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Joy Noble was up early making breakfast one Saturday morning when she glanced out of the kitchen window of her West Perth home. Outside she saw the naked body of a young woman spread-eagled on the back lawn. At first she thought it was her daughter and she ran through the house shouting: ‘Carline.’ In fact, it was the body of Constance Lucy Madrill, a 24-year-old social worker who lived in nearby Thomas Street. She had been raped, strangled and dumped on the Nobles’ lawn. The attack had taken place in the girl’s own apartment, while her flatmate, Jennifer Hurse, slept. No one could explain why the attacker had dragged her all the way to the Nobles’ lawn, then abandoned her. An Aborigine had probably done it, the police concluded – even though there were no records of Aborigines in Western Australia attacking white girls. And it certainly had nothing to do with the shootings three weeks before, the police said.

Six months passed uneventfully. Then on the thundery night of 10 August, Shirley McLeod, an 18-year-old science student at the University of Western Australia, was babysitting Carl and Wendy Dowds’ eight-month-old son, Mitchell. When the Dowdses returned from their party they found Shirley slumped on the sofa with a peaceful look on her face like she had just fallen asleep but in fact, she had been shot by a .22 rifle and was quite dead. Baby Mitchell was unharmed. There could be no doubt that this killing was linked with the murders in January.

Perth experienced mass panic. The West Australian advised people to lock their doors at night – unheard of in Perth before that time. Babysitters were warned not to sit near windows, and there were proposals to close the old alleyways that ran down the back of people’s houses. The police began to fingerprint every male over the age of 12 in the city, at a rate of 8,000 a week.

Then, on Saturday 17 August an elderly couple was out picking flowers in Mount Pleasant when they spotted a rifle hidden in some bushes. It was a Winchester .22. The police believed that it had not been discarded but hidden there so it could be used again. They staked out the area for two weeks before a truck driver named Eric Edgar Cooke turned up, looking for the gun.

Cooke had been born in Perth in 1931 with a harelip and a cleft palate. Early operations improved his condition, but his speech remained blurred and indistinct and his appearance was mocked by others. From an early age he suffered severe headaches and blackouts. These were aggravated by a fall from a bicycle and a dive into shallow water at 14. Doctors suspected brain damage, but X-rays and an exploratory operation revealed nothing.

At home as a teenager, his father had beaten him regularly. At 16 he spent three weeks in hospital after trying to protect his mother from one of his father’s onslaughts. He told the doctors he had been fighting with other boys.

Expelled from several schools, Cooke had quit completely at the age of 14. He had taken a series of manual jobs, none of which lasted long, before being called up for National Service. In the army, he was taught how to handle a rifle.

In November 1953 he married an 18-year-old immigrant from England called Sally. The couple had seven children – four boys and three girls. Their first child was born mentally handicapped and their eldest daughter, one of twins, was born without a right arm. Nevertheless it was a happy household. Cooke was a faithful husband and a loving father. Other children from all over the neighbourhood came to play in the Cookes’ house.

However, behind it all was what Sally Cooke described as her husband’s ‘restlessness’. She could not keep him at home. He constantly went out on sprees of petty thieving. He had burgled some 250 houses and spent three short terms in prison before the police picked him up as a murder suspect.

At the police station Cooke claimed to have been at home on the night Shirley McLeod was killed. His wife said he was not. Then Cooke confessed.

On the way home from bowling that