‘Yes, I see,’ he said. ‘But what’s the actual key? We have some posters and a string of numbers. How do the numbers relate to them?’

I pointed to Victory 1945. It was her attachment to that film that had given it away – using its title twice had been the detail that let me in. ‘There are numbers on each of these posters. The date that the film or play is showing. Those must be the keys.’ I wrote them down.

‘I hope you enjoy long division,’ he muttered. ‘You know …’ He drifted off thoughtfully.

‘What?’ I said.

‘These dates.’

‘Yes?’

‘Well, no. It’s nothing. Forget it. Let’s go downstairs and see what we can make of them.’

In the kitchen, we stared at the page again. I tried every mathematical formula I could think of to relate the date figures to the strings of digits in the book – taking one from the other, multiplying, dividing. None of the products made any intelligible number, though – nothing that was the right length for an identity card, telephone number or anything else. I had presumed that, having realized the posters were the key, it would all be over from then. That had been hubris and now I was being punished for it.

‘Was she a maths genius?’ asked Tibbot after a while.

‘Not as far as I know.’

He furrowed his brow. ‘Maybe we’re looking at it the wrong way. Maybe they don’t go together like that. You know I said about patterns being a way into understanding the cipher? Well, look at how many double digits there are. And a triple. That can’t be completely random.’

He wrote the first string on his pad. DD2261033445298. Then he wrote the opening date of the play Daisy, Daisy, 26/03/42. ‘Lots of the same numbers,’ he said to himself, comparing the two. He started crossing out numbers from the first string. ‘Do this,’ he said. ‘For every digit that you find in the date, cross off the first time it appears in the column.’ He turned his page around to me. It now read 2261033445298. ‘That’s a telephone number for sure,’ he said, his face betraying his satisfaction.

I jumped up, exhilarated. ‘Yes. God, yes!’ We quickly turned all the other strings into telephone numbers. The second column, of three-letter strings, was still a mystery, but we had taken a huge leap forward. Lorelei hadn’t been some mathematical genius; she had simply dropped random digits, taken from the show dates, into the original telephone numbers. That disguised the telephone number. The rule was that each random digit had to be placed somewhere before it occurred in the original telephone number. ‘How did you guess?’ I asked as we went to find a call box, trying to keep my excitement in check.