Sherlock Holmes kept his promise. At one o'clock, he rejoined us, accompanied by a small, elderly gentleman whom he introduced as Mr. Acton, the victim of the original burglary.

"I wanted Mr. Acton to be present while I set out the details of this Reigate puzzle," said Holmes. "As you'll discover, he has a strong interest in the affair."

At that moment, the butler came in and summoned us for lunch. After we had eaten, we retired to the drawing room, and Sherlock Holmes said to our host: "Colonel Hayter, I fear you must regret inviting a troublemaker like me into your home."

"Not at all," replied the colonel warmly. "I consider it a great privilege to be able to study your methods up close, although I confess I am utterly unable to work out how you reached the conclusions you did."

"Forgive me," said Holmes. "As Watson knows, it is my habit to give little or nothing away during the course of an investigation. Now that the case is solved, I'm happy to explain everything."

And so, we settled back in our seats and listened.

"Gentlemen," Holmes began, "one of the most important skills in detective work is knowing which clues are crucial and which ones are less important. In this case, I was certain that the most vital clue—the key to solving the whole problem—was the small piece of paper found in the dead man's hand.

"The first thing I realized was that the burglar couldn't have torn the paper from Keegan's hand. According to the story told by the Cunninghams, the burglar ran away immediately after the shooting, so he wouldn't have had time.

"If the burglar didn't tear the paper, then the only person who could have done it was Alec Cunningham, who had a few moments alone with the body before his father and the servants arrived.

"Inspector Forrester ignored this possibility because he assumed the wealthy and respected Cunninghams couldn't be involved in the crime. I always consider everyone as a potential suspect, regardless of their reputation. I follow only the facts. So from the beginning, I was suspicious of Mr. Alec Cunningham.

"Now, let's look at the scrap of paper Inspector Forrester showed us. It was immediately clear to me that it was part of a remarkable document."

Holmes took out the scrap of paper and showed it to us. "What do you notice about it?" he asked.

"It looks uneven," said the colonel.

"Exactly!" said Holmes. "There's no consistency to it. It's like every other word was written by a different person. And if you look closely, you'll see that's true: the note was written by two people, each writing alternate words. Notice the firm handwriting of 'at,' 'to,' 'learn,' and 'maybe,' compared to the softer, weaker style of 'quarter,' 'twelve,' and 'what.' Do you see?"

"By Jove, now that you've pointed it out, it's obvious!" exclaimed the colonel. "But why would two men write a letter like that?"

"Because they were involved in some criminal activity," explained Holmes. "One of them didn't trust the other and wanted to ensure that his partner shared the blame. What better way to do that than to make the partner write the letter jointly?"

"What's more, it was clear to me that of the pair, the one who wrote 'at,' 'to,' 'learn,' and 'maybe' was the leader."

"How could you tell?" I asked. "Is it because his handwriting suggests a stronger, more forceful character?"

"Perhaps," said Holmes, "but there's also a more straightforward reason. If you look closely at the writing, you'll see that the man with the stronger handwriting wrote his words first, leaving blank spaces for his partner to fill in. These spaces weren't always big enough, so the second man had to squeeze in the word 'quarter' to make it fit between 'at' and 'to.'"

"An impressive deduction, Mr. Holmes!" exclaimed Mr. Acton.

"Thank you," said Holmes. "I've studied handwriting for many years, and I once wrote an academic paper on it. My expertise has allowed me to see more in this sample than the average person would. For instance, I'm certain that the bold, strong hand was written by a young man, whereas the weaker script was from an elderly person. I've also noticed similarities that suggest they are related by blood.

"In total, I made twenty-three deductions, but I won't bore you with them. They deepened my certainty that the Cunninghams, father and son, wrote this letter."

We all examined the scrap of paper again, and I was amazed at how much Sherlock Holmes had discovered from it.

"Having analyzed the note," Holmes continued, "the next step was to visit the crime scene. I went with Inspector Forrester and checked everything thoroughly. From examining the body, I determined with certainty that the bullet was fired from a revolver from a distance of around four yards. This disproved Alec Cunningham's claim that the two men were struggling when the shot was fired.

"Both father and son claimed the burglar escaped through the hedge into the road. But there were no boot marks in the muddy ditch just beyond the hedge. This convinced me that the Cunninghams had lied about the burglar.

"Inspector Forrester saw all this too, but he was so convinced of the Cunninghams' innocence that he missed the obvious conclusion. This shows how our preconceptions can blind us to the truth."

By this point, I needed to consider why the Cunninghams might have committed the crime. Why did they kill William Keegan? Why did they stage a burglary at their house? And were they also behind the real burglary at Mr. Acton's a few nights earlier?

"I recalled something you mentioned, Colonel," I continued. "You said there was a lawsuit between Mr. Acton and the Cunninghams. It struck me that they might have broken into Acton's house to steal a document important to their case."

"Exactly," Mr. Acton confirmed. "I have a legal claim on half their estate, and I possess a document proving it. If they had obtained and destroyed it, our case would have been ruined. Thankfully, the paper is safely kept in a strongbox at my solicitors."

"There's our motive for the initial burglary," Holmes smiled. "It was likely a risky plan, probably Alec's idea. Finding nothing, they attempted to make it seem like a regular burglary by taking whatever items they could find.

"That much was clear. What puzzled me was William Keegan's involvement and why they ended up killing him. To answer that, I needed the missing part of the note. I believed Alec had torn it out of Keegan's hand and put it in the pocket of his dressing gown, but was it still there? To find out, I decided to return to the house.

"When we were outside the side door, the Cunninghams joined us. It was crucial they didn't learn about the torn paper scrap, or they would likely destroy the rest of the note. Inspector Forrester was about to tell them, but fortunately, I collapsed and faked a fainting spell, changing the subject."

"Are you saying your fainting was an act?" the colonel exclaimed, amused.

"From a medical standpoint, it was quite convincing," I admitted. "I was completely fooled."

"Thank you," said Holmes. "In my line of work, a bit of acting can be useful. After 'recovering,' I needed a sample of old Cunningham's handwriting to confirm he co-wrote the note. By pretending to make a mistake with the reward notice, I got him to write the word 'twelve' for comparison."

"And here I was worrying about your mental state," I chuckled. "What a fool I've been!"

"Not at all," said Holmes. "I appreciated your concern! Once we reached upstairs, I needed to distract them for a moment so I could take the note. I did this by accidentally knocking over the jug and fruit bowl. As expected, I found the note in Alec's dressing gown pocket. But before I could grab it, the Cunninghams attacked me. They would've harmed me, too, if you hadn't intervened just in time. I can still feel the young man's hand around my throat while his father tried to pry the paper from my hand.

"When the inspector and I questioned them afterward, the son stayed silent. He behaved aggressively, almost like he was ready to harm anyone who approached him.

"The father, however, realized it was over and confessed everything. It turns out, William Keegan had secretly followed his employers on the night of the burglary at Mr. Acton's. When he threatened to report them to the police, Alec, being dangerous, saw the fake burglary as a chance to get rid of him. He and his father then wrote this message to Keegan."

Holmes showed us the note, now complete with the missing part attached.

"As you can see," said Holmes, "it's an invitation to Keegan to meet with Alec, suggesting he'll make him some offer to keep silent. But in reality, Keegan was being led to his death. And as for the 'Anne Morrison' mentioned, Cunningham Senior explained she was Keegan's fiancée."

"I must commend you on solving this incredibly challenging case, Mr. Holmes," said Colonel Hayter.

"And I must agree," added Mr. Acton. "That was truly impressive work."

Holmes nodded appreciatively to both of them before turning to me.

"Watson," he said, "I believe our peaceful retreat in the countryside was quite successful, don't you think? I already feel much better, and I'll surely return to Baker Street tomorrow, refreshed."