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Kogoro is hired as a bodyguard for a woman who has been receiving death threats. The letter warns she will be killed at 6:00PM at her birthday party.
Due to being chosen to particpate as a baton twirler during the Grand Opening of the Beika Park's Flower Clock, Ayumi has been practicing her moves in front of the clock every morning. When she invites Conan and the others to watch, they witness a drunk man wandering around and generally being a nuisance. The next morning, the man is found dead, his head smashed on the stone number 6.
6:00PM hits and the woman dies as described in the letter. Many people at the party describe the culprit, but none of the descriptions match up.