The fake solution is of course the bread-and-butter of misdirection techniques in mystery fiction. If you have mystery and the explanation to that mystery, what better way to fool the reader than by creating another fake solution to the problem? For example, a crime scene that is dressed like a suicide.would technically be a fake solution already. Or perhaps the suggestion of supernatural powers at an impossible crime scene, like a locked room mystery, would be like a kind of a fake solution. The basic set-up would be to have a mystery, and then present the fake solution, and then the real solution to shock the readers.
The fake solution can of course have several origins. Often, the true criminal plants fake clues to guide the detective and other characters away from the truth. But sometimes, it's just a coincidence, with several circumstances and the stars lining up to create an evenly plausible, alternative interpretation of the clues. This difference between a fake solution created on purpose, or by coicidence can have big ramifications for the tone of a mystery story, but functionally, they don't differ very much.
And now we've arrived at today's topic, because there's an inherent problem to the fake solution. While there might be various reasons for the existence of a fake solution within the story, the fake solution is, in essence, always something that is aimed at the reader: it is directly meant to deceive the reader, to lure them in a trap and lead them away from the true solution. But obviously, the fake solution also needs to be discussed in the work itself. Someone needs to bring the fake solution up, and it has to be cleared up first before the story can move on to the true solution (and often, the true solution is in fact built upon the fundamentals of the fake solution).
The question that arises is: who should propose the fake solution?
A genuine fake solution is fairly complex: any genre-savvy reader will recognize a half-hearted attempt at a fake solution and not fall for it. In terms of complexity, it should not differ too much from the real solution. But that means that not any character in a story should be capable of making the inferences needed to reach the fake solution. As it's essentially a trap set for the reader, the character setting the trap off should be someone as intelligent as the reader, which in mystery novels is often the main detective character.
But authors like Ellery Queen and Anthony Berkeley also showed the dangers of using the protagonist to fall in the fake solution trap: it hurts the detective's credibility if they keep falling for the fake solutions. The Greek Coffin Mystery gave Ellery a very good reason to keep his mouth shut until he was absolutely sure about a solution, because that case showed how fallible he actually was. He was still prone to fall for fake solutions later in his career though. Berkeley's Sheringham on the other hand was basically created to fall for one fake solution after another, and many of his stories with Sheringham convinced he solved the case, while the real culprit is revealed to go scott-free. The fake solution and protagonists falling for them also connect to another problem of mystery fiction: if the detective is shown to be fallible, and the notion of fake solutions exist, how can we ever know for sure the final solution presented in the story is in fact correct? This problem is one that is explored in works of the authors above, but also an author like Norizuki Rintarou, but as I pointed out, this is a result of undermining the detective's authority though fake solutions.
So a different solution is The Foil Detective. If an intelligent character is needed to fall into the trap of the fake solution to serve as a substitute for the reader, but the author does not want to undermine the infallibility of their detective protagonist, the obvious solution is to create a second detective character to propose the fake solution instead. These characters are often presented as rivals to the protagonists, who think they managed to outsmart their opponent, but are then revealed to have stepped into the fake solution trap. I guess this is a variation on the Worf Effect: the Worf Effect, named after the character in Star Trek: The Next Generation refers to having an established "strong" character lose from a new enemy to show how powerful they are. The Worf Detective on the other hand is first established as a worthy detective rival, only to lose to the real protagonist in order to show their superiority in mystery-solving. The whole reason to their existence is in fact to lose, to make the protagonist character look better.
I mentioned Ellery Queen several times now, but while in the novels it was often Ellery himself who fell for the fake solution, he was spared that fate in the 1975-1976 Ellery Queen TV series. An original character called Simon Brimmer was created as the Foil Detective, as a rival detective who fell for the fake solutions, only for Ellery to show what the real solution was. The solutions proposed by Simon were often quite complex on their own, and could've made for a nice detective story on their own, but it was his fate to be the eternal loser, so each time Ellery would conjure up a clue that Simon had missed in his haste and then proceed to reveal the true solution to the tale.
An interesting example is Hattori Heiji from Detective Conan: while he is a regular member of the cast now and shown to be as sharp as the protagonist, his first appearence (The Diplomat Murder Case) actually had him act exactly like the Classic Foil Detective, falling for the fake solution planted by the real culprit. He recovered from that, but his case is an extremely rare one.
The reason why I started thinking about fake solutions and Foil Detectives though is Kizoku Tantei ("The Aristocrat Detective"), a TV drama airing right now in Japan, based on the book series by Maya Yutaka. In it, we follow a fairly capable female detective and her attemps to solve all kinds of crimes (some of them of the impossible kind), but who in the end is also upstaged by the titular Aristocrat Detective. What is amazing about this series is how each single episode has at least two solutions: the fake solution proposed by the female detective, and then the true solution as revealed by the Aristocrat Detective. Both solutions are always quite impressive, and often the fake and true solutions are closely related (the fake solution is always used as a basis for the true solution). This structure of having dual solutions does not originate from the original stories by the way, so it's in fact the screenplay writer who comes up with an extra fake solution for each episode, which is an impressive feat. But I think it's very unique to have the Foil Detective (the female detective) as the main character of the series, as she is proven to be fallible detective in each and every episode.
The Foil Detective is thus a product of misdirection, and a sad one too: their fate is to be wrong each and every time! Their only goal is to fall for the fake solution and hopefully drag the reader/viewer along with them. The Foil Detective is nothing more but a small hindrance to be stepped upon on the way towards the true solution. It just makes you feel sorry for them. Destinated to fail forever. All just because we don't want a detective story to be too easy.
Anyway, I only wanted to give these poor creations some attention, but this post has gone on for too long, so I'll wrap it up. The Foil/Rival Detectives I mentioned above are obviously just a very, very, very small selection, so are there any others you thought were particularly memorable?