A lot of attention has been focused on how Sherlock faked his own death. In my opinion, Sherlock did not fake his own death. However, Sherlock’s apparent death is not the main mystery - the main mystery is the meaning of the Final Problem. (I will come back to Sherlock’s apparent death.)
The Final Problem is the term used by Moriarty to describe the resolution of his relationship with Sherlock. To understand what Moriarty means, let’s examine what Moriarty wants. Also, let’s take a look at what Sherlock wants in order to understand how he may respond to Moriarty’s schemes.
A) For Moriarty himself: A “diversion”, someone like Sherlock who is a challenging adversary for his schemes. So, Moriarty wants Sherlock to be alive.
B) For Sherlock: A Sherlock who cannot thwart his schemes. So, he wants a Sherlock who does not have public support and does not have the support and resources of the police.
In short, the solution to the Final Problem for Moriarty is that Sherlock continues to challenge Moriarty to provide a diversion, but that Sherlock does not have the public or police support to actually impede Moriarty’s schemes. Moriarty wants to “burn the heart out” of Sherlock, not kill him.
A) For Sherlock himself: The means and opportunity to dismantle Moriarty’s web. So, he needs to learn about Moriarty’s connections and schemes and be in a position to manipulate those – which effectively means he needs to be able to impersonate Moriarty. (And to live obviously.)
B) For Moriarty: To be disabled and incapacitated. If Sherlock could learn everything there is to know about Moriarty’s network, then ultimately, the goal would be a dead Moriarty.
In short, the solution to the Final Problem for Sherlock is to find something that informs him of Moriarty’s network. (He also could find some way to compel Moriarty to reveal his network, but that is unlikely considering that Mycroft tried and failed already.)
In summary, Moriarty wants a live, but discredited Sherlock (not a dead Sherlock – a dead Sherlock does not provide a diversion). Sherlock wants the means and opportunity to pose as Moriarty in order to dismantle Moriarty’s network.
In The Fall episode Moriarty has set up a plan to discredit Sherlock. He posits a riddle “I O U” about how he will discredit Sherlock. I agree with other bloggers who have suggested that I O U is an alpha-numeric code for the stories “The 12 Brothers”, “Hansel and Gretel”, and “Cinderella”, as they appear in the edition of Grimm’s fairytales that Moriarty leaves for Sherlock. The final story is “Cinderella”, a story in which a sudden celebrity is reduced to lowest level – Moriarty’s plan for Sherlock.
In the final scene on the roof with Sherlock, Moriarty schemes to have Sherlock jump from the roof. However, Moriarty has made arrangements to save Sherlock from dying. (I am getting back to the point about the suicide.) If Sherlock were to actually commit suicide, it would not only take away Moriarty’s only “distraction”, but also probably put a large target on Moriarty’s back as Sherlock’s brother Mycroft could very likely have Moriarty assassinated.
In the final scene, there is a person directly underneath Sherlock and Moriarty with some equipment on the bench. The equipment is an inflatable device (there are two large red inflatable bags with white markings and a gas canister in a green bag strapped across these. The person is on the phone looking up and down the street, waiting for a signal from or through Moriarty to inflate the device in order to catch Sherlock and prevent his death from the fall. This is Moriarty’s plan – to make Sherlock feel so beaten that he attempts to commit suicide, but then to prevent that suicide – thus “burning the heart out” of Sherlock, further solidifying Sherlock’s public disgrace (can’t even kill himself), and not running afoul of Mycroft (and his access to all manner of government resources).
The truck that pulls in after the busses is arranged for by Moriarty to hustle in the landing pad, and hide it from the general public. The people on the ground at the time are partly Moriarty’s people who would keep the public away so that the landing pad can be hidden away. So, the bike rider is actually Moriarty’s helper, not Sherlock’s as some have suggested.
The person under Sherlock and Moriarty may appear to be a person out for some shopping. However, the person does not get on the bus when it pulls in, does not have a purse, and the backs the person has put on the bench are heavier than plastic shopping bags and have large white markings (that is not reflection of the sun, which was behind clouds).
It seems like a rather clever and subtle plan from Moriarty, doesn’t it. But, Sherlock is one step ahead. If Moriarty wants Sherlock to think he is committing suicide, only to save Sherlock, Sherlock can foil that plan by actually making everyone think he has committed suicide. That would actually free Sherlock to infiltrate and destroy Moriarty’s network. As we know from previous stories, Moriarty doesn’t get his hands dirty and runs most of his network through email and texting. So, what would Sherlock need in order to impersonate Moriarty?… Moriarty’s cell phone. So, from Sherlock’s point of view, the last story also becomes Cinderella – if Sherlock can get Moriarty’s phone (like a glass slipper) he can impersonate Moriarty.
So, how does Sherlock’s plan play out. First, he has Mycroft kidnap and torture Moriarty in order to spur Moriarty to take decisive action against Sherlock. Second, Sherlock and Mycroft set a trap for Moriarty to find out more about his background and history. The trap is the so-called reporter Kitty Riley. She is not a reporter, but is one of Mycroft’s agents. The evidence is that the story that she shows to Watson at her apartment is bylined “By Kitty Riley”, however, when the story runs in The Sun under the headline about Sherlock’s suicide, it is bylined “From Luka Plumbelow” – so Kitty Riley was simply a cover. The unusual use of the word “from” in the byline and the unique name are cues to Mycroft’s operatives that Sherlock is indeed safe. The ruse with Kitty Riley was a way to learn more about Moriarty, so that Sherlock could better infiltrate his network – as Irene Adler had said – the problem with a disguise is that one is always disguised as oneself. So, we can see that Moriarty has a background with children and with medicine – perhaps he studied as a pediatrician at some point. The cover story clearly provides a lot of leads for Sherlock to investigate.
Let’s get back to what happens on the roof. Sherlock plays Moriarty in order to get Moriarty to reveal more of the contingencies that he has arranged – such as the assassins keyed to Sherlock’s 3 confidantes. Then Sherlock steps to the ledge to get ready to jump, and he sees something and smiles. He sees one of the assassins who have been hounding him and killing the competitors whenever one of them shakes his hand. He smiles at that point because he sees the opportunity to eradicate Moriarty. He steps back off the ledge, engages Moriarity and cues Moriarty with the phrase “shake hands”. He expects that when Moriarty shakes his hand that the assassin will shoot Moriarty as they have other competitors. (These assassins will not know Moriarty as Moriarty – nobody does except for Sherlock. They are likely to see him as another competitor for Sherlock’s supposed decryption key. So, they would shoot Moriarty if necessary.) However, Moriarty surprises Sherlock by killing himself. Sherlock is clearly shocked at this as he yells “No” and literally falls back in shock.
We see Sherlock confused and ready to jump. He is confused because he is not sure if Moriarty’s plan to save his life will be implemented with Moriarty out of the way. Perhaps there was a signal that Moriarty would have need to give. That is why Sherlock takes a long time to jump, and has several gesticulations – in order to alert the supposed Moriarty henchman to get ready.
When Sherlock jumps, he clearly does expect to survive. We can see that the phone on which he leaves his final note is not his usual phone. The phone he uses at this time and leaves on the roof has a camera – the phone he usually uses does not have a camera. He leaves the “note” so that the public will believe he has, in fact, died. (He also takes Moriarty’s phone with him.)
Sherlock jumps, and is saved by Moriarty’s henchman. The truck blocks John’s view, and serves as a way to bundle off the landing pad. Molly has arranged to have hospital staff rush out to put Sherlock on a stretcher and bring him in quickly, and also to quietly bring Moriarty’s body off the roof. Sherlock likely (as has been suggested elsewhere) took a drug to feign death to fool Watson.
So, as a result of Sherlock’s plans – Moriarty is dead, but no one knows that; Sherlock is alive, but everyone thinks he is dead; he has Moriarty’s phone so that he can pose as Moriarty to all of Moriarty’s contacts; and he has lot of biographical material through Kitty Riley to piece together Moriarty’s identity. Sherlock did not fake his death – because he had concluded that Moriarty would actually not let Sherlock die. So, Sherlock (with Mycroft’s help) has everything he needs to infiltrate and destroy Moriarity’s network.
(Incidentally, Sherlock can scour Irene Adler’s phone for messages from Moriarty and follow those back to piece together a schedule of where Moriarty was and as a template to learn how Moriarty communicated with his network.)