“Excuse me?” she said.

“Alex Cale never found the lost diary of Sir Arthur Conan Doyle. He lied.”

“How do you know that?”

“There’s one piece of evidence that doesn’t make sense. There’s one thing that doesn’t belong. Once I figured out what that was, the whole story unraveled.”

“And that thing was…?”

“The manuscript! What’s the story, as we know it now? Cale spent twenty years working on that thing. It was supposed to be the culmination of a life’s work. And then, at long last, he finds what he’s been looking for. The diary. After all these years, he can finally complete his manuscript… But he doesn’t? He’s too busy in the three months after he found the diary to include its contents in his masterpiece? It doesn’t make any sense.”

“But wait, all we have is one backup copy of one draft of his manuscript. Maybe that chapter was in a different file. Maybe it was in a different draft. We have no way of knowing.”

“True,” said Harold. “But think about this. What did Alex’s sister say about his mood after he found the diary?”

Sarah raised her eyes, trying to remember. “She said he didn’t want to celebrate,” Sarah finally replied. “She said he wouldn’t talk about what was in the diary. He didn’t tell her anything. She said for those last months, whatever he found in the diary made him nothing but miserable.”

“Does that make any sense? Or was it that not finding the diary, and deciding to lie to the public, made him nothing but miserable? In the time since Cale supposedly found the diary, did he ever divulge, to anyone, even the slightest hint about its contents? Or anything about where he’d found it?”

“No.”

“Is there any hard evidence, besides Alex’s word, that he actually found that diary?”

“No.”

“So which is more probable: that Alex Cale solved the greatest mystery in the history of Sherlockian studies, but refused to tell anyone how he’d solved it or what the answer was, and then neglected to write about it in his almost-completed book; or that he lied about finding the diary in the first place?”

Sarah nodded, admitting that Harold had a point.

“Okay then,” she said. “If he never found the diary, then who killed him?”

At this, Harold had to smile. The explanations really were the most fun part of being a detective.

“No one,” Harold said. “Alex Cale killed himself.”

If Sarah had been surprised before, now she was dumbfounded.

“Bullshit,” she said.

“ ‘When you have eliminated the impossible, whatever remains, however improbable, must be the truth.’ ”

“I’m going to assume Sherlock Holmes said that?”

“Yes. And he’s right. I know it’s improbable, but it’s the only way to explain everything.”

“Okay then,” said Sarah as she plopped herself down on the bed. “Explain everything.” She sat looking up at Harold like an eager audience member at the opening curtain of a play. She’d never looked at him like this before. The sensation was exhilarating.

“The first thing that needs explaining is, why would Cale lie about finding the diary and then attend the convention? What the hell was his plan? He was just going to show up at the lecture the next morning empty handed and say he was sorry? The suicide explains it. He never intended to make it to the lecture. His plan, from day one, was to announce that he’d found the diary and then kill himself under suspicious circumstances, making it look like the diary had been stolen. He ransacked his own room. He opened and closed the door to his room three times in the night, to simulate having received potentially murderous visitors. And remember, no one claims to have visited Cale at any point in the night. Sure, the killer wouldn’t, but would two innocent Sherlockians really lie about it to the cops out of paranoia?”

“He strangled himself with his own shoelace?” said Sarah, swinging her feet off the edge of the bed as she spoke. “Is that even possible?”

“ The medical community is split about that one,” said Harold. “Some think it’s possible, some think it isn’t.”

“How in the world do you know that?”

“I’ve read a lot of mysteries. This isn’t exactly the first time the issue of self-strangulation has come up. Plus, he might have used a tool for help. Do you remember at the crime scene? There was an antique pen on the floor by the body. The same model that Conan Doyle used. What if Cale used the pen to tighten the shoelace around his neck? Then it fell away when he collapsed. The pen would make it easier for him to tighten it initially, before he lost muscle strength.”

“But it might not even be possible?”

“You’re being kind of glass-half-empty about this, don’t you think? It might be possible. Neither of us is a doctor. But even if we were, we couldn’t rule out the possibility, not for certain.”

Sarah smiled. She was enjoying this.

“This happened in a Holmes story, you know. Not the strangulation via shoelace. But in ‘The Problem of Thor Bridge,’ a woman killed herself in such a fashion that it looked like murder. She did it in order to frame her husband’s mistress.”

“Doesn’t the word ‘elementary’ appear in a different story? You told me that.”

“Yes. It does. When Cale wrote ‘elementary’ on the wall, he wasn’t pointing us toward ‘Thor Bridge.’ He was pointing us toward A Study in Scarlet, like I always thought, which is where the killer leaves a message on the wall in his own blood. And whose blood was on the wall?”

“Alex’s!” said Sarah buoyantly.

“And then, secondly, the word ‘elementary’ is from the story ‘The Crooked Man.’ To be honest, I have no idea what that story has to do with Cale’s death. It’s another story where what looks to be murder actually isn’t. One Colonel Barclay appears to have been murdered by his wife. But Holmes deduces that the man actually died of shock, and the wife was silent about it because she was with her lover at the time. It’s sort of a weaker version of ‘Thor Bridge,’ really. I don’t know what Cale meant by that message. Yet.”

“So why’d he do it?” Sarah said. “Why did Alex lie about finding the diary and then kill himself while making it look like the diary had been stolen?”

Harold paused. He realized that he’d been pacing back and forth across the room as he’d been speaking. He planted his feet into the carpet as he continued.

“I have no idea,” he said. “That will be the next step in our investigation.” The next step. Our investigation. Harold liked the promise implicit in those phrases. “But there are a few possibilities that come to mind. What if he did it to frame somebody? Like in ‘Thor Bridge.’ ”

“Who did he frame?” Sarah swung her feet off the edge of the bed as she spoke.

“Sebastian Conan Doyle,” said Harold. “Ten to one all the cops think he did it.”

“Actually, I’ll take ten to one that all the cops think you did it, but I see your point.”

“Cale hated Sebastian. They’d been fighting for years, with increasing bitterness. They’d been racing each other to find the diary. Maybe, for his final trick, Cale decided to screw Sebastian over once and for all. By announcing he’d found the diary, he’d throw Sebastian off the scent. Then, by killing himself and making it look as if someone else stole it, he’d ensure that Sebastian would go off and spend years trying to find the murderer. He’d spend all this time and energy doing things like… well, like hiring me, but he’d be looking in the wrong place. Because no one stole the diary from Cale. Plus, all the cops would declare Sebastian their number-one suspect. Even if they never arrested him, because he didn’t actually kill anyone, he’d be tarred with suspicion for the rest of his life. Cale dies a martyred hero, and Sebastian lives a villain.”

Sarah raised her eyes to the ceiling, pondering everything Harold had just said. It was a lot to take in, but she seemed to be reasoning through it in her head, searching for flaws in his logic. Based on her grin, and the constant swinging of her legs off the edge of the bed, it didn’t look as if she’d found any.