Chapter 35

While the competitors sat through the talks and lectures, in a temporary office at the host school the judges were working overtime on the papers.

Nearly four hundred students had sat it, all to be marked in two days. It sounds gruelling, and the volume is less than you'd think — chiefly because very few students solve all six problems, and maths has the merit that either you can do it or you can't, a sheet holding nothing but a formula or two being the easiest kind to mark.

A complete solution, on the other hand, slows everything down, because for those the judges apply their full attention, all but taking a magnifying glass to each step. Every mark awarded at a final is the product of that scrupulousness.

Marking is divided by question — some judges take the first, some the second, and so on — and since each problem needs a good deal of working, the answers are written on separate sheets, which saves the markers considerable trouble.

By the afternoon of the second day everything was marked. That wasn't the end of it, though: with the answer sheets separated, they had to be reassembled before the scores could be entered.

The judges were not new to this, and inside an hour they had everything sorted again.

The office had six computers, so six of them entered scores. One picked up a paper as before, saw the mark for the first problem and raised an eyebrow — a second full-marks answer, at this late stage.

He entered it, turned two pages, and his eyes widened at the second. Full marks again? With only a few papers left he kept going, and after the third his expression turned serious and he kept turning.

Having reached the last, he went back to the front and read the candidate details: room three, name Li Lan.

He picked the paper up and started reading it properly, and the judge opposite noticed. "Another full-marks answer taken your fancy, Teacher Wang?"

He knew Teacher Wang had a weakness: entering scores, he could never resist a proper look at a high or perfect paper. His argument was that although the candidates were only students, being students was exactly the point — you found genuinely interesting approaches in them.

Teacher Wang waved him over. "Teacher Zhao, come and look at this one."

Teacher Zhao wasn't especially interested, and he had a few papers nearly done; being caught by Teacher Wang meant losing ten minutes. "You go ahead. I've a few to finish, I'll look afterwards."

He'd expected that to settle it and for Teacher Wang to read it alone. Instead Teacher Wang got up and brought the paper over. "No — I want you to look at this student's paper."

Teacher Zhao glanced at it and found, unsurprisingly, full marks on the first problem — and something familiar about the paper. He checked the name. "Ah, Li Lan. I remember her." He'd marked a portion of the first problem, and she was one of the few with full marks, hence the impression.

Teacher Wang's hand didn't stop turning pages, which puzzled him. Was the second problem good as well? Since each judge marks only one question, nobody knows how the rest went until the scores are entered.

He was mildly surprised at the second. "Full marks on that too?" Uncommon, but not unheard of. Hardly cause for a fuss.

Teacher Wang kept going: third problem, fourth, and the last. By the end, Teacher Zhao was studying it as intently as he was.

Full marks. All six.

"That isn't possible," he said, looking at the total.

Teacher Wang was entirely serious. "Since the domestic final was aligned with the international format, very few students have taken full marks."

"Three years. The last full-marks final was three years ago — the year we did ourselves proud internationally, six gold medals and the overall championship." China has always been formidable in the mathematical olympiad, though the overall championship doesn't come every year.

"Quite." Teacher Wang said it with feeling. Since that year there had been gold medals but no championship in three.

A perfect score always draws attention, and before long the marking judges had gathered for a second review.

---

"Has anyone found anything to deduct for?"

"No. This paper is textbook — no, a model answer. I can't find anything."

"Nor me. And the reasoning is extremely clear. You can see the whole thing went down in one pass, no hesitation anywhere."

"Agreed. And the approach is rather unusual — an ordinary student wouldn't think of that theorem."

In the temporary office the judges gave their views on Li Lan's paper, and after a second marking it remained watertight.

Teacher Wang looked round at them. "If nobody objects, then Li Lan's is the only full-marks paper of this final."

"No objection. Let's settle it — it's about time we had a perfect score at the top." Several heads nodded.

Judges at an olympiad don't only mark. Anyone selected to mark has years of competition experience and is a senior member of the organising committee, so they have full authority over scores and placings at a final.

Teacher Wang adjusted his glasses. "Settled, then. I hadn't expected this year's perfect score to come from Henan — they've rarely produced results like this."

A judge who hadn't noticed where she was from was surprised. "Henan? I'd assumed one of the strong Zhejiang schools. That is unusual — you seldom see Henan even among the national firsts."

Another took it up. "Never mind national firsts. Their best result on record is a national second some years ago."

"Well, this has come out of nowhere. Let's hope they keep it up."

Having said their piece they dispersed, and Teacher Wang sat back down, entered Li Lan's score and carried on with the remaining papers.

---

On the final morning they assembled at eight, and unlike the previous days the students' faces fell into two camps: half who thought they'd done well and could hardly wait for the announcement, and half who thought they'd failed and were miserable about it.

For the two days before the results, everyone had the ease of an exam finished; as the announcement approached the nerves came back, and Li Lan's two companions were no exception.

The tall boy behind her stretched forward, saw her sitting beside Deng Hua looking calmly out of the window, and asked, "Li Lan, they announce the results at the ceremony. Aren't you nervous?"

She wanted to say she wasn't. Maths isn't like the arts subjects — compare answers afterwards and you know roughly where you stand. But faced with how tense he was, she hesitated. "A bit."

"Exactly," he said mournfully. "Maths isn't like an arts subject, you do know how you've done, and until they read it out you can't help being nervous. You just can't."

She looked at him with nothing to say. If you know how it works, why raise it? Reassurance? Seeing her turn back to the window, he assumed she was too nervous to talk and went to find the other boy instead.

Deng Hua, listening, concluded they'd be going home empty-handed again, sighed, and sent a text he'd already drafted: the ceremony ended at eleven, their flight was at three, and this year's results were no different from usual — as expected.

At half past eight the competitors and their supervisors filed into the hall, where a banner had been hung above the platform for the closing ceremony of the twenty-fourth national high school mathematics competition final.

At nine, everyone present, it began.

Unlike the ceremonies on television where prizes are given one at a time, the numbers here made that impossible, so after brief opening remarks the committee went straight to announcing this year's national firsts, seconds and thirds.

Thirds first: eighty-nine students, called up in turn to collect certificates. Some looked crushed; others took a third and remained full of fight. It was a national final, and the audience wasn't stingy with its applause.

Hearing two familiar names among them, Deng Hua abandoned the last of his hope. No miracle this year. Lost in his own thoughts, he entirely failed to notice that Li Lan hadn't moved.

Only once the thirds had all collected their certificates did it register that she hadn't left her seat at any point — and he assumed he'd missed her name. "Er — Li Lan, did I not hear your name? Have you been up and back already?"

Before she could answer, the tall boy, returning with his own third, glanced at him and blinked. "What are you talking about, sir? Li Lan wasn't in the thirds. We were just saying — she doesn't talk much but her results are genuinely good. She was first in the province, after all. A second's got to be a certainty."

Deng Hua truly hadn't pinned any hope on her, and looked at her with delight. "Is that right? I'm sorry, Li Lan, my mind was elsewhere. If you weren't in that list, you've got a second?"

The surprise had arrived too fast for coherence.

She was about to say something when the seconds began, and hearing the names and schools start, he spoke rapidly. "I wasn't paying attention before. I'll listen properly this time. We're not missing the seconds."

And he fixed his attention on the platform. Li Lan opened her mouth and closed it again.

The seconds were a longer list: a hundred and fifty students. He watched expectantly right up to the reader leaving the platform, and having heard her name nowhere at all, said vaguely, "Have I missed her name again?"

The two boys were less theatrical about it but equally lost for words, and equally surprised. "We didn't hear it either. So Li Lan is—"

"A first?" Deng Hua got the words out with difficulty.

At which she offered, without total certainty, "Probably. I did say it went all right."

The three of them looked at one another. They knew that — but who could have guessed that "all right" meant a national first? Surely it meant a third.

"Why didn't you say so properly? I thought we had three thirds again," said Deng Hua, somewhere between laughing and not.

"Mostly because I don't know what standard everyone else is at, so I couldn't be sure. It was a feeling. Though if I'm not in either of the first two lists, it should be a first." What she didn't say was that her target wasn't only a first but the top sixty, since only the top sixty are recommended to Tsinghua or Peking — and saying so would plainly not have been believed.

She'd barely finished when the firsts began: a hundred and thirty-four students this year, read from the bottom of the list upwards, with the top sixty entering the national training squad and winning recommendation.

The three of them listened hard. Not the first. Not the second. Not the tenth. Past the hundredth, and no Li Lan.

Deng Hua's hands closed together. Inside the top hundred?

Then inside seventy.

Then sixtieth — everything after this was the training squad — and still no Li Lan. The three of them looked at each other, confirmed they all meant the same thing, gripped hands and wanted to shout, but didn't dare in case they missed it. They shook their joined hands silently and waited.

Soon it was the top ten, and with her name still unread the three of them began to suspect the organisers had left her out and she was a third after all. Third place read out, and not her.

They've missed her, surely they've missed her. Second place now, and Deng Hua's hand was close to cramping from gripping so long. He was about to disentangle himself and offer to go and find the organisers with her when he heard a familiar name.

"And now, the only student to take first place with a perfect score in this competition — Li Lan, of the Henan delegation. Please join me in congratulating her."

Applause came down like thunder over a rising murmur of talk.

Li Lan smiled at the three stunned faces and went up. On her way, the announcer carried on. "We understand this was Li Lan's first mathematics competition, and she has taken full marks at the final at her first attempt — the first perfect score in three years. Li Lan's ability is evidently considerable."

Seeing her reach the platform, he added a question. "Does Li Lan have any secret she'd share?" The hall stopped clapping, hoping for something usable.

"Er." She hadn't expected that, thought about it, and offered, tentatively, "Do lots of problems? Lots of practice?"

He caught it neatly. "Quite so — practice in maths is well attested from every quarter. Hard work would appear to be the only condition for success."

She collected her certificate and walked back down through fresh applause.

At her seat, the three of them were still dazed.

A national first. Full marks.

You couldn't say nobody would follow her, but in Henan there was certainly no precedent — and by Deng Hua's reckoning it would be a decade at least before another student from the province matched it.

"You're an absolute monster," said the tall boy, coming to and thoroughly impressed. "When you came first in the league I wondered if it was luck. That was small-minded of me." People in his class called him a top student. Next to Li Lan he was nothing, and the real thing had been sitting beside him.

There's a saying that when the gap between two people is wide enough, envy has trouble surviving — as here, with two national thirds against a perfect national first. The gap was too wide, and being schoolchildren, envy struggled to take.

Deng Hua came to as well, grinning so hard his eyes vanished. He genuinely hadn't seen it coming: the student he'd rated least had produced an enormous upset. Never mind a national first — a perfect national first.

"Excellent. Li Lan, you've done the province proud." He laughed out loud, genuinely delighted. He hadn't been involved in competitions for many years, but he could feel how long Henan's committee had been swallowing this, and her result was a shot in the arm.

He got out his phone and wrote a new message: results in — Li Lan, national first, full marks — and typed it in a state of high excitement, and sent it with enormous satisfaction.