Four would be too few. Ten would be too many. Five or nine would presumably produce an unaesthetic, wonky effect.
So the smiling attendants on the test run of the Beijing to Shanghai high-speed rail link revealed precisely six to eight of their teeth to display their pleasure as the train pulled out of the capital. It had, admitted chief conductor Gao Dan, taken considerable practice; in some cases, with chopsticks jammed between their jaws.
Extending 820 miles (1,318km), and spanning seven cities and provinces, China's landmark line was built in 39 months at a cost of 221bn yuan (£21.4bn). But as those gleaming white teeth attest, no detail of this massive project was too minor to be subject to official scrutiny.
The new link not only slashes train times between the country's political heart and its financial powerhouse, it also proclaims its power and accelerated development. It is no coincidence that the line opens to the public on Friday 1 July – the 90th anniversary of the Chinese Communist party.
"This is the pride of China," said He Huawu, chief engineer at the ministry of railways, minutes before the train pulled out of Beijing South station at 9.01am.
It glided into Shanghai's Hongqiao station at 1.45pm, having briefly touched 190mph; usually it will restrict itself to 186mph. Officials said that 1,500 test trains had clocked up around 2m miles shuttling back and forth since exercises began in mid-May, but this was the first public glimpse of the flagship project.
China is building the world's largest high-speed network, with around 10,500 miles completed or under construction. It has said it plans to spend $30bn (£19bn) this year alone.
But the scale of its ambition has been brought into question by concerns about waste, corruption and safety – particularly since the railway minister, Liu Zhijun, was dismissed this spring for "disciplinary violations".
In March, China's state audit office said nearly $30m of funds for the line were embezzled or otherwise misappropriated during one three-month period of construction last year. The cases are under investigation.
But Hu Yadong, vice minister of railways, told a news conference last week: "We will not slow down the pace, and there will be no cut in investments."
The government has cut the top speed of the trains from 217mph to 186mph; a decision variously ascribed to safety concerns, environmental worries or simply a need to cut ticket prices by reducing fuel consumption.
Even so, the Beijing-Shanghai link halves the journey time by rail from around 10 hours – at its fastest – to just four hours and 48 minutes. It appears an easy sell for business people, delivering a smooth journey with mobile phone signals (and, soon, onboard Wi-Fi) and none of the hassle of airport security. Airlines are reportedly slashing ticket prices already.
Officials say they plan to run 90 trains a day, at 186mph and 155mph. Tickets for the fastest trains cost from 555 yuan (£54) for standard seating. Upgrade to business class, for 1,750 yuan, and you gain fully reclinable seats with individual entertainment systems. In first class, which is pitched between the two, you get Jackie Chan's The Spy Next Door on shared overhead screens.
Meanwhile, through the picture windows, labourers can be seen toiling in the fields. In one spot, three farmers in straw hats were dragging a plough through the rocky soil.
Given the uneven nature of development in China, some see the country's massive investment in high-speed rail as a folly driven largely by the desire for prestige. While this link along the wealthy east coast is expected to make money, others are struggling. Some suggest expanded flights and freight rail capacity would be more sensible ways to connect remote areas.
"[The network] will be a liability, not an asset, for China," Zhao Jian, a professor at Beijing Jiaotong University, told Reuters last week. He cited the example of a Henan-Shaanxi line, designed for 37 million passengers a year, which reported fewer than 2 million in its first six months of operation.
Others fear that poorer travellers – such as tens of millions of migrant workers – will struggle as expensive high-speed services replace much slower, but much cheaper, trains.
But supporters believe high-speed rail will help drive development in the poorer central and western regions, spreading wealth from the wealthy east and south.
No one is more enthusiastic than Xu Yifa, who spent the first six years of his working life shovelling coal – 8,000 tonnes in all, he estimates – into a steam train.
"We couldn't even have dreamed of this. It's hard to imagine China's railways could develop this fast," said Xu, now the deputy secretary of the Zhengzhou railway hub, as the train glided through Hebei province.
"It feels so smooth and comfortable. You can't compare it. [Back then in 1965] it was very shaky."
After almost half a century working on, driving and then overseeing trains, he was thrilled by the changes in China's railway system – and keen to share its benefits.
Beijing's ambassador to the UK suggested last week that Chinese firms could help build a high-speed line between London, the Midlands and the north, saying the country had "the knowledge, expertise and experience".
"Of course! There's no argument," Xu declared when asked whether Britain should buy Chinese.
"China should be the first choice."