Amanda Knox, the American student accused of involvement in the murder of Meredith Kercher, calmly went to Italian classes the day before her arrest and wrote an imaginary letter to her mother in which she referred to the killing as a "mystery" and talked about future shopping trips.

Sources at the University for Foreigners in Perugia, which Ms Knox and Ms Kercher began attending in September, said that on Monday November 5 students were asked to write a letter "to whoever you like" as a test of their Italian language skills. Although the body of Ms Kercher had been found the previous Friday morning at the cottage she and Ms Knox shared with two Italian female students, Ms Knox sat in the front row of the class and penned a letter to her mother Edda in Seattle.

In the letter, extracts from which appeared yesterday in the Italian press, she told her mother she was "shaken" and "nervous" because of the murder, adding that she did not want to sleep at the cottage any more. "I can't think about anything else," she wrote. "What happened is still a mystery." She told her mother she looked forward to going shopping with her for clothes, adding "I have not finished with Perugia yet".

Police said the letter, which has been added to the growing dossier of evidence on the murder, offered "psychological insight" into Ms Knox's state of mind. "Its all about her, not about the victim" one source close to the investigation said.

New witness 'saw Meredith suspects together'

Amanda Knox, Raffaele Sollecito and Rudy Guede were see at the house in Perugia where the American student died

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• Murder in Perugia

BACKGROUND

• Meredith Kercher: Q&A

• New DNA not from Meredith suspects

• Timings crucial to Kercher murder investigation

Related Links

• Meredith suspect blames girlfriend

• Timings crucial to Kercher murder investigation

• Meredith or Madeleine: it's trial by media

Teachers at the university said they had been aware that Ms Knox lived in the same house as the murdered woman, but did not learn she was a suspect until her arrest on November 6, the day after the writing test. They said Ms Knox had been a keen and punctual student, "always in the front row", and had talked a lot about Seattle, which is twinned with Perugia.

Police said Ms Kercher's killers appeared to have tried to incriminate the four Italian students who lived in the house below by smearing blood in their rooms after the killing. The house was empty at the time because the four students had gone home for the All Souls long weekend. But Ms Kercher, who had a relationship with Giacomo Silenzi, one of the four, had been given the keys so she could look after a cat with a torn ear.

The police hypothesis is that the killer or killers knew this, and took the keys from Ms Kercher before or after sexually assaulting and then murdering her.

It has also been claimed that Ms Knox boasted to friends about finding the body, and seemed relatively unmoved when first questioned by police. In a statement to police after her return to Britain from Perugia Robyn Butterworth, a close friend of Ms Kercher and like her an exchange student from Leeds University, said Ms Knox appeared "very strange" and "over the top".

"I remember Amanda also kept going on about how she found the body. It was as if she was proud to have been the one who found it," she said. "I just remember thinking at the time at the police station that Amanda's behaviour was very strange. It was as if she wasn't bothered at all."

She recalled that Ms Knox, speaking loudly in English "to all and sundry" had described returning to the house to find the front door open and then going into the bathroom that she and Meredith shared. "She was saying how she had seen blood on the floor – I remember her saying it was menstrual blood. She also said she had taken a shower. I remember her also saying that the toilet was full of shit. She kept saying the word shit over and over again. This behaviour seemed a little strange to me."

She said Ms Kercher had often upbraided Ms Knox for not flushing the toilet, one of the many points of friction between the two women, who according to friends also fell out over Ms Knox's habit of bringing home "strange men" she had picked up in bars and Internet cafes.

Ms Knox, 20, her boyfriend Raffaele Sollecito, 23, and a Congolese bar owner, Diya "Patrick" Lumumba, 37, are all in prison just outside Perugia and are being held on suspicion of murder and sexual violence. Mr Sollecito and Mr Lumumba are alone in their cells, while Ms Knox is sharing a cell with an Italian woman also accused of murder.

Mr Lumumba says he was never at the house, and witnesses have testified he was at the bar he owned in Perugia that evening. Italian media reports, not so far contradicated by police, say that no trace of Mr Lumumba's DNA or prints have been found so far in the cottage. However investigators say there are "holes" in his alibi.

Ms Knox and Mr Sollecito also claim not to have been at the house, saying they arrived the next morning at the same time as police to witness the discovery of Ms Kercher, semi-naked under a duvet with her throat cut. However Ms Knox had earlier told police she was at the house the night of the murder and heard Ms Kercher screaming from her bedroom while Mr Lumumba was with her. She said her recollection was "confused" because she and Mr Sollecito had been smoking cannabis.

Mrs Sollecito's lawyers say no traces of blood had been found on his knives or trainers, though this has yet to be officially confirmed. Mr Sollecito's father Francesco, a urologist from Bari, said: "He is upset by the fact that a girl who he had only just met and who he treated so well has drawn him into this terrible episode". Dr Sollecito said he had not spoken to Ms Knox's parents during visiting hours at the prison, partly because they did not speak Italian and he had little English but also "because I can't imagine what we could have to say to each other".

Police have examined Raffaele Sollecito's car, an Audi, for any traces of blood on the pedals. They have also conducted forensic tests at his ground floor flat on Corso Garibaldi, a hilly street close to both the University for Foreigners and the scene of the crime. They have taken away Mr Sollecito's collection of knives and violent Japanese comic books.

Lawyers for Ms Knox and Mr Lumumba said that they would lodge appeals today against a decision by Claudia Matteini, the investigating judge, to confirm their arrest for up to a year, pending charges.

Mr Lumumba's Polish partner Alexandra Beata, the mother of their baby son, said after visiting him: "He has nothing to do with this. He strongly believes in justice and I hope that in the next few days all this will be resolved."

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