One piece of a sad, grim puzzle was solved last weekend when police confirmed that human remains found in a beach cave in Kanagawa Prefecture were those of a 21-year-old British woman missing since last July. The other piece of the puzzle -- who killed her, how, where and why -- is not quite in place, although police are holding a suspect in the case on other charges. It is to be hoped for the family's sake that this crime will be solved as soon as possible.

Lucie Blackman, a former British Airways flight attendant, came to Japan last May and found work in Tokyo's Roppongi district as a bar hostess. Many young, pretty, foreign girls like Blackman do. The details of her last day are well-known: She left her Shibuya apartment at 3 p.m. on July 1 after receiving a phone call from a man, called her roommate at 5 p.m. to say she had gone for a drive with a client and was heading for the coast, and called again, finally, around 7 p.m. to say she would be home in an hour. The next, and last, call the roommate received was from an unidentified man, telling her that Blackman had "joined a cult" and would not be coming back.

It was confirmed this week that Blackman's last call was made from a cell phone owned by Mr. Joji Obara, a 48-year-old businessman whom she had met in Roppongi and whose condominium is just 200 meters from the cave where her dismembered body was found buried. Mr. Obara, who has been indicted in six other cases in which women were drugged and raped, one fatally, has been a suspect in the Blackman case virtually from the start. Yet, even now, he is being charged only with abandoning a corpse. People both here and abroad have had trouble understanding the roundabout, step-by-step way police have pursued this high-profile case, which has even been a subject of discussion between Prime Minister Yoshiro Mori and British Prime Minister Tony Blair. Police officials, however, have defended their tactics, citing the need to build up a case painstakingly, on the basis of solid evidence. And they received support from an important quarter this week when Mr. Tim Blackman, Lucie's father, described the investigation into his daughter's disappearance as "first-rate" and said he was confident of a speedy outcome. "I think everyone will be surprised how fast the police move now," he said.