: How does one write a character smarter than oneself? How does one write a "genius" character? I don't mean a scientific genius, or someone who is a prodigious talent in math or chess or something

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I agree: it's a tricky problem.

Some additional thoughts that I have beyond what others have said:

You can simply say that the character accomplished something without giving all the details of how he did it. Like, it's easy to write, "He invented a time machine." How, exactly, does one go about building a time machine? I have no idea. Or he could say, "I noticed that the shirt he was wearing had a type of stitching used only in Philadelphia in 1993 and 1994, and so ..." Just what about it makes it possible to tell that? I have no idea.
The character can know something he needs to know right now, out of all the possible things that one might know. While in real life to know that one particular fact would require a vast knowledge, you can pick the one particular case. Okay, that may not be very clear. What I mean is, say, a character could see a scrap of paper with one word on it and say, "Hmm, 'paradicsom', of course that's the Hungarian word for tomato ..." I know that because I just picked a random word and a random language and looked it up. But for a character to recognize an obscure foreign off the top of his head would require that he be a master of many languages. (Unless we suppose that he was just lucky and stumbled on one of the few dozen foreign words he happens to know.) The same could be done with scientific or historical facts. (Actually probably better with scientific facts, that might be harder even in these Internet days to look up if you don't already know the answer.)
You can have the character figure out the solution to a problem from sketchy information. In real life there might be many answers that would fit the available data, but the character manages to pick the right one. Think of the Sherlock Holmes stories. Like, in one of the stories Holmes tells Watson that he sees he has been out in wet weather and that he has a clumsy servant. Of course Watson is amazed and asks how he could know this since he is now wearing dry clothes and Holmes has never met his servant. Holmes tells him that he deduced this because Watson has some scratch marks on the heels of his shoes where someone had carelessly damaged them while scraping off mud. But how does Holmes know that a servant did it, rather than Watson himself, or his wife perhaps? How does he know that Watson was out in the rain and not that Watson was walking near a pond on a sunny day? Or that the thing scraped off was mud and not that Watson accidentally stepped in horse droppings? Or hundreds of other possible scenarios? But of course, in the stories Holmes astounding conclusions from meager evidence are always right.
As others have intimated, in a story you can fit the world to the character's plan rather than the other way around. In real life, a great plan can be ruined by inconvenient side difficulties. Like, "Then we'll swim across the river and escape on the other side." "But, you can't swim straight across the river, the current's too strong. You'd end up at least a hundred feet downstream, where the banks are far too steep to just climb out." "Oh. I hadn't thought of that." In a story you can make sure that the only difficulties that arise are ones that you can think of solutions for.

One important thing is to make sure that all your contrived solutions don't look contrived to the reader.

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Primarily, cheat by writing the story backwards. Start from the end revelation of the implicit story (the crime) and progress towards beginning, iteratively removing any simplicity.

Start with the outcome, the rather simple final set of events that is to be discovered. Then take it apart: tools, witnesses, methods, motives.

Take a look at each of them. Whenever you see something overly simple, replace it with something ambiguous, deceiving, non-obvious, or outright fake. Unlike the real wise guy, you don't have to limit yourself to things they can do. You can modify circumstances, personalities, environments to fit your convoluted needs.

Then, when you have the whole set of utterly corrupted clues, start writing the explicit story, what the readers will see. Distribute the clues throughout it, and then have the investigator come to the right conclusions, correctly recognize lies and deceits, and present the outcome as result of detailed analysis, a set of random pieces matching in the end, ingenious mind combining them, while in fact it was constructed from a kit of parts with a builder's manual you have created before starting on the explicit story, and only made the process seem unguided while you, the writer, were the guide.

(just to add: this is how math exercises are written. How do you get that complex equation to resolve to "2"? Start with "2", then keep multiplying by expressions that resolve to identity, add expressions that resolve to zero, square both sides, shift expressions between sides, divide by some red herring, and when your equation looks mangled enough, write it down as the subject of the exercise.)

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Just a few suggestions.

Technology. Advanced technology can look like magic, and is not necessarily obvious to your "average inspector". E.g. the criminal could use tiny robotic spiders, which can crawl around the victim's house, eavesdrop on people (so that the criminal knows things nobody else could possibly know), send back data about where everybody is, or film the code that opens a safe.
Social engineering. Maybe inspector A is not stupid, but a sufficient number of victims is. Think of internet scams: even if only 1 percent of people are gullible enough, a criminal can still make lots of victims by sending around huge volumes of e-mails. This gives the criminal an edge over the inspector, who may not even believe that people will fall for the scheme.
Wealth. A rich criminal can buy people in high places, and can get things done which are not in the power of a "simple" inspector.

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Find people smarter than you to help you.

As an example, Susan Elia MacNeal, the author of the Maggie Hope mysteries, didn't know anything about code-breaking when she started writing books about an American mathematician who ends up in WWII London and becomes a British spy. But she did have lots of friends at MIT, so she started asking them about cryptography. She used their help to make Maggie brilliant at seeing and cracking codes.

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The character has to tailor a solution to fit a given problem, but you are not so limited. You can come up with a problem to fit a clever solution.

Take some obscure thing you happen to know, that an everyman wouldn't be expected to know: say, that the Chinese for "I'm going to hit you with this giant phone" sounds very similar to a phrase meaning "Thank you coming to visit me." Now, imagine a situation where this could be used to pull off something seemingly impossible: say, verbally threatening Person A while Person B can hear, but without letting Person B know that anything worrisome is going on. Write G into this situation. It's not easy, but it's a lot easier than the reverse.

For bonus points, note that you now have G hatching a plan involving making a giant weapon that looks like a phone. If you come up with an additional problem facing G that can also be solved ingeniously using a phone-club, then G looks especially brilliant--he's elegantly solved two problems with the same ingenious device.

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You have several advantages over your characters:

You get all the time you need to conduct research.
You have time to think about each thing they will do or say. You get to think through the implications of the situation they're in, and the effects of their actions.
You can constrain and adjust your story world so that your character can excel in it.
You can construct the story to guide the reader away from areas that you know less about, and toward areas where you know more.
Depending on the extent of your research and thought, most of your readers won't know as much as you do about the subject of your character's expertise. Mostly you don't have to be smarter than experts, you only have to know more than your readers. (Caveat: Some of your readers may be experts, and they may be annoyed at the flaws you and your characters exhibit.)
Your readers want you to succeed in entertaining them. They will (sometimes, to some extent) give you the benefit of the doubt.
The Writing Excuses podcasters offer this advice for speculative fiction: Take one unimportant detail and get it exactly right. This can lull readers into accepting that you know what you're talking about, which gives cover to make up all kinds of implausible stuff. This may also work for criminal enterprises.

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One way would be to sort of "cheat", if that would be acceptable to you. What I mean is that you can try to find some good ideas in real life. Real life is full of strange and wondrous things. Google things like "top criminals of all time" or something in those lines to find a criminal that might suit your character or has made an interesting enough scheme to fit what you're looking for, then take the idea and change it enough that it couldn't be easily recognizable. You wouldn't be the first writer to search for inspiration in real life.

“Good writers borrow, Great writers steal.” ;)

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