We are introduced to two new characters, Detective Kusanagi and Yukawa Manabu, a physics professor at Imperial University, who are playing a game of chess. It's a foregone conclusion that Yukawa will call checkmate as Kusagani stares at the chessboard for twenty minutes trying to think of a move that will save him. Kusanagi complains that chess should be more like shogi, Japanese chess, since it allows a player to use pieces taken from the enemy, but Yukawa challenges him to "think about the situation logically" instead of resorting to excuses. Kusanagi gets a phone call from the police department informing him of a body that has washed up on the shore of the Old Edogawa river.

At the crime scene, the police find a body whose face has been smashed beyond recognition and whose fingerprints have been burned off. In addition, they find the clothing from the body, half burned, in an oil drum not too far away, indicating that the murderer had intended to completely burn the victim's clothing but wasn't able to finish the job. Also nearby is a stolen bicycle, brand new except that its tires have been punched with holes and flattened. It seems like it will be difficult to identify the body.

Kusanagi gets a phone call from Mamiya, the division chief at police headquarters, who assigns Kusanagi to question the owner of the stolen bike. Kusanagi brings the owner of the bike to the police station where she positively IDs the bike. It turns out that she filed a police report on the very same day, March 10, that the bike was stolen. They learn from her that the bike had been stolen between 11 a.m. and 10 p.m.

The forensics team makes a rough sketch to approximate the appearance of the murderer, but it is too vague to be of any use. Later, they discover that a person staying overnight at certain hostel, Shinji Togashi, failed to check out on March 11. A hair found in his room matches that of the body washed up from the Edogawa River. In addition, the fingerprints on the stolen bike match those of the body too. The police conclude that the victim is Shinji Togashi, Yasuko's ex-husband.