"Does China still insist on families having only one child?" asked the e-mail.
The panel answered questions on everything from Aids to Taiwan
"No," said our panellists, as we recorded a unique edition of Talking Point from Tsinghua University in Beijing.
Fortunately, we had an audience of students, so I asked them.
"How many of you are the only child in your family?"
Nearly every student in the audience (and one of our panellists!) raised their hand. It was a far better answer.
What did the students themselves want to know? They asked questions about the environment, Aids, and about travelling overseas.
Did the panellists think it was a good idea for Chinese students to spend time abroad? "Yes", was the answer.
So, again, I asked our audience, "How many of you would like to travel abroad?"
Many Chinese children have no brothers and sisters
There was much uncomfortable shifting in seats, and nervous glances, as they tried to work out what the acceptable response would be.
Eventually, a few hands went up, followed by a few more.
This was all new territory for them, and for us.
No one had vetted our e-mail questions, and we got answers to them all: Taiwan, Tibet, human rights, multi-party democracy.
A snapshot, perhaps, of how China is opening up - loosening the controls, experimenting with a greater degree of freedom.
Although when I watched the recording transmitted in China, to the handful of people who are allowed to watch the BBC, the e-mails on Taiwan and human rights were both blacked out.
It was the end of a fascinating and complex week in China, during which, among other things, I acquired a new name from the market traders just down the street from my Shanghai hotel.
"Hello," they greeted me as I walked by. "Hello, Bagwatchdvd ..."
Then it dawned on me: bags, watches and DVDs are what they sell, not what they call their customers.
Shanghai's built environment is changing rapidly
Prada and Gucci bags, Rolex watches, brand-new Hollywood movie DVDs - not one of them genuine, not one of them what they purport to be.
What you see is not necessarily what you get in China, and after 10 days there, I'm still not sure how much to believe of what I saw.
Gleaming glass and steel skyscrapers in Shanghai?
Real enough, of course, but are they symbols of real economic prosperity, or of an unsustainable property boom, built on blind faith and dodgy loans?
Yes, China is booming - just look at the label on your camera, your TV set or the trainers on your feet.
But how much of your money is reaching the people who made them? How much real prosperity have China's 900 million rural dwellers seen?
And although people are certainly happy to talk openly to foreigners in a way that they certainly wouldn't have been 20 or 30 years ago (or indeed wouldn't be today in many other one-party states), I didn't hear anyone say anything really disobliging about the Chinese Communist party.
I saw a show village with villas fit for Californian millionaires - perfectly average homes, I was told - and met a farmer in the company of no fewer than nine local party officials.
On the other hand, we had lively debates on air, and no one seemed unduly concerned about the prospect of a late-night knock on the door from the security men in leather jackets.
China is a land of contrasts and contradictions, wherever you look.
A Communist party running a capitalist economy, an ancient culture now adapting to become a high-tech economic miracle.
Puzzling, fascinating, intriguing, bewildering.
I think it is time I went back.
You can hear Robin chair a special edition of Talking Point, where we put your questions to Lei Xiong, Director of the Chinese News Agency and Professor Xiguang Li of Tshinghua University, Beijing.
Watch Talking Point