In New York City in 1947, a radio news broadcast goes out across the city. In a luxurious apartment, a shot rings out and the killer leaves, dropping the gun on the floor. His dying victim crawls across the floor to the wall outlet and pulls the plugs on the television and clock at exactly 10:25 p.m.
At the radio station, radio host Simon Brimmer is narrating his newest detective saga for The Casebook of Simon Brimmer
. Once Simon brings another case to a successful conclusion, he leaves the studio and complains to the producer that the show was dull as dishwater. Detective writer Ellery Queen is dozing near the coffeepot, and Simon wakes him up and notes that he dozed off during the radio. Ellery apologizes, saying that he's been working 48 hours straight on a deadline, and says that he isn't interested in ghostwriting for Simon. A call comes in for Ellery from his father, Inspector Richard Queen. Inspector Queen asks him to stop by at the victim's apartment, and ignores Ellery's objection that he's on a deadline. Ellery leaves, stumbling through the studio, and Simon calls the newsroom and tells them to find out everything they can about the current police investigation.
At the murder scene, Inspector Queen explains that the victim left a dying clue that makes no sense. The victim is Monica Gray, a top fashion designer. Ellery concludes that she's vain based on the framed photo she kept of herself, and liked puzzles based on the crossword she was working on. Inspector Queen concludes that Monica was working in her studio on designs, but Ellery is noted in the fact that each year, Monica christened her line after a different woman: Lady Ruth in 1945, Lady Thelma in 1946, and Lady Dulcea this year. The Inspector concludes that Monica was working on the 1948 collection, heard the doorbell, and went out into the foyer. She opened the door, meaning that she probably knew the murderer, went to the middle of the room, and was shot. Ellery finds a design sheet for the Lady Norma collection. The Inspector continues, noting that the murdered assumed Ellery was dead. There were no pens or pencils, and the bedroom was too far away. Monica crawled to the plug, unplugging the television and the clock, but the Inspector has no idea what she was trying to say. Ellery examines the television and discovers it was on Channel 4, and Inspector Queen says it was broadcasting an experimental late-night news program.
Ellery wonders if Monica meant to pull out both plugs, but then realizes that his father is trying to trick him into taking the case. He can't resist coming back, however, and concluding that Monica was seeing a man. He explains his deduction: there's a pipe there and a medium-sized smoking jacket in the closet with fresh tobacco crumbs. The initials C.M. are on the jacket. Ellery then leaves to finish his book, pausing only to recover the glasses that he absent-mindedly left behind.
The next morning, Ellery is working on his novel when the phone rings. His father yells at him to answer it and gets no response. It's Lt. Velie with a report for the inspector. Inspector Queen yanks the paper out of his son's typewriter to get his attention and explains that they know who probably did it: Carson McKell, the financier and philanthropist. Carson is married and lives in Monica Gray's apartment, and his name is on the gun license. The Inspector leaves while Ellery wonders if Carson smokes a pipe.
The Inspector and Velie come to see Carson at his office. Carson's son Tom is there and Carson admits that he expected the police to visit him. He admits that he knew Monica but refuses to answer any questions about his personal relationship with her. Carson says that he gave Monica his gun for protection from burglars, and reluctantly admits that he had a key to her apartment. The Inspector asks Carson if he had an alibi, and Carson has no answer.
Carson is indicted and leaves the courthouse without giving a statement. Tom insists to the reporters that his father is innocent and drives off with his father, his mother, Marion, and their counselor, Ben Waterson. As their chauffeur Ramon drives them home, Carson apologizes to his wife for the insinuations that he had an affair, and Waterson warns that it's a difficult case. Tom considers making something turn up, and soon.
Ellery is out with his young cousin Penny, and she is bored with skating. She suggests they find out why Tom and Carson's secretary Gail Stevens have been following them, and Ellery goes after them. They apologize and admit that they didn't want to bother with him, but Ellery is eager to find a distraction from Penny. They get lunch and Mark and Gail insist that Carson couldn't have committed murder. They want Ellery to talk to Carson for ten minutes. Ellery accepts to get out of escorting Penny around town.
At his apartment, Carson explains that he met Monica in an elevator, met with her on Thursdays, and started seeing her socially. Marion admits that she suspected that Carson was involved with another woman, and finally confronted him. he told her the truth and promised to terminate the affair. Ellery wonders why Carson took the risk, and Carson explains that he wore a disguise: a false mustache, glasses, and a funny hat. Carson tells Ellery that on the day of the murder, everyone had left the office and he finally called Monica. There was no answer at first, but Monica finally picked up and said she had a headache and didn't want to meet with him that night. She sounded hoarse and said she was tired. Carson went to see her anyway, but lost his nerve and went to a bar. He drank too much and doesn't remember which bar he ended up at. He tries to describe the bar without success, and Ellery goes into the next room to use the McKells' phone. He calls his father asks if he checked out Carson's alibi. The inspector says that he assigned five men with photos to check out every possible bar, and no one recognized Carson. Ellery tells the McKells and Gail what his father has learned, and Carson admits that his hired detectives haven't had any better luck.
As Carson goes on trial, Ellery reads about the case in the paper as his father comes in. Inspector Queen suggests that he come to the courthouse to hear Carson's testimony. Ellery says he has a date with his publisher, but his father knows better and gives him directions. At the courthouse, Ellery listens as a fingerprint expert testifies that Carson's fingerprints were in Monica's apartment. On cross-examination, Waterson suggests that due to a recent repainting, other fingerprints could have been obliterated. However, the district attorney reiterates that Carson's fingerprints were there. Next, the DA questions the maid, Cora Edwards, who confirms that Monica had a regular male visitor on Thursday nights, a visitor who smoked a pipe. Cora also testifies that Monica had said that she was meeting someone the night of the murder, the same pipe-smoking visitor. Carson then takes the stand and gives his story, but the DA points out that Carson bought a gun for Monica but not for his own wife. The DA then points out that Carson has failed to identify the bar where he claims he was drinking.
Ellery leaves to get some air and Gail goes after him. As they walk, Ellery notes that she's romantically interested in Tom, and Gail admits that she has to convince Tom she isn't interested in his millions. Ellery is distracted when he notices a boy defacing a political poster. He meets with Carson and shows him the photo they showed to the bars, and then reminds them that Carson wore a disguise. They soon find a bartender, Matthew Thomas Cleary, who identifies Carson once he dons his disguise. The DA cross-examines him and Cleary confirms that Carson donated $10 to the charity box. The bartender also clearly remembers that Carson left at 11 o'clock, the same time that he went out to get his evening paper.
The jury returns a verdict of not guilty. Carson and his family thank Ellery and leave, and Simon approaches Ellery. He congratulates him on clearing Carson and suggests that he and the McKells listen to Simon's case that night.
Ellery and the McKells celebrate and Ellery notes that Monica was a cryptic woman. A waiter brings in a radio and Ellery tunes it to Simon's show. Simon adds a new segment to his show, a commentary on current crimes. The radio host says he has information that the police lack, and interviews Cora. She knows that Monica had one other visitor who she showed her gun to, but she never told the police because they believed Carson was the killer. As the maid tells who the other visitor was, Marion shuts off the radio and admits she saw Monica that day. Carson's wife admits that she had a motive, but she didn't kill Monica. She didn't say anything because she was embarrassed, but was curious to know more about her husband's mistress. Marion went to the apartment as the charity chairman of the building, they talked for a while, and Monica made a donation. When Ellery points out that Cora testified that Monica showed Marion the gun, Marion explains that Monica took her to her bedroom office to write a check, noticed the gun in her drawer, and showed it briefly to Marion.
The waiter interrupts to inform them that Inspector Queen and Velie have arrived. They ask Marion for her alibi and she says that she was in their apartment alone. She says that she ordered some sleeping pills from the pharmacy across the street, but that he came at 9 o'clock. Marion says that she woke up at 10:30, thinking someone had come in, but admits she has no way to prove that. Inspector Queen asks her to come along for more questioning, and suggests she bring Waterson with her. Tom angrily tries to intervene, but Waterson stops him and says that he'll handle it. The waiters arrive with the celebratory cake but no one is in a mood to celebrate.
The police charge Marion with the murder, but Ellery objects and argues with his father. Ellery figures that the DA is looking for a scapegoat after he was embarrassed in court, but Inspector Queen says he's doing his job. Ellery storms out and Velie explains that the DA has been on the inspector's back. Velie notes that there was a robbery in the store and Ellery asks for fact sheets on the crime. Later that day, Velie brings them to Ellery who goes over them. After Velie leaves, Ellery tries to work out the facts and then calls Gail. He confirms that she lives a few blocks from the McKells and tells her not to make any plans for that night. When she wonders if he's asking her on a date, Ellery says that he isn't and that he'll explain later. After Gail hangs up, Carson calls her into his office and suggests that he's going to confess to Monica's murder to stop them from prosecuting his wife. He believes that due to double jeopardy, he can't be prosecuted a second time. Waterson warns against it, noting that Cleary clearly alibied him. Gail agrees and Waterson says that the scheme would do Marion more harm than good. Carson reluctantly drops his plan, but notes that his detectives have only turned up useless information like the fact that one of Waterson's partners represented Monica in a copyright infringement suit. As Gail leaves, she tells her employer that she is meeting with Ellery, and that it was important to Ellery that she lived near the McKells.
That night, deliveryman Eddie Carter comes to Gail's apartment with a package of sleeping pills. As she takes some money out of her purse, she removes a bracelet and says she was supposed to take it in for repairs. Gail then takes out a wallet and pays for the delivery from a large wad of bills. Once Eddie leaves, Ellery emerges from the next room and says that she was very convincing. He then takes Gail out into the hall and closes the door, but reveals that Eddie jammed the lock so he could get in. Ellery figures that Eddie will wait until she goes to sleep and then come back at 10:30.
Right on time, Eddie enters Gail's apartment and starts going through her purse. Ellery confronts him and Eddie tries to run, but trips over the end table that Ellery put in his path. Eddie tells them to go into the bedroom so he can get out of town, but Ellery says that Eddie is in a lot of trouble. Ellery asks Gail to make some coffee and says that need to relax and talk. Eddie reluctantly does so and Ellery explains that the thief had to be an inside man. He confirmed that almost every robbery occurred after Eddie made a delivery of sleeping pills, but Eddie dozes off and Gail admits that she put sleeping pills in the coffee just as she and Ellery planned.
The interrogation continues downtown at the station and Eddie admits that he was in the building the night that Monica died. When Ellery suggests that he cooperate, Eddie admits that he broke into the McKell apartment at 10:30 and can testify that Marion was asleep in the bed. He didn't steal anything because Marion woke up briefly and called out. The DA reluctantly admits that Marion is off the hook and they're right back where they started. He wonders if Eddie killed Monica, but Ellery points out that Eddie had his own gun and that Monica didn't order sleeping pills. As Ellery and his father leave, Inspector Queen receives a letter from Monica saying that Tom came to visit her on the night of her murder, tried to strangle her when she refused to stop seeing Carson, but panicked and ran away. She left the letter with a friend to be mailed in case of her death. As Inspector Queen prepares to arrest Tom, Ellery points out that they can't seem to get away from the McKell family as suspects.
Carson and Waterson accompany Tom to the police station, where the Queens show him the letter. Tom admits that it's true that he went there and lost his temper, but Monica was alive when he left. Waterson notes that Tom must be telling the truth, since Monica wrote the letter. Tom explains that he soon realized that his father was seeing Monica, and went to see her at 8 o'clock that night. he finally ordered her to stop seeing Carson and she snapped at him. When she ordered him out, Tom started to choke her but then backed away, shocked, and left her apartment. At 10:30 he was alone on the streets without an alibi. Carson realizes that Monica sounded hoarse and called off their date after Tom attacked her. Ellery points out that Monica's mysterious friend didn't mail the letter in immediately after Monica's death, and Tom explains that the friend blackmailed him and demanded $500 a week, sent to a post office box. Tom finally hired a detective to watch the box, but no one picked it up. Ellery notices that Carson is disturbed, and the financier explains that the same person was blackmailing him over the affair. Once Monica was dead, he stopped paying. Ellery figures that the blackmailer must have come to the apartment to take the letter, and Waterson suggests that the blackmailer must have killed Monica.
Before they can figure out who the blackmailer is, Simon arrives and Ellery introduces everyone. The radio host knows about the note and that someone must have been there the night of the murder. When Ellery confirms his suspicions, Simon says that's the last piece of the puzzle and that he'll announce his solution on the air that night. Once he leaves, Ellery admits that Simon is onto something, and they'll find out that night.
The Queens are at home and listen to Simon as he explains that Monica was a one-man woman. Each year she kept company with a different man, and Simon has confirmed that each one had an alibi. He believes there was a new man in her life, and he was the one who took the note. Simon cuts to a commercial and Ellery starts going through his files looking for an address. He locates it and asks his father to get squad cars to the location. As they drive there, Simon continues and starts to identify Monica's new lover. Ellery turns off the radio and says that he knows who Simon is going to identify. He has his father write down the names of the three lovers: Hurt, an actor who played Hamlet, and a French diplomat named Claude. As Ellery drives, he explains that each year Monica named her line using an anagram of her lover. Hurt equals Ruth, Hamlet equals Thelma, and Claude equals Dulcea. Simon figures out the anagram naming and realized who the current man was. Inspector Queen finally despairs of Ellery's driving and switches with him, and Ellery reminds his father that the new design line was named Norma: an anagram of Ramon, the McKells' chauffeur.
Simon names Ramon on the air as the chauffeur listens and packs. The radio host speculates that Monica and her new lover argued, and then Ramon grabbed the gun and shot her. Ramon looks out the window, unaware that Velie and his men have the building surrounded. Ellery and his father arrive and they move in. Inspector Queen calls on Ramon to come out but they get no response. Breaking in, they realize that Ramon is heading for the roof via the fire escape. Velie gives chase across the rooftops and corner Ramon the edge. Desperate, the chauffeur tries to jump but falls short and plummets to his death.
The next morning, Inspector Queen overhears Ellery making plans to have all of Monica's belongings delivered somewhere. Ellery explains that he's been up all night reading the script for the news program that was on the air when Monica died. Inspector Queen says that the case is over, but Ellery explains that Ramon wasn't the murderer and he knows who did kill Monica. He promises his father that at 10;25 that night they'll have all the proof that they need.
That night, Ellery gathers all of the suspects and recreates the news broadcast in the studio. He explains that Ramon was the blackmailer but someone else killed Monica. Ellery then shows them his recreation of Monica's apartment, using the furniture from her apartment. The detective recreates her death and shows them how Monica dragged herself to the television. However, she dropped the sketch at hand when she could have used it to indicate Ramon was her killer. There was also a car-shaped planter on the end table that Monica could have used to implicate Ramon. Ellery has Monica's television hooked up and explains that the broadcast was very carefully timed. They settle in to watch the broadcast. At 10:25, there is a weather broadcast and a picture of the sun. Ellery notes that Carson and Marion had alibis and Gail had no motive, but Tom has motive and no alibi. Tom tries to leave but Velie stops him. Carson demands an explanation and Tom admits that he went back to apologize. However, Ramon came out and Tom realized that Monica was stringing Carson along while having an affair with the financier's servant. Tom then knocked on the door, barged in, threatened her, and took away her gun when she went for it. He admits that he doesn't know if it was an accident, but tells his father that he would have confessed if Carson or Marion were in danger of being convicted.
As Tom is taken away, Inspector Queen gets a call. Simon congratulates Ellery and suggests that they have lunch, but Ellery isn't interested. Inspector Queen informs his son that they have another bizarre murder for him to solve, and Ellery can't resist.