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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.

The Whole Deal 08/10/48
The Lucky Lady 15/04/38
A Month in the Country 16/06/39
Double or Quits 05/01/47
Daisy, Daisy 26/03/42
Victory 1945 10/09/46

‘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.

‘Those doubles. It’s because she was lazy. Say she has to drop a false three in; it has to come somewhere before the first genuine three so she knows that the new first three is the false three. Sometimes she couldn’t be bothered finding a random place for it, so just stuck it right in front of the genuine one. She wasn’t always that lazy, but she was enough times for it to stand out.’ I was impressed.

The street was busy again as people returned home from the Liberation Day parade. Across town, the Politburo would be taking its fleet of black limousines to the faceless prefabricated block next to the National Observatory in Greenwich Park that some unknown wag had dubbed the ‘Concrete Kremlin’. From the top of that hill, they could look down on all eighteen million citizens of our new republic – or across to DUK London if they wanted to see what they were missing.

We entered the call box, ready to find out what Lorelei had been hiding. I dropped a penny in the slot and dialled 0 for the operator.

17

‘What number, please?’ she asked.

‘Exchange 213; number 4598.’

‘Please hold, caller.’ I waited. So much was riding on this. There was silence, a few clicks, and then the operator was back. ‘That number does not exist,’ she said. I thumped the side of the box in fury.

‘No line?’ Tibbot asked, disappointed.

I didn’t answer, as if acknowledging the failure would make it solid. I spoke again into the receiver. ‘Try exchange 812, number 9932.’

‘Please hold, caller.’ Again, I waited. Then the same deadpan voice. ‘That number does not exist.’ When the next number produced the same result, the operator’s tone changed. ‘Please stay on the line,’ she said. I heard muffled voices, as if she were speaking to someone behind her. Then she returned.

‘Caller, who are you trying to reach?’ There was something frightening about that question, as if it were something she had been instructed to ask me. I hung up immediately.

‘What’s wrong?’ Tibbot asked.

‘She was speaking to someone. About us.’

‘No, no, they get these calls all the time.’

‘She was!’

He huffed and blew out his cheeks, not wanting to argue more. ‘Maybe they aren’t telephone numbers after all,’ he said, changing the subject. It couldn’t be true – we had both been so certain. ‘Still, let’s try the rest.’ I must have looked worried. ‘It’s fine,’ he insisted.

I dialled 0 once more, hoping that it would be a different operator. It was, thank heaven – a warm Scottish accent asking me for my desired line. Still tense, I tried another number, hoping.

‘That number does not exist.’

At that, Tibbot gestured to me to hang up. ‘Hazel told you that the book has been up there since before her parents divorced, yes?’ he asked, when the receiver was down.

‘That’s right.’

‘So it’s at least a few years old. And the phone network was improved a couple of months back: all residential lines got new numbers, didn’t they? If these are phone numbers at all, it looks like they’re out of date. Maybe Lorelei stopped whatever she was doing; or there’s a newer list somewhere.’ I didn’t know what to say; it was crushing. ‘Look, keep trying, but let’s not get our hopes up.’ I nodded and tried again. But there was only the message ‘That number does not exist’ that told me the call would not be answered. Then it was the sixth of seven entries. I read out the number without much hope and heard the familiar silence. Then a clicking. Then the operator’s voice.

‘Connecting you now.’

And then – incredibly – a distant ringing that said we had made a connection. Tibbot punched the air before pressing his ear next to mine so he could hear. We were on tenterhooks, barely daring to breathe in case it somehow caused the line to cut out. It rang and rang.

‘Are they there?’ Tibbot asked, frustrated. ‘Answer the bloody thing.’

After a full minute without an answer, I gently placed the handset back in the cradle and pressed the button to return my money.

‘But it’s better than nothing. I suppose they haven’t had their number changed,’ I said, doing my best to remain positive. I pondered for a second. ‘Is it just residential numbers that changed?’

‘Yes.’

‘So this one might be a business or government number?’

‘Yes,’ he said, nodding. ‘Yes, you might be right. Try it again.’ I hardly needed to be told. Once again, there was silence, clicking and the faint ringing, as if the other telephone were a few metres along the street and we could just reach out and touch whoever was standing beside it. But it rang and rang without a voice coming on. I hung up for the second time. Still excited, I tried the final number, but the result was back to ‘That number does not exist’.