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In the Sherlock Holmes story "The Adventure of the Priory School", Holmes shows perhaps the most amount of interest in the reward money. Holmes initially confirms the terms of the reward with the Duke who offers it:

“The fact is, your Grace,” said he, “that my colleague, Dr. Watson, and myself had an assurance from Dr. Huxtable that a reward had been offered in this case. I should like to have this confirmed from your own lips.”

“Certainly, Mr. Holmes.”

“It amounted, if I am correctly informed, to five thousand pounds to anyone who will tell you where your son is?”

“Exactly.”

“And another thousand to the man who will name the person or persons who keep him in custody?”

“Exactly.”

And then Holmes requests the appropriate amount of six thousand pounds as his reward.

My friend rubbed his thin hands together with an appearance of avidity which was a surprise to me, who knew his frugal tastes.

“I fancy that I see your Grace’s cheque-book upon the table,” said he. “I should be glad if you would make me out a cheque for six thousand pounds. It would be as well, perhaps, for you to cross it. The Capital and Counties Bank, Oxford Street branch, are my agents.”

Yet, the Duke ends up making out a cheque for twelve thousand pounds, assuming generously that Holmes and Watson both deserve the reward.

“I must put it plainly, Mr. Holmes. If only you two know of this incident, there is no reason why it should go any farther. I think twelve thousand pounds is the sum that I owe you, is it not?”

Finally, it's indicated that Holmes is very happy about the reward money, which is again a little out of character for him.

Holmes folded up his cheque and placed it care- fully in his note-book. “I am a poor man,” said he, as he patted it affectionately and thrust it into the depths of his inner pocket.

Was the cheque actually made out for twelve thousand pounds, and if so, did Watson get his share? Why was Holmes particularly excited about the money in this case?

Note: In the Granada TV adaptation of this story, the waters are muddied even further, as it is shown that the Duke makes it out to twelve thousand and Holmes is surprised by it, uttering "This is a king's ransom", and the Duke responds as if to say it is an appropriate amount given the magnitude of Holmes' help. This seems to indicate Holmes received the entire amount himself.

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    He's paying them both the full reward in hopes of buying their silence. Were it not for the earlier remarks, Holmes's comment at the end might be construed as trying to reassure a man who does not trust their honor, but really does have good reason to want silence. (If for nothing else, the sake of his legitimate son.) The earlier remarks are more mysterious.
    – Mary
    Commented Jul 18, 2023 at 0:56

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[Spoilers below.]

To quote a fictional character on the other side of the law, "It's not about making money, it's about taking money." To see this, note that the first excerpt continues with one more question from Sherlock Holmes to the Duke:

"Under the latter heading is included, no doubt, not only those who may have taken him away, but also those who conspire to keep him in his present position?"

Holmes is about to reveal two things to the Duke that the Duke already knows, and that Holmes already knows that the Duke already knows, but that the Duke does not know whether Holmes knows. So he's making the Duke promise to give a reward for something that by this point is no longer a mystery to the Duke. And not only this, but the Duke (who was already in distress) is hearing this line of questioning and is probably now uncertain and worried about what Holmes knows, but has to pretend to truly desire a solution to the "mystery". In other words, Holmes is having a bit of fun toying with the Duke before the big reveal.

Holmes did this to the Duke earlier in the story, when it was suggested he return to London.

"This northern air is invigorating and pleasant, so I propose to spend a few days upon your moors, and to occupy my mind as best I may. Whether I have the shelter of your roof or of the village inn is, of course, for you to decide."

In this case, Holmes also acts guileless, but knows that the Duke will not want him to stay at the village inn, because it will set off the rumor mill. Thus, the Duke has to acquiesce to housing Holmes and Watson. So Holmes seems to enjoy forcing the hand of the Duke, while feigning ignorance of what he was actually doing intentionally.

We also see that Holmes wanted to maximize the Duke's consternation with the revelation,

“I accuse you,” said he. “And now, your Grace, I’ll trouble you for that cheque.”

Holmes could have put things a bit more delicately, making reference to the other characters who actually planned and carried out the kidnapping. He would have still collected the same amount of money. But, by making the above clarifying question earlier in the conversation, he put himself in a position where he could accuse the Duke in the big reveal. Why does Holmes do this? It seems to be for the same reason that he investigates cases -- because he finds it interesting to do so.

And this connects to the conclusion, where he says that the payout is the most interesting object he encountered on the visit. Holmes finds the payout interesting, because it says something interesting about how humans will give up large sums of money for the sake of their reputation. This strong need makes humans -- even powerful ones -- easily toyed with, and Holmes finds exploiting this phenomenon interesting and enjoyable.

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