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“And how did he kill Mr Clarck?” I asked.

“I’ll never be able to confirm my theory now, but I don’t think Johnson killed Ernest Clarck. He simply waited until a dead body was wheeled out of the ward that he knew Seldom visited. The bodies are left in a little room on that floor, with nobody watching them, sometimes for hours.

All he did was go in and jab the needle of an empty syringe into Clarck’s arm, leaving a puncture mark to make it look as if he’d been murdered. In his way, the man truly intended to do as little harm as possible. To understand his reasoning, I think we have to start at the end. I mean, with the group of Down’s Syndrome children. He may have begun to have thoughts in that direction when his daughter was refused a lung for the second time. He was still working then, driving the group of Down’s Syndrome children to school by bus every morning. He started to think of them as a bank of healthy lungs which he was allowing to get away every day, while his own daughter was dying.

“Repetition leads to desire, and desire leads to obsession. Perhaps at first he thought of killing only one of the children, but he knew it wasn’t easy to find a compatible lung. He knew too that many of the parents at the school were devout Catholics. It’s very common for parents of such children to turn to religion. Some even believe that their children are angels. He couldn’t choose one of the children at random and risk the transplant being refused again, nor could he simply drive the bus off a cliff-the parents would immediately have suspected something and refused to donate organs. It was common knowledge that Ralph Johnson was desperate to save his daughter and that, shortly after she was admitted to hospital, he had checked whether it would be legal for him to donate a lung himself by committing suicide. He needed someone to kill the children for him.

“This was his dilemma until he read, either thanks to Mrs Eagleton, or in the paper, the chapter about serial murders in your book. It gave him the idea he needed. He worked out a plan. It was simple: if he couldn’t get someone to kill the children for him, he’d invent a murderer. An imaginary serial killer who would fool everyone. He’d probably already read about the Pythagoreans, so it was easy for him to come up with a series of symbols that would be seen as a challenge to a mathematician. The second symbol-the fish-might, however, have had an additional private connotation: it was the symbol of the early Christians. It may have been his way of signalling that he was getting his revenge. We know too that he was fascinated by the tetraktys symbol-he drew it in the margin of almost all his books-possibly because of its correlation with the number ten, the full basketball team, the number of children he was thinking of killing.

“He chose Mrs Eagleton to start the series because it would be hard to find an easier victim: an elderly lady, an invalid who stayed at home alone in the afternoons. Above all, he didn’t want the police to be alerted at the start. This was a key element of his plan. The first murders had to be discreet, imperceptible, so that we wouldn’t be on his trail immediately and he’d have time to get to the fourth murder. He only needed one person to know-you. Something went slightly wrong with the first murder but he was still cleverer than us and he didn’t make any more mistakes. So, in a way, he won. It’s odd, but I can’t quite bring myself to condemn him. I too have a daughter. You never know how far you’d go for your child.”

“Do you think he was planning to save himself?” asked Seldom.

“We’ll never know,” answered Petersen. “When the bus was examined, it turned out that the steering had been tampered with. In theory, that would have given him an alibi. On the other hand, he could have jumped from the bus sooner. I think he wanted to stay at the wheel as long as possible, to make sure the bus fell down the slope. He Only jumped once it had crashed through the barrier. He was unconscious when they found him and he died in the ambulance on the way to the hospital.” The inspector glanced at his watch and beckoned to a waiter. “Right, I don’t want to be late for the service. I’d just like to say again how much I’ve appreciated your help, both of you.” And he smiled openly at Seldom for the first time. “I read as much as I could of the books you lent me, but maths was never my strong point.”

We stood and watched him head towards St Giles’s Church, where a large crowd was already gathered. There were a few women in black veils, and some had to be helped up the front steps and into the church.

“Are you going back to the Institute?” asked Seldom.

“Yes,” I said. “In fact I shouldn’t have taken any time off now: I’ve got to finish and post my grant report without fail today. And you?”

“Me?” he said. He glanced in the direction of the church and, for a moment, he seemed very alone and strangely helpless. “I think I’ll wait here until the service is over. I’d like to follow the procession to the cemetery.”

Twenty-Five

I spent the next few hours, stumbling more and more often, like a tired hurdler, as I filled in a series of ridiculous boxes on my report form. At last, at four o’clock, I printed up the files and slipped the pages into a large manila envelope. I went down to the secretary’s office, asked Kim to make sure it was posted to Argentina that afternoon and left the building feeling slightly euphoric at my liberation.

On my way back to Cunliffe Close, I remembered that I had to pay Beth my second month’s rent, so I made a slight detour to get money from a cash machine. I found myself retracing the route of a month earlier, at almost exactly the same hour. The afternoon air was just as warm, the streets just as quiet. Everything seemed to be repeating itself, as if I were being given a last opportunity to go back to the day when everything started. I decided to walk along the same side of Banbury Road-the side in the sun-brushing past privet hedges, submitting to the mysterious conjunction of repetitions. When I reached the turning of Cunliffe Close I saw the last shred of the badger’s skin still lying in the road. That hadn’t been there a month earlier. I forced myself to look at it. The passing cars, the rain, dogs, had all done their work. There was no blood left, just a last piece of fur-covered skin, like a strip of dried-out peel. A badger will do anything to save its young, Beth had said. Hadn’t I heard something similar that morning? Yes, Inspector Petersen had said, “You never know how far you’d go for your child.” I stood frozen, my eyes glued to that last remnant, listening in the silence. Suddenly, I knew. I saw, as if it had always been there, what it was that Seldom had wanted me to see from the start. He’d told me, almost letter by letter, but I hadn’t listened. He’d repeated it, a hundred different ways. He’d put the photographs under my nose but all I’d seen were M’s, hearts and eights.

I turned round and walked back up Banbury Road, impelled by a single thought: I had to find Seldom. I went through the market and along the High, then cut through a passage to get to Merton as quickly as possible. But Seldom wasn’t there. I stood for a moment at the window of the porter’s lodge, slightly disorientated. I asked if Seldom had come back at lunchtime but nobody remembered seeing him since first thing that morning. It suddenly occurred to me that he might be at the hospital, visiting Frank Kalman. I had a few coins in my pocket so I called Lorna from the pay phone in the college and asked her to put me through to the second floor. No, Mr Kalman hadn’t had any visitors.