three different solutions to the last finale question!

If you distinguish between the first question and the second question!

That is, for each question, three different solutions are given!

"."hiss……! "

They gasped, their faces pale!

It's as if a layer of white paint has been painted on the face!