Lots of clever detectives here! Well done Steven, Forres Academy; Soh Yong, Raffles Institution; Fiona, Stamford High School; Julian, Helen and Ben from Hethersett High School; Anne, Peter, Becky and Darren, Bourne Grammar School; Scott and Sam, St Peter's College, Adelaide, South Australia; Ren, James and Tim, Madras College; Daniel and Mike, King Edward VI School, Bury St Edmunds; Dilara and Ece, IRMAK Primary School, Turkey.

These are the statements:
Alice: I know who killed her
Ben: I killed her
Carol: Ben killed her
Donald: It wasn't Ben or Carol.

This is Ben's solution:

Carol did it because Donald said that Ben and Carol didn't do it so that meant that either Ben or Carol was a murderer. Ben said he killed her and he was lying so that meant Carol killed her! (Alice said I know who killed her and that meant she did not know).

Case 2: Just one person lies Ben did it and Donald was telling a lie. Carol said Ben killed her and she was telling the truth. Alice didn't actually say that Ben killed her, but she said I know who killed her which did not mean a particular person.