I wanted to explain, but she wouldn’t let me. ‘Don’t say anything. You do your thing, I’ll do mine – there’s no need to explain. I’ve said everything that I want to: you can go now.’

I had to leave.

That evening after I got home I sat in my room and looked in silence at the memorial photograph of Xiaoyu. I was beginning to feel that I might have been too cruel to Huang Yiyi. In the photograph, Xiaoyu’s eyes were bright; only she and I knew the secret behind them.

I held Xiaoyu’s photograph, feeling absolutely heartbroken.

The only thing that cheered me up was that Huang Yiyi behaved completely differently after that, concentrating entirely on her work. What surprised me though was that she had cut her hair into what was then the most popular style, a short bob; and when I saw her in running clothes setting out for a jog first thing one morning, I was amazed. I knew she was trying to make a statement: she had made up her mind and was getting ready to start the assault on RECOVERY.

Not long afterwards, at one of our regular weekly meetings, she set out a very daring plan. After spending a certain amount of time feeling her way forward, she had gone back to her original idea, that RECOVERY was a cipher created by combining three of the original encryption methods: a substitution cipher, a transposition cipher and an algorithmic cipher. It was shape-shifting, complex, cunning, but that did not necessarily mean that it was also particularly difficult. Chen didn’t agree with her ideas at all; he said, hadn’t she got stuck in her old rut? The exercise last time proved that it was a dead end! She said that she had changed some of her original ideas, and that even though the exercise had demonstrated that there were problems with her theory, it hadn’t proved that it was a dead end. There were two options which could explain why the exercise hadn’t worked.

‘What two options?’ I asked.

She said one possibility was that her ideas about the key to the cipher were not correct; or that she was right about most of it but wrong in some of the details. At that time she was still convinced that she was right in principle, but there was a problem in one of the links in the chain. The other possibility was that she was completely right about the key and that there was something wrong with RECOVERY, that there was some kind of intrinsic problem with it.

‘What do you mean?’ asked Chen. ‘There’s a fundamental problem with RECOVERY?’