On the 15 (and a half) Types of Impossible Crimes

There’s been no end to the ingenuity of the impossible crime genre. When you see murders committed inside of perfectly sealed rooms, and stabbings in virgin snow where the killers leave no footprints, you’re only taking the daintiest of baby-steps down the iceberg of magic murders. Take a few steps further and you’ll find yourself barreling into the realms of animated murderous snowmen, disappearing hotel rooms, witchery, teleportation, telekinesis, premonitory dreams, apparitions, flying men, transmogrification, impossible golf shots, men dying from falls when there’s no elevated surfaces for miles, time travel, people running through solid brick walls, and even the apparently magical disintegration of a man in front of witnesses. All of which, mind you, must be explained through perfectly human means without reliance on far-fetched science-fiction technology or preternatural agency — or, if sci-fi tech and ghostly happenings are commonplace in your world, their rules must still be adhered (and are usually exploited to establish the impossibility…). A whole world of man-made miraculous murders that would have the skeptics of our world taken aback! When you imagine the impossible crime problem, you imagine a scenario which absolutely cannot be taken at face value, and which the characters in the story have to battle with the reality of, whether it’s through disproving the supernatural or an ostensible suicide. There’s an impossible crime tale for damn near every insane scenario under the sun a person could think of.

…Or so I said in On a Defense of the Impossible Alibi Problem. A perfectly good introductory paragraph, wasted.

The impossible crime tale seems to be a favorite of people looking to create taxonomies. From solutions to situations, the impossible crime sub-genre more than any other seems to invite people to create lists trying to chronicle every little manner of plot, style, and form that exists. You might argue that this is a testament to the sheer formulaicity of the impossible crime story, or a testament to the magnetism of its versatility…

Just like I’ve done before in attempting to produce a list of 50 solutions to the 3 principle impossible crime genres, I will here be attempting to produce a list of all every conceivable manner of impossible crime situation — within reason. I will only be adding to this list if I feel like the entry is all of (a.) something that meaningfully alters the presentation of the impossible crime, (b.) something that meaningfully alters the potential explanations to the crime, and (c.) categorically non-specific so to be applicable to a suitable variety of stories. This is primarily because the minutiae distinguishing two locked-room mystery situations is a lot less significant than the minutiae distinguishing two solution types — this also means I can provide less “theoretical” entries than I could before.

Over at The Invisible Event, Jim Noy has actually covered a lot of our bases on his own post a few years back on the same topic. My intention here is not to contradict him, but rather to supplement his list with a few potential entries I feel worth pointing out. I will be covering a lot of re-tread ground here, so in the interest of keeping Jim’s contributions and my own separated I’ll simply be listing Jim’s entries first in one set and then mine at the end. I’ll be supplementing each category with a paragraph or two explaining the concept too — just so that this is my post, and nobody else’s!

Without further ado…


1.) The Locked-Room Mystery

The grandfather of mystery fiction and the perennial favorite of all impossible crime aficionados, locked-room mysteries scarce warrant an introduction. You have a murder committed within a room locked, sealed, and barred from the inside so that every entry is blocked-off. The only key to the room is inside of the victim’s pocket, so the killer must be still inside of the room… and yet they are not! The implication is that the killer has someone walked through the walls or vanished into thin-air…

This is the most popular form of impossible crime, and examples are a-plenty. Edgar Allan Poe’s “Murders in the Rue Morgue”, popularly (and debatably) considered the original detective story, Clayton Rawson’s Death from a Top Hat, and John Dickson Carr’s The Hollow Man (also known as The Three Coffins) all features killers who seem to vanish into mid-air within a locked room…

1.5.) The Judas Window Locked-Room

Not, perhaps, a separate situation altogether, but a prominent enough sub-sub-subgenre to warrant mention, this is one of those “Doylist Impossibilities” I invoke in On a Defense of the Impossible Alibi Problem. The situation is entirely the same as a traditional locked-room mystery, with one caveat: there is a single suspect locked inside of the room with the victim, so that it appears entirely impossible for them to be innocent of the murder! The situation is only impossible if you, as the reader accept the condition that this person is innocent and the murder must’ve been committed by an external agency.

I’ve named this one after the most prominent example, John Dickson Carr’s The Judas Window. This situation is a favorite of many cases of the Phoenix Wright: Ace Attorney video game series in which you defend clients falsely accused of murder — more often than not, this accusation comes as a direct consequence of the defendant being locked in the same room or sealed in the same general location as the victim. Edward D. Hoch, the “Master of Short Stories”, also produced more than a handful of these, such as “A Shower of Daggers”.

2.) Footprints in the Snow

…or sand, or dust. These crimes involve a man found murdered in a vast expanse of snow! The killer definitely murdered the man from close-quarters, and the man was murdered after the snow had finished falling… so how could the killer have committed this murder without leaving his footprints in the snow!? A killer who can somehow float over the snow…

John Dickson Carr dealt with the problem most notably in The White Priory Murders, and his French-speaking disciple Paul Halter also wrote these in, among others, The Lord of Misrule and The Gold Watch. Christianna Brand produced one of these in Suddenly at his Residence using dust, and Arthur Porges’s “No Killer has Wings” and Hal White’s “Murder at an Island Mansion” are two examples of this problem on sandy beaches.

3.) Psychological Impossibility

We’re starting to get into the abstract. A man’s death is caused not by direct murder, but instead by a behavior that is so absurdly unbelievable it defies every known principle of human psychology! The most famous example of this is Father Ronald Knox’s “Solved by Inspection”, which involves a man who starves to death in a room surrounded entirely by safe-to-eat food that he could’ve eaten at any moment.

4.) Impossible Physical Feats

Humans are constantly displaying their infinite capacity for improvement. Records are always being broken, and the human condition forever expanding. But in these stories, these feats of athleticism swerve from the superhuman straight into the supernatural. A man cannot run from California to New York in a matter of hours, neither can a man leap from the top of the Eifel Tower and land with not a single scratch on his body…

The Stingaree Murders by W. Shepard Pleasants features a knife that’s hammered into the wooden boards of a boat so tightly that not even Mike Tyson himself could remove it without causing significant damage and creating noise that would assuredly not go unnoticed — naturally, the knife is removed. Death in the Dark by Stacey Bishop tells of a baffling murder in which a killer is somehow able to make an eagle-eyed shot at his victim in pitch-black darkness! Impossible Bliss by Lee Sheldon involves a nearly-impossible perfect golf shot from a nearly-impossible angle that not even the most seasoned of pros could achieve!

5.) Killer Rooms

Without fail, every single time a man sleeps in the bed in room 405 of the Dickson Inn, he never wakes up… and is found the next morning, having died of heart failure at precisely midnight… The killer room involves spaces that seem to have the uncanny ability to indiscriminately cause death without human intervention. Even more baffling, these situations may have bizarre, hyper-specific conditions under which these deaths occur…

Impossible-crime-oriented BBC drama Jonathan Creek has an episode episode titled “Mother Redcap” involving an inn where bizarre deaths seem to constantly occur within the same room, at the same time… Max Afford’s “The Vanishing Trick” involves a “kinda haunted” room that constantly swallows up servants and sends them to God-knows-where…

6.) Invisible Murderer

A murder who is mysterious able to pass under your nose without detection, strangle a woman in plain view of a crowd of hundreds without being seen, and murder in rooms guarded on all sides. This impossible problem involves the situation of a murderer who is able to defy detection even when the situation dictates that they would be seen.

Such an impossible crime makes up the principle murder of Christianna Brand’s Death of Jezebel, in which a murder is committed in front of a crowd of hundreds of spectators to a medieval pageant at top of a tower, the only viable entrance to which was also in view of the audience. Derek Smith’s Whistle up the Devil features a murder in a jail cell whose sole door was observed by the narrator and a reliable witness at all times the murderer must’ve walked through the door, and yet neither of them saw any such killer…

7.) Vanishing

Whether person or object, the problem of an impossible vanishing involves something disappear when there’s no reasonable way for this to occur. While it can often overlap with locked-room mysteries, footprint mysteries, or invisible criminals, this class of impossible crime also accounts for people vanishing in front of witnesses like a magician, or thefts of objects while in another character’s hands…

Roger Ormerod’s More Dead than Alive features a world-renowned magician who seems to disappear impossibly from his locked-and-sealed laboratory. Edward D. Hoch wrote multiple stories featuring a Great Thief-cum-Detective Nick Velvet, including the impossible caper “The Theft of the White Queen’s Menu” in which three impossible thefts occur: the theft of a roomful of furniture in a matter of just a few minutes, the theft of a roulette wheel from a crowded casino and yet nobody saw it leave, and the theft of rival thief The White Queen’s menu while it is held in her hands! Quite spectacularly, Paul Halter’s story “The Celestial Thief” involves the disappearance of all of the stars in the night sky as an astronomer is watching them from his telescope!

8.) Materialization

Diametrically opposite the previous category, impossible materializations involve the production of an object or person where it very well could never have been! A man manifesting within a sealed room, a plane appearing in the sky when it had nowhere from which it could’ve come, and poison appearing within a test-tasted dish…

James Yaffe’s “The Case of the Emperor’s Mushrooms” involves the murder of Emperor Claudius of Rome, who dies to a plate of poisoned mushrooms — quite mysteriously however, the royal food-tester had eaten a portion of the food without dying, and so the poison must have appeared while in the emperor’s hands…

9.) Prophecy, Clairvoyance, and Predictions

The fortune-teller tells you that you will die on June 4th, 2022 at 5:25 PM… and, lo and behold, you find yourself dead at the appointed time! People coming into possession of knowledge which they should never have been able to learn makes up this class of impossible problem.

There are, in fact, two real-world examples. “The Greenbrier Ghost” of West Virginia is a story about a woman who divines knowledge of the cause of her daughter’s death when the young women’s death was named natural. “The Horse Room” involves a group of women named the Blondie Gang who were robbing casinos blind in the 1940s, and the way they managed to cheat at horse-race betting in a room where no information could travel in or out… John Dickson Carr’s The Reader is Warned also involves a psychic predicting a murder, down to the very minute it’ll occur.

10.) Ghost, Witches, and Miscellaneous Supernatural Jiggerypokery

This, ultimately, is a “miscellaneous” category for all impossible crimes that appear to be ghosts, magic, or the supernatural at work but don’t fit into the other categories for being too specific. The appearance of a floating ghost in a room, a woman casting a spell that appears to come true, or the commission of a seance all fall into this category.

John Sladek’s Black Aura has a man suspended in mid-air and walking without any support in front of witnesses, and Hake Talbot’s Rim of the Pit features floating men, ghosts, seances, and nearly every supernatural occurrence you could hope to dream of. “Miracle on Christmas Eve” by Szu-Yen Lin involves the impossible delivery of gifts by a man who could only be Santa Claus himself… Also, suffice it to say, Scooby-Doo anyone?

11.) Impossible Technology

Mind-reading devices, hover-boards, and teleportation machines don’t exist… or do they? The impossible technology problem involves story where a piece of technology is presented as entirely genuine, but there is no scientific way for such a machine to exist. How could this bizarre feat be faked and manufactured?

In The Great Ace Attorney 2: Resolve of Ryuunosuke Naruhodou‘s third case, Twisted Karma and his Last Bow, defense attorney Ryuunosuke Naruhodou is commissioned to defend a scientist of murder. This scientist constructed a teleportation machine that’s capable of de-materializing a man in one place, and rematerializing him in another spontaneously. He was demonstrating the machine at a science exhibition when the device malfunctioned, causing the man to appear above a glass tower, suspended freely in the middle of the air! The man would then crash through the roof of the tower where it would be impossible to approach him… and yet, when the police arrive, the man was stabbed to death. Because of the location of the body, it’s only possible for your defendant to have stabbed the man before his teleportation! And so, in order to prove his innocence, you also have to prove how the entirely impossible feat of teleportation could’ve been faked in front of a massive audience…

12.) The Inverted Howdunit

One of two Impossible Alibi problems I described, this Doylist impossibility tiptoes the line between the inverted mystery (mysteries in which we know of the killer and their plot ahead of time) and the impossible crime. In the Inverted Howdunit, we are privy to the identity of the killer very early — however, unlike most such stories, in the Inverted Howdunit we only know the killer’s identity, but we do not know how they committed the crime… or how they managed to construct an airtight alibi! This impossibility hinges on knowing the identity of the killer, but it appearing nonetheless impossible for them to be guilty.

Roger Ormerod’s Time to Kill features a murder by an ex-convict — however, the ex-convict never once left the narrator’s sight during the period during which the murder must’ve taken place! In Detective Conan Volume 2, the case “Mysterious Shadow Murder Case” involves a man who committed murder while unmistakably in another country at the time… Agatha Christie’s “A Christmas Tragedy” has Miss Jane Marple describe a murder she once solved in which she knew the killer’s identity… and yet the killer had an impenetrable alibi!

13.) Suspect X

Nine people are trapped together on an island. One person wanders off, leaving the remaining eight people together in the dining room. The ninth person is soon heard screaming, and when the eight people arrive…. they find him dead! And yet, this is impossible… he hadn’t committed suicide, everybody was watching each other at all times..! Is it possible that an Xth suspect was on the island, killing them from the shadows?

Suspect X is the second “impossible alibi” problem I described in my post on the topic. This impossibility essentially dictates that, in a closed-circle mystery, the crime is only possible if you assume the presence of one extra person whose existence in the closed-circle is itself also impossible. The solution could involve explaining the presence of this extra person, or ways for the killer, who is among the original cast, to commit murder despite being under constant surveillance.

Such problems appear in Agatha Christie’s And Then There Were None, in which the entirety of the cast is dead, and all apparently murdered, while isolated together on an island; NisioisiN’s Zaregoto – The Kubikiri Cycle, in which the narrator’s friend’s computer is destroyed while every living member of the cast is together in the dining room; Derek Smith’s Come to Paddington Fair, in which the victim is shot by a bullet from a prop gun which was at one moment loaded with blanks but later loaded with live ammunition, even though every member of the cast is incapable (by alibi and testimony) of tampering with the gun.

14.) Biological Impossibilities and Illogical Causes of Death

Biological impossibilities are any mysteries in which the victim faces a death which utterly defies human physiology and logic. Initially, I was going to have a separate category for “impossible falls”, those stories in which the victim falls to their death despite the lack of an elevated surface within any reasonable distance, but I decided to consolidate those two categories hear under the blanket of “Illogical Death” since I felt like they were conceptually similar enough.

Robert Randisi’s (awful) “The Hook” involves the serial killings of women who have had all their organs removed quite impossibly, despite the presence of only a very small incision through which removing the organs so cleanly would be impossible. Both Paul Halter’s “Jacob’s Ladder” and Mack Reynolds’s The Case of the Little Green Men involve a man falling to his death despite there being no elevated surfaces nearby. John Dickson Carr’s Gur Erq Jvqbj Zheqref and the first case of The Great Ace Attorney both involve a death by curare when ingested — curare can only cause death when it enters the bloodstream, and is harmless when imbibed. Paul Halter also wrote “The Robber’s Grave” in which a patch of grass is unusually unable to grow no matter what… Soji Shimada’s “The Executive Who Lost His Mind” involves someone who was murdered only minutes ago, but their corpse suggests that they’ve been dead for years…

15.) The Lonely Boat

A boat floats in the middle of a lake with a lone fisherman in it. The fisherman suddenly keels over and dies, and when the boat is recovered he’s found stabbed to death! Such a death is impossible — it would’ve been impossible for anyone to approach the boat without attracting attention or getting wet, so how much a man wind up murdered while isolated in the middle of a body of water?

I was initially unsure about whether or not to include this one, as most variations on this problem strongly overlap with the “invisible murderer”. However, I believe this problem meets all three of my criteria in theoretically creating a significant distinction in how the crime is presented and resolved…

Such a problem occurs in Joseph Commings’s “The Spectre of the Lake”, in which two men are shot from close-range in the middle of a lake, and both of John Dickson Carr’s “The Wrong Problem” and W. Shepard Pleasants’s The Stingaree Murders, in which a man is stabbed in an isolated boat.

Death of Jezebel (1949) by Christianna Brand

Amazon.com: Death of Jezebel (The Inspector Cockrill Mysteries Book 4)  eBook: Brand, Christianna: Kindle Store

Agatha Christie. Margery Allingham. Dorothy L. Sayers. Ngaio Marsh. These four names have been carved into the annals of crime fiction history as the “Queens of Crime” — the highest of the highest examples set in detective fiction, the grand dames of murder, the gold standard of mysteries for a century to come. These four women were the superpowers in crime writing culture in their time…

But nobody’s ever been satisfied with just four of anything, right? Four is such an awkward number. Three’s much nicer, but… well, it isn’t very nice to say that someone doesn’t deserve their decorated reputation. That isn’t to say I wouldn’t, but I want this to be a positive piece so, instead, I’d like to make a case for a fifth Queen of Crime. A brilliant writer who put to paper three accepted masterpieces and at least three more nearly-comparable efforts in about the same amount of books it took Dame Christie to grow out her training wheels, and one of the unsung heroes of the women of the Golden Age of Detection: Christianna Brand!

Christianna Brand’s literary career started in 1941, when she wrote a murder mystery featuring Inspector Charlesworth, called Death in High Heels. The novel was inspired by her fantasies of how she’d get away with killing bothersome customers and co-workers while she worked as a salesgirl and, evidently, crime writing proved to be a cathartic outlet for her unsavory tendencies as she almost immediately wrote and published Heads You Lose, the first of her longest-running series of novels featuring Inspector Cockrill. She had a steady output of detective fiction featuring primarily Inspector Cockrill for the next two decades, before slowing down but still occasionally publishing the odd crime novel or children’s book well until her death in 1988.

In 1948, she published Death of Jezebel, a locked-room mystery where Cockrill’s career is still recovering from his blunder in Green for Danger, her most famous novel, a 1944 mystery set in a military hospital during wartime bombings. Consequently, he is at odds with a local police inspector, who also just so happens to be Brand’s secondary series sleuth Inspector Charlesworth and who isn’t entirely convinced Cockrill is up to snuff to solve this mystery. Though Death of Jezebel novel is technically a crossover between the two, it’s primarily a Cockrill novel, with Charlesworth ultimately failing to solve the crime before Cockrill.


Her name is Isabel Drew. But her company prefers “Jezebel”. It’s been years since Drew compelled her best friend Perpetua Kirk to engage in drunken adultery with Earl Anderson, even though she had only just recently gotten engaged to her loving fiancé. Cruelly, when the fiancé shows up looking for Perpetua, Drew led him straight to the scene of her infidelity and, horrified, he immediately drives his car into a wall, killing himself.

Since then, his death continues to linger over the company like a nasty miasma. Drew, Anderson and Kirk, all still together in spite of the horrible events years prior, are set to premier in a historical medieval pageant at the Homes for Heroes Exhibition, with this animosity culminating in each of the trio receiving death threats, promising their demise at the Exhibition. Not willing to sacrifice the pageant, the three bring in Inspector Cockrill to defend them, falsely hoping that the deaths, if any should there be, would occur between shows…

And yet, to the horror of thousands of spectators, in the middle of the pageant, as seven knights ride out onto stage on their horses, Isabel is thrust from the peak of the tower on which she stood, and is found to have been fatally strangled just a few minutes before her fall. On one side of the tower, a door was locked and bolted from the inside, and guarded on the outside by one of the crew… and on the other side of the tower, an open archway exists, in full view of the massive audience, all of whom swear that nobody ever went into it since all of the actors rode out on stage. A seemingly impossible case of strangulation and defenestration, committed inside of an empty tower nobody could’ve ever entered, in front of a reliable crowd of thousands of witnesses.

And so, the game is afoot, with Inspectors Cockrill and Charlesworth on the tail of a dangerous killer armored with unparalleled ingenuity.

Death of Jezebel represents the greatest example of and the logical extreme of Brand’s greatest strength as a puzzle-crafter: her mastery over the dramatic logical reversal. Brand is borderline Machiavellian in her ability to plant ideas and theories into the reader’s brain, convince them they thought of it themselves, shred it to pieces and move on. Brand is a puzzle-crafter who is able to lay down pieces with such a casual frankness that it’s always hard to tell when she’s trying to hide something from you, or if she’s trying to hide the fact she isn’t trying to hide anything at all… False solutions that play on theories the reader will assuredly have at that point in the game, clues that never mean quite what they seem they should… and in the middle of Death of Jezebel, during a long series of false confessions, possibly the single most damnably mischievous and mean-spirited “meta”-misdirection I’ve seen in this genre, period end, which I would love to talk about in a little spoiler-dedicated section at the end of this review, as it aligns somewhat with a complaint many people have with this book….

Oh, and never-you-think that all of this misdirection, cluing, red herring planting, game-playing, manipulating and mind-reading Brand’s engaging in is wasted on a solution that isn’t worth her efforts. Brand demonstrates marked ingenuity and cleverness in her locked-room puzzle, creating a solution that, while somewhat convoluted (is that really a bad thing?), flows brilliantly and organically from the information we’ve been given, and which could truly only work in this set-up. The solution is devilishly macabre and novel, and beyond daring and clever, and hits like a bolt of lightning when it’s revealed.

As a puzzle mystery, locked-room or otherwise (but especially for locked-room mysteries), Death of Jezebel has become the gold standard for me. It’s become an example I try to follow in my own impossible crime writing in cluing, misdirecting, and solving, and the example against which I measure nearly every locked-room mystery novel I read. It’s impossible to describe just how formative this novel has been in guiding my experience with reading and writing puzzle mysteries for years since I’ve read it. I’ve read mystery novels that surprised; this one took it a step further and inspired.

And hark, O Ye Socialites of the genre, for no Brand is ever just a simple, cozy, humdrum puzzle plot. As with any of her mystery novels you can select at random, the characters in Death of Jezebel are described and developed with a surprising amount of that ever-elusive third-dimension, and a persistent charm. Even the bleak, more toxic cast of Death of Jezebel sticks out to my mind years after I first read the book, and the clarity and complexity in which their flaws are drawn gives them a sort of bizarre negative charm; Perpetua Kirk is one of my favorite suspects in a mystery novel ever. And mind you, I’ve never been one much to get too caught up in the literary merits of a Golden Age mystery — puzzle first, and all that — but Brand’s skill at eliciting immediate familiarity with her core players is still worth mentioning, even for someone like me who usually doesn’t care.

The novel pips along chipperly in a marked contrast to its somewhat un-cozy, darker narrative, and manages to be reliably playful when it knows it ought to be. And yet, there’s also its own fair share of grittiness and frankness that you rarely see from this genre, in this period of time. As with her puzzles, Brand’s stylization is, put simply, daring. I also consider Death of Jezebel one of her better-paced mysteries. Many of her other novels take too long setting the stage, and the interpersonal dramas, before getting to the murders, but the more concise, elegant dynamics between the central trio in Death of Jezebel let Brand get to the mystery quickly without necessarily sacrificing the human element that she’s always handled so well.

I’m sure you can tell, given I’ve had not a single negative word to say about this novel from beginning to end, but I absolutely adore Death of Jezebel. I can say with no reservations, no doubt, and no trepidation that this is my favorite locked-room mystery ever written, my favorite puzzle plot ever conceived, my favorite piece of misdirection, and my favorite mystery novel ever written, period, and has been wildly influential to me as a reader and writer of puzzle plots and impossible crimes. It is, in my opinion, the greatest effort by one of the greatest practitioners of the Golden Age mystery, who should be better known than she is. Book-for-book, Brand would make Agatha Christie sweat if the two decided to compete. No complaints, no negativity. Death of Jezebel is a masterpiece, and anyone and everyone with half an iota of interest in anything crime fiction could do much worse than to pick it up for themselves, and then read four more Brands immediately after…

All rise for the newest Queen of Crime.

*** SPOILERS ***

One of the most frequent complaints I see levied against Death of Jezebel is the false solutions being annoying and not credible. In any other mystery novel, I’d accept that a pointless series of false confessions is annoying and detracts from the work, but in Jezebel I feel as if the greatest piece of misdirection in the novel would be lost without them.

Many locked-room mysteries make the mistake of tipping their hand by not letting the reader get to intimately investigate key pieces of information that highlight the vulnerabilities in the set-up. In pure spite of that, Brand boldly reveals the most important half of the solution in the middle of the book. Christianna Brand reveals the actual solution in the middle of a long series of fake solutions, at a point in the novel when it’d be unthinkable for the writer to reveal the real solution, and so she never has to actually prove it wrong. We’ve already subconsciously accepted that there’s no way this is going to be a real answer, presented in the middle of five other fake confessions, in the middle of the book. When the detective gives some flimsy excuse proving this solution wrong… we just sorta go “okay, that’s fair” and immediately X out that line of reasoning from our brain. The book tricks us into taking the CORRECT answer when it’s presented to us, distrusting it, and immediately throwing it out and just deciding to never think about it again for the rest of the book without any great deal of logical effort from her part. This is absolutely brilliant, even if S. S. Van Dine wouldn’t necessarily approve, and I could not imagine this book without this fantastic piece of false-solution-based misdirection.