That really did make me think. Yes, I had written to Anderov more than a month ago, but he still hadn’t replied. Why not? And another thing: why had Huang Yiyi gone to all the trouble of setting me these four ciphers – surely it couldn’t be just for fun? What was she up to? And another thing: recently she had been holed up in her office all day banging away at something, so what was she doing? If Chen was right and she was just messing about, why would she be so mysterious? But if she wasn’t messing about, then what was she doing? Cracking ciphers is hard work – you don’t want your office turned into a workshop with lots of noise and banging about.

While I was still all confused, Huang Yiyi knocked on the door and came in. The second she came through the door she asked me if I had cracked the ciphers. I pointed to the four plain-text messages and said something about her being full of energy. She retorted rudely, ‘You’re so unimaginative. Even though this may seem just a bit of fun, why would you criticize a cryptographer for creating this sort of puzzle? At the very least it means that she lives in a world of ciphers.’

I asked her to come to the point and tell me the real reason why she had set me the four problems. She explained that they represented four different types of ciphers: the bottle was a transposition cipher, the letter a substitution cipher, the book a book cipher, and the playing cards an algorithmic cipher. Nowadays these are all basic cipher forms.

‘But,’ she explained, ‘it doesn’t matter whether it’s a mid-level cipher or one of these new high-level ones – they are all just more or less complex variants of these old types. For example ULTRA (that is, the Enigma machine) is an algorithmic cipher encrypted with a substitution cipher. The complexity comes from the encryption – modern ciphers are all based on algorithms.’

I understood what she meant. ‘And when you use that method to make them more difficult to work out, they become mathematical puzzles.’

‘Exactly. So when you encrypt them in the most difficult way to work out, how many kinds of cipher are there?’

‘There are only a handful of viable possibilities: first, a super-large-value algorithmic cipher encrypted with a medium-large-value algorithmic cipher. The second is a super-large-value algorithmic cipher encrypted with a transposition cipher. Third, a super-large-value algorithmic cipher encrypted with a substitution cipher. Finally, a super-large-value algorithmic cipher encrypted with a transposition and substitution cipher. Those are the most important kinds; any other kind of cipher is impossible in conjunction with an algorithm.’