From child prodigy to chief scientist

Chapter 117 It's settled, it's settled.

He had already deeply memorized what those American team members had just said.

He's determined to show them the true strength of the Chinese team at this IMO.

Xu Xiao wasn't worried about Pan Hong and Ge Xijie; both of them already possessed the ability to achieve a perfect score.

However, the other three teammates still have some problems to varying degrees.

Xu Xiao carefully analyzed each of their previous test papers, found out why they lost points, and explained the reasons from the root cause.

The three team members weren't embarrassed at all at being taught by Xu Xiao, a child.

After all, Xu Xiao's mathematical ability is undeniable, and everyone admires him wholeheartedly.

Xu Xiao's small-scale research projects were indeed very effective. He didn't just simply explain the problems; instead, he explained how to construct one's own problem-solving approach from each student's perspective.

Even head coach Fei Ran had never given them a similar feeling.

Two days later, the first day of the IMO officially began.

After two days of adjustment, the team members have recovered their physical condition and have basically adapted to the local time difference.

As per Fei Ran's request, everyone except Xu Xiao, who can answer the questions in English, must answer them in Chinese.

Although Pan Hong's performance in English was acceptable, it wasn't as fluent as Xu Xiao's, so using Chinese would have been a safer option.

No one had any objections to this arrangement.

After this period of intensive English training, they are all able to understand English test papers and have made significant progress.

As the exam was about to begin, each member of the Chinese team received two sets of exam papers.

One set consists of the original English exam paper, while the other set is a translated Chinese exam paper.

To save time, most team members chose to look at the Chinese test paper first. Only if they encountered any unclear meanings would they look at the English test paper for comparison.

Xu Xiao naturally didn't need to do that, since his plan was to answer in English anyway, so he directly picked up the original English exam paper: "Let a1, a2, ..., an be positive integers with 1 ≤ a1..."

Prove that there e ists a nonempty subset of these numbers who se sum is a

power of 2.

This is a number theory problem. Based on the given conditions, prove that you can select several numbers such that their sum is a power of 2.

This level of question naturally posed no pressure to Xu Xiao. After the bell rang to start the exam, he picked up his pen and began working on it.

We use induction:

"For n=1, a1=1=2^0, the statement holds."

"Assumetrueforn=k.Forn=k+1："

"If ak+1=2k+1, the first k numbers satisfy——————"

Using mathematical induction, Xu Xiao skillfully completed the inductive construction and proved the existence of the problem.

The last two questions were a bit more difficult, but they still didn't pose any problem for Xu Xiao.

Although he had done a very good job, it still took him more than an hour to solve the three problems successfully.

Normally, Xu Xiao would have already handed in her paper early by now.

However, this IMO was indeed very important, so Xu Xiao patiently checked it several more times, not letting go of any detail.

Seeing that there was still plenty of time left after the check, Xu Xiao decided to think about other solutions to each problem and start deriving them directly in his mind, trying to accumulate some fragments of inspiration along the way.

Xu Xiao and the other students handed in their exam papers only after the bell rang to signal the end of the exam.

After leaving the exam room, Xu Xiao met with her teammates and deliberately emphasized that everyone should not discuss the questions with each other, but simply forget what they just took the exam.

Even if we want to go over the questions, we should at least wait until after the exam the next day.

After lunch, everyone obediently returned to their rooms to rest and prepare for tomorrow's exam.

The questions on the second day were generally more difficult.

In particular, question 6, a number theory problem, not only tested the application of Fermat's Little Theorem, but also required candidates to construct a special infinite sequence, making it one of the more difficult questions among the final questions.

However, after these days of intensive training, none of the six Chinese team members were stumped by the problem, and they completed the proof in a clever and rigorous manner.

Emerging from the examination hall, everyone could finally unload the burden on their shoulders.

The six team members were finally able to get together and discuss the six questions they had taken in the past two days.

"The IMO questions seemed pretty easy this time; they weren't as difficult as the CMO questions from before."

"For today's question 6, is that infinite sequence constructed like this? —"

"Yesterday's third question should have involved summation and scaling using the condition yz≥1, right?"

Seeing that everyone's questions were a bit confusing, Xu Xiao simply relied on her strong memory to write down the questions and her solutions on paper.

Looking at the question that Xu Xiaofu presented, everyone felt that it was basically the same as the original question.

After verifying Xu Xiao's solution, the team members were in a very good mood.

"My approach to each question is similar to yours, and I don't think I made any mistakes."

"For this problem, could we first construct a similarity proof to demonstrate concyclicity, and then use a harmonic point sequence for derivation?"

"Holy crap, I think I got all six questions right!"

To Xu Xiao's great delight, none of the other team members showed any regret for getting the questions wrong after seeing their answers.

This proves that none of them were stumped by any of the questions, and their problem-solving approaches were all correct.

Even if they don't all get a perfect score, their scores will certainly not be low.

Seeing this scene, Fei Ran knew that the team's first place was definitely in the bag.

The rule for 1M0 is that each question is worth 7 points, with a total score of 42 points.

Based on previous years' scores, if the team's average score can exceed 35 points, winning the championship is basically not a problem.

Based on their earlier score estimates, everyone's actual scores should be significantly higher than that.

Even if teams from other countries perform exceptionally well, it will be difficult for them to pose a threat to the Chinese math competition team.

After two days of examinations, this year's IMO has entered the marking phase.

Based on past practice, the marking process usually takes three to four days to determine the final scores and awards.

During this period, the organizers did arrange some other activities, but overall the schedule was very flexible, and each national team was fully able to organize some activities on their own.

Team USA has already organized a pool party where the players swam and had water fights to release the stress of their previous exams.