On A Defense of the Impossible Alibi Problem and “Doylist” Impossibilities

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. However, there’s one situation which is so sedate in its presentation, and which, in our world, wouldn’t make anyone bat an eye, that has been something of a point of contention in the impossible crime world: the impossible alibi problem.

The “impossible alibi” puzzle comes is essentially this: we know that the killer has to be this specific person (or someone among a closed circle of suspects with proximity to the crime), usually by insistence of the book or narrator, but this specific person (or every person in aforementioned closed circle of suspects) has an apparently unassailable alibi. Usually, this alibi is vouched for and reaffirmed in some way by the narration — when the guilty party is definitely one specific person, the book also usually goes an extra step to assure the reader they aren’t being hoodwinked and that the crux of the puzzle turns decidedly on this person’s guilt. Consider if you will Columbo, where they always open an episode by revealing the killer and how they carried out the crime, and the puzzle is in figuring out how Columbo solves the mystery — the “howcatchem”. By then removing the actual knowledge of how the killer committed the crime from the formula and giving them an airtight alibi, the “impossible alibi” problem can straddle the howcatchem with the locked room mystery with ease.

What I would say makes it hard to see this problem as “an impossible crime”, per se, is that if the crime were to occur in our world we would simply not pursue it as such — and, save perhaps for the detective, nobody in the book is approaching it from that angle either. Someone who isn’t the suspect could have just as, if not even more easily, committed the crime and the “impossible” problem melts away. The problem is possible… but only so long as you take it as the events of the novel being experienced from the perspective of someone impartially involved with the affair, that is. The murder is only “impossible” to us as readers, and nobody else, and only as long as we wholesale accept a certain premise.

This is far from a fair criticism to levy against the “impossible alibi” plot. Consider if you will what I like to call “The Judas Window Problem”: a murder is committed in a locked and sealed room, only of course, inside of the room isn’t just the victim’s body, but also a living individual presumed to commit the crime; it is only when we accept that this person is innocent that the crime takes on its “impossible bend”. In many cases, there does end up being some physical evidence at least lightly suggesting that the person in the room is innocent, but there are also more than a few cases where there isn’t and the detective investigates more out of personal interest. Does it stop being an “impossible crime” story simply because you’re missing hard, physical proof the suspect is innocent? Does it become “a totally possible crime which only incidentally features a sealed room and the exact kind of trick that would be used to commit a locked-room murder elsewise” simply because the book expects us to accept some premise that wouldn’t necessarily be accepted within the confines of the story? If it feels like we’re suddenly splitting hairs here, why is it suddenly a different story when we’re expected to accept one person’s innocence, when the alibi problem is only the dichotomous opposite of accepting one person’s guilt?

Four years ago, on The Reader is Warned’s post on this very topic, Dan suggests that the “impossible alibi” problem doesn’t deserve to be called an “impossibility” because alibis don’t hold water under scrutiny and are “meant to be broken down” — and, specifically, because the suspects say “I wasn’t there”. There are two points here, “the alibi is meant to be broken” and “alibis are flimsy because they’re based on testimony”, which will be dealt with reversely.

The second point is markedly unfair; there is no novel out there claiming to feature an “impossible alibi” problem where the problem begins and ends with all of the principle suspects saying “I wasn’t at the crime scene, I was in my room!”. A crime where someone is murdered in an immediately accessible location, but everyone promises they were somewhere else with next to no corroborating information would never pass snuff as an “impossible alibi” problem. It’s when other people’s testimony and physical evidence starts to make it appear as if every alibi is assuredly true when the impossibility starts to take form.

Consider Roger Ormerod’s Time to Kill, wherein the detective all but assures us that an ex-convict he’s playing pool with is the culprit of a murder on another floor of the hotel in which they’re playing, which was proven by autopsy to have occurred during the ongoing pool game. Or, the locked-room mystery and impossible-crime story by popular Japanese author NiSiOiSiN, Zaregoto: The Kubikiri Cycle, where one of the crimes is the destruction of the narrator’s friend’s computer while every member of our classically-styled stranded island closed-circle cast testifies that every other person was in the same room at the same time at the critical moment, which is known to be the period of time when everyone was assembled together. Consider Agatha Christie’s “The Christmas Tragedy”, where we’re 100% guaranteed to the identity of the culprit but reliable testimony places him elsewhere at the time of death.

Now, of course, you could argue a lot of things that end up explaining the problem away, even though you seem to have physical evidence and other testimony supporting the alibis. Seemingly reliable testimony was actually fudged to provide the culprit with an alibi; perhaps, somehow, the time of death was obfuscated; perhaps the killer used some bizarre, unknown trick to make it look like he’s in one place when really he isn’t; perhaps the killer wore a disguise; perhaps a once-thought-dead individual in a closed-circle is actually alive, having faked their death; perhaps the crime was committed remotely through some unknown means.

…Which brings us to the first of the earlier two points. Yes, these are all possible explanations to the “impossible alibi” problem… but they’re also all possible solutions to any other number of impossible crimes! Any trick you use to commit a murder under these conditions will, like it or not, play under the same rules, with the same train of thought as the resolutions to any impossible crime, whether it’s a locked-room mystery, guarded rooms, or an invisible killer. I’d go so far as to suggest that a guarded-room mystery is fundamentally exactly the same as some styles of the impossible alibi problem in terms of how the impossibility is established and how it can be resolved. The possibility of faking alibis doesn’t preclude these sorts of problem from impossibility status, because the very heart of impossible crimes is “an entirely possible series of events fraudulently established as apparently ‘impossible'”. All impossible crimes are built on the conceit of the situation being faked in some way; there’s no reason to discriminate against the airtight alibi on these grounds, when there’s sufficient supporting information making every alibi apparently airtight and credible. Is the killer never committing murder despite being in front of the detective’s face at the key moment not impossible enough?

The “impossible alibi” differs in no way from any other impossible problem.

Does it require the onus of special care in setting up the alibis to truly and properly make them appear reliable and airtight? Yes, but in very much the same way guarded rooms demand the onus of special care in establishing the faithfulness of the guards, the way that the Judas Window problem demands special care in establishing the innocence of the person locked inside of the room, or the same way that locked-room murders demand special care in establishing when, where and how the door was locked, the same way that snowprint murders demand special care in establishing when the footprints were created and when the snow stopped…

Can the information that establishes the alibis as credible be forged? Yes. The same way the details the establishes the lockedness of a locked-room, or the nature of a snowprints mystery can be faked and forged. Faking the details and making them appear reliable is quite literally the heart of misdirection and deception. All details can be faked, forged, and tricked, not much more more difficultly than an alibi could be — and all deceptions which are considered true and proper solutions to each and every single one!

Does it demand extra conditions to function as an impossibility for the reader? Yes; in fact, it’s the perfect polar opposite to the Judas Window problem. One demands you accept the guilt of a person known to be inside of the room; the other demands you accept the innocence of a person known to never be at the crime scene.

At this point, I propose establishing categories of impossible crimes dubbed “Doylist” and “Watsonian”. A “Watsonian” impossible crime is an impossible crime for the benefit of the characters in the story. Your locked-room murders, your snowprint murders. Murders which, should they occur in our own world, would demand acceptance of no conditions beyond the existence of the crime itself to be considered “impossible”. The “Doylist” impossible crime is an impossible crime for the benefit of the readers. Murders which demand acceptance of some additional premise which nobody in the story is obligated to accept but which we, as readers, must note when considering the problem. Naturally, the impossible alibi falls under this category, but it is not alone; the “Judas Window Problem” falls under this category. I’d also argue defensible coincidences, like “rooms inciting heart attacks”, more than fit here, for demanding the reader accept the condition that there is foul play, and that it involves the “killer” room. Guarded rooms also demand to some degree our acceptance that the “guards” are reliable and faithful for the impossibility to function, and many versions of the “invisible killer” problem demand our good faith that the crimes aren’t suicides or that witnesses aren’t lying.

The “impossible alibi” is more than deserving of being considered an impossible crime problem, true and proper, even if it does demand the special “Doylist” distinction — something which it wouldn’t even be the first to do. Any mystery where the problem relies on the assurance that the killer is one specific individual, or one among a static group… and where sufficient evidence is provided to allow that the killer could never have even approached the crime scene… is as worthy of its impossible status as any other. In solidarity with the “impossible alibi” problem, I will use it as a category for “impossible crimes” in this blog from this point going further, as long as I feel comfortable asserting that the novel does in fact create an impossible situation from the alibi problem, or as long as someone doesn’t convince me that I’m wrong.

So, what do you say? Do you believe that the “impossible alibi” problem is a fair classification of impossible crime, or should it stay firmly out of the realm of the impossible for good…?

11 thoughts on “On A Defense of the Impossible Alibi Problem and “Doylist” Impossibilities

  1. TomCat June 29, 2021 / 5:59 am

    Ha! This subject comes up every few years, but my answer has remained the same. An unbreakable, cast-iron alibi can only be considered an impossible crime if the murderer appears to have been physically unable to have committed the murder. So no manipulations of clocks and witnesses or relying on railway or theater tickets. The murderer must appear to have been physically incapable of having carried out the crime, because he/she was wounded, locked up or supposed to be dead. One of Christie’s mysteries is a perfect example of the impossible alibi and Monk had some good one. Like the murderer being either in a coma or in orbit at the time of the murder. So an impossible alibi has to create an actual impossible situation and works best in an inverted detective story.

    However, my rule to determine whether, or not, an alibi qualifies as an impossible problem is not watertight as I’ve come across several examples that cleverly bypassed it. There’s a fabulous radio-play from the Suspense series, “The Too-Perfect Alibi,” which achieves the same effect without relying on a physical impossibility. Just one of the cleverest alibi-tricks on the book played to great effect with an unforgettable ending. You can find the episode everywhere online (even YT) and more than worth the 30 minutes it takes to listen to.


  2. scottkratner June 29, 2021 / 5:30 pm

    I agree with your point entirely, Isaac— and I’m afraid not with Tom Cat’s. After all, what we refer to as impossible crime story is really a misnomer. None of these are true impossibilities but only illusory “apparent” possibilities… otherwise we’d never be able to have solutions for them. And an apparent impossibility is an apparent possibility, whether it is a matter of broken legs or timetables. I think And Then There Were None both provides a demonstration of this point and also of how a single work can transfer several times from one category to another.


    By the end of chapter 3 And Then There Were None book has established itself as a whodunit— but only in terms of the question who is U. N. Owen? (and of why has he enticed his guests to the island). Though no deaths have yet been committed, the concept that Owen may be a dangerous “homicidal” lunatic is suggested by the judge at the end of this chapter (though the reader no doubt already assumes that Owen IS homicidal, based on his awareness of Christie’s oeuvre).

    Though Marston dies at the end chapter 4, it is only at the end of chapter 7 section 2 (nearly 1/3 into the novel) that it is agreed by the characters that Marston’s death and that of Mrs. Rodgers were murder, and not until chapter 9 section 5 that Justice Wargrave states “It is perfectly clear. Mr. Owen is one of us!” thus establishing it as a closed circle mystery (though, there again, Christie readers have long before assumed this).

    It technically remains a pure closed-circle whodunit— never entering the impossible crime genre— until Vera’s hanging and beyond. For, even after her death, there are really still 2 apparent possible explanations for the murders:

    1. That Vera is the culprit (though her revealed thoughts make this possibility seem extremely psychologically unlikely)

    and, much more likely:

    2. That Phillip Lombard is the culprit, and that the fiendish Mr. Owen merely underestimated the resourcefulness of his last intended victim. The only point working against this explanation is the reader’s expectations of Mrs. Christie, and how her novels generally deliver surprise.

    (Incidentally, the earlier seaweed-on-the-hook incident and the apparent death of the judge would seem to exonerate Vera from being Mr. Owen, but closer reflection reveals that this is not actually the case— that section is indeed possibly consistent with her being Mr. Owen)

    And Then There Were None does not actually enter the realm of impossible crime (though when it does, it does so with great impact) until the latter part of the Maine / Legge conversation in the epilogue, when Maine demonstrates the apparent of any of the ten island corpses having committed the murders (which, in a sense is a matter of timetables AND physical in capability— one establishing the other).

    And it remains a general impossible crime novel for a page or so into the confession manuscript, until it becomes apparent that Justice Wargrave is the author of that manuscript— at which point the novel becomes an example of that subset you’ve been describing: the impossible alibi story. For, until he explains the mechanics of his own faked death and his post Vera-hanging measures (and he takes several pages to I’ll help gets around to that), we know who the killer is, but it is not known how he could have possible accomplished it.

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  3. TomCat June 30, 2021 / 6:24 am

    After all, what we refer to as impossible crime story is really a misnomer.

    No, it’s not. Everyone who obsessively read impossible crimes and locked room mysteries (hi!) know the apparent impossibility is nothing more than illusion and not something out of a ghost story or the science-fiction and fantasy genre. The impossible in an impossible crime described an extra obstacle in a crime that the detective and reader have to clear to reach a perfectly logical and natural explanation. It simply described the effect it tries to achieve and not something that actually defies the laws of nature.

    The all-important difference between a normal alibi and an impossible alibi is that in the former the murderer only has to account for his movements at the time of the murder, which can be done in a variety of ways like manipulating clocks, witnesses or the temperature of the corpse – none of which can be described as genuine impossibilities. An impossible alibi is when the murderer appears to have been physically unable to have committed the crime. For example, the murderer is confined to a wheelchair and somehow found a way to stab or strangle someone standing at the top of a flight of stairs. Nobody else is in the (locked) house, but the fact the murderer is unable to walk is a better, practically immovable, alibi than tinkering with clock hands and train tickets. It’s an apparent impossibility. You mentioned And Then There Were None, but Christie wrote a much better and clearer example of the impossible alibi, (ROT13) Qrngu ba gur Avyr. That one actually has two impossible alibis for the prize of one.

    So I remain steadfastly of the believe that there’s something as an impossible alibi and what makes an alibi an impossible problem, but I’ve no hope whatsoever we’ll ever reach a clear consensus on it. I’ve learned that much over the years. 😉


  4. scottkratner June 30, 2021 / 10:59 am

    But if I’m (apparently) in France when the victim is stabbed in the US, it is no different than if the victim is manually strangled and my hands are (apparently) paralyzed. In both cases there is an ostensibly insurmountable physical impediment (distance or physical handicap). In both cases, it is a matter of inopportunity— it seems impossible that I could have done it, an apparent impossibility achieved by an opportunity deception (as opposed to a motivational deception, which is employed to make it appear that some WOULDN’T have committed the crime).

    The methods by which different opportunity deceptions are achieved are varied (but note that in both the Christie title I cited and the one you did, the deceptions are achieved by a time-shift alibi). You say that certainly alibis are better than others, and I’ll grant that— an X-Ray of shattered limbs is more persuasive than the testimony of a friend that I was at his house at the time. But ultimately, that is a matter of degree of credibility, not category of effect— as we would say in stage magic (my field of profession) the methods and their effectiveness vary but the desired effect is the same: the apparent absence of opportunity. Granting that one is more convincing than other, the distinction is arbitrary— a chosen point along a continuum of persuasiveness.

    You bought up a key point— the distinction between method and effect. Yes, readers are well aware that the apparent impossibilities in this genre will turn out to be illusory, just as most audiences watching my “magic” realize it is nothing of the kind— by calling something an impossible crime story or a magic shows we are discussing the apparent effect rather than the understood truth of the matter. But we don’t change the title of a magic show just because my deception techniques are unconvincing (though admittedly “less than magic show” would be an applicable title to some of my past performances). And any effort to achieve an apparent of inopportuntiy must be categorized as “impossibility” regardless of the nature or effectiveness of the method. If no one could have killed X because a drunk, visually impaired, and ethically dubious witness swears that no one came near the room, it’s still an impossible crime tale, just a lousy one.


    • TomCat July 2, 2021 / 6:11 am

      This is why we’ll never agree on what, exactly, constitutes an impossible alibi or if it even exists. As you said, the distinction is (mostly) arbitrary. And dictated by personal preferences. I just make a clear distinction between a murderer fabricating an alibi to account for his movements/whereabouts at a certain time and a murderer being alibied by some kind of physical restraint or obstacle. I find this a handy distinction, because the latter takes the form of an impossible crime and relies on a very different type of trickery than the former. A physical/impossible alibi usually requires a bit more ingenuity than a normal alibi, which can be fabricated by playing with clock handles or hoodwinking witnesses. But then again, I’ve come across numerous exceptions to my own rule. So I don’t see that alibi edition of Adey and Skupin’s Locked Room Murders coming anytime soon.

      If no one could have killed X because a drunk, visually impaired, and ethically dubious witness swears that no one came near the room, it’s still an impossible crime tale, just a lousy one.

      Only in the hands of a lousy mystery writer. A good writer would leave open the door to an impossible crime while dissecting this puzzlebox witness. Who’s he? Why was he there? Is he involved or was he used to muddle the waters? Does he have a reason to be speaking the truth now?

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      • scottkratner July 11, 2021 / 4:59 am

        I still think you’re making an illusory distinction, confusing the level of merit of an alibi with its category or basic nature. I’d like to discuss this (this will be lengthy but I think worthy of reading— I hope so, because it took long enough to write), but I find ROT13 far too cumbersome and time consuming, so…


        There. That should take care of it!

        To illustrate, I’ll use Simon Doyle’s alibi for the death of his wife Linnet. Although there are other alibis essential to the central deception in the story— including Jackie’s alibi for the death of Linnet, and Simon’s alibi for the deaths of Louise Bourget and Salome Otterbourne— only Simon’s alibi for the Linnet murder is a falsified alibi (the others, while orchestrated to aid deception, are in themselves truthful claims of impossibility).

        An important thing to keep in mind is that, although physical injury and incapacity are involved, Simon’s alibi is essentialy (as are most alibis) merely a matter of inaccess to location. After all, nowhere is it suggested that because of his leg injury, Simon was unable to hold a gun in his hand or press the trigger, but rather that, because of his injury, he could not have been at Linnet’s bedside at the necessary time in order to kill her.

        Broken down into its composite parts, the deception of Simon’s alibi (and the roots of its deceptiveness) can be stated as a series of syllogisms which prove to be either invalid or valid but containing false premises. First is the over-riding claim of the impossibility:

        1. If Simon had received an incapacitating leg injury from the gunshot fired by Jackie, he would not have been able to rush to his wife’s bedside, kill her, and return to the salon in the necessary span of time (i.e. the time between when Cornelia and Jim Fanthrop left the salon and when Simon was found there by Dr. Bessner a few minutes later).

        2. Simon did receive an incapacitating leg injury from the gunshot fired by Jackie.

        3. Therefore, Simon could not have rushed to his wife’s stateroom, killed her, and returned to the salon during the required period.

        This is a valid syllogism, but an unsound one, as one of the premises (2) is false.

        However, this false belief that Simon did receive an incapacitating leg injury from the gunshot fired by Jackie is itself a composite of two false beliefs which can represented by two invalid syllogisms. The first is that which convinces Cornelia (and the reader) that Jackie has shot Simon:

        1. If Jackie really shot Simon, she would have pulled the trigger, the gun would have made a firing noise, Simon would clasp his leg, wincing, and red liquid would appear through the handkerchief he held to it.

        2. Jackie did pull the trigger, the gun made a firing noise, Simon clasped his leg, wincing, and red liquid appeared through the handkerchief he held to it.

        3. Therefore, Jackie really shot Simon.

        While both premises are true, a false conclusion is possible because the syllogism is invalid, an example of the form employed in nearly all imitation of actions, known as “affirming the consequent”:

        ⁃ If a, then b.
        ⁃ B.
        ⁃ Therefore a.

        Which is the same form that can also give us:

        1. If Jack the Ripper killed Agatha Christie in the late 1880’s, she would be dead today.
        2. Agatha Christie is dead today.
        3. Therefore, Jack the Ripper killed Agatha Christie in the late 1880’ s.

        The second syllogism… the one that convinces us that Simon received his incapacitatiing injury at the time of Jackie’s gunshot is also a matter of “affirming the consequent”:

        1. If the gunshot fired by Jackie actually did go into Simon’s leg and shatter the bone, he would have an incapacitating injury several minutes later when Dr. Bessner examined it.
        2. Simon’s leg did have an incapacitating injury when Dr. Bessner examined it.
        3. Therefore, the gunshot fired by Jackie actually did go into Simon’s leg and shatter the bone.

        Cumulatively, these points have the effect of providing a convincing “impossibility,” but broken down its apparent how flawed this reasoning is. And it should be pointed out that even the confirmation of the incapacitating quality of Simon’s injury is wholly dependent upon the testimony of Dr. Bessner, which itself could possibly be false (Christie does not resort to this deception here, but certainly she has employed an accomplice doctor’s false testimony of diagnosis to provide an impossibility on at least one other notable occasion!).

        Simon’s alibi is also bolstered by several other elements, including the (true) impossibility of him committing the subsequent murders, his apparent enmity with the accomplice who commits those crimes, and even the unanticipated alibi created by Andrew Pennington’s attempt on Linnet’s life. But, while each of these elements adds to the apparent impossibility of Simon’s guilt, no individual point holds up to scrutiny. If one were to be asked “is it possible to stage an apparent shooting?” “Is it possible that the individual murders were committed by different people?” or even “is it possible to shoot oneself in the leg to match an earlier faked injury?” no one would doubt such a possibilities. It is the artful cumulative of individually not-entirely-impregnable-points that leads to a wholly convincing “impossibility.”

        And further reinforcing the deceptiveness of Simon’s alibi is one bit of quite-arguably impermissible deceit on the part of Christie. I don’t use the term “cheating,” as it implies the existence of genre rules— an concept with which I don’t concur— but surely there are reader expectations governing the genre, and foremost among these is the prohibition of falsehoods made by the author. But, as vehemently as I’ll defend Christie’s honor regarding Roger Ackroyd, I don’t see how the final word of this sentence can escape such complaints: “She was trembling violently, and her eyes, dilated and frightened, were staring at the crimson stain slowly soaking through Simon’s trouser leg just below the knee where he held a handkerchief close against the wound.” What “wound”? Certainly “apparent wound” would be a giveaway, but as written, it is a falsehood.

        So, what Simon’s alibi amounts to is a claim of impossibility, substantiated by (as you put it) “a physical restraint or obstacle.” Of course, it ultimately proves to be a false claim of impossibility, based on a (at the essential time period) false physical restraint or obstacle.

        Now, let us compare that to what you refer to as a mere matter of “a murderer fabricating an alibi to account for his movements/whereabouts at a certain time.” Let’s take a rudimentary example:

        The coroner confirms that Mr. Rossiter was bludgeoned between 9:00 and 9:30pm at his residence. Mr. Garmisch, known to be an enemy of Mr. Rossiter, is questioned.

        “You suspect me of Rossiter’s murder?!” Garmisch cries. “But I couldn’t have done it. You tell me he died between 9:00 and 9:30. But from 8:00 to 10:30 I was five miles away at The Royal Theatre watching ‘Dr. Tanner Can’t Eat.’ Here’s my theatre stub.”

        What have we here? An alibi— though admittedly a poor one. A “normal alibi” as you put it, a matter of “relying on railway or theatre tickets.” But what truly distinguishes it from the kind of alibi you describe as “impossible.” In essence, it is exactly the same as the claim made for Simon Doyle— a claim of PHYSICAL impossibility of opportunity, based on inaccess to location at the time of the crime. For, if Garmisch were indeed at the theatre from 8:00 to 10:30, he could not have been at Mr. Rossiter’s sometime between 9 and 9:30 to kill him, for it is a PHYSICAL IMPOSSIBILITY for a person to be at two different places at the same time. IF TRUE, this definitely qualifies as a “physical restraint or obstacle.”

        Of course, there is a difference in merit between Simon Doyle’s alibi and that of Mr. Garmisch. But before exploring that, let me emphasize my key point:

        ALL ALIBIS ARE CLAIMS OF IMPOSSIBILITY. It is only the level to which these claims convince that differs.

        Now, let us look at the syllogisms that represent Mr. Garmisch’s alibi:

        1. If Mr. Garmisch was at the Royal Theatre from 8:00 to 10:30, he could not have been at Mr. Rossiter’s residence between 9:00 to 9:30 to kill him.

        2. Mr. Garmisch was at the Theatre Royale from 8:00 to 10:30.

        3. Therefore, Mr. Garmisch could not have killed Mr. Rossiter at the stated time.

        Now, let us presume that Mr. Garmisch’s alibi was a false one, and that he did indeed kill Mr. Rossiter. Also presuming that the coroner’s information is accurate regarding time of murder, and knowing that the above syllogism is formally valid, we know that premise 2 must be false. And again, as with Simon’s alibi, the falsity of that premise is accounted for by “affirming the consequent.”

        1. If Mr. Garmisch spent the whole evening at the theatre, he would have a torn theatre ticket to show for it.
        2. Mr. Garmisch has a torn theatre ticket.
        3. Therefore, Mr. Garmisch spent the whole evening at the theatre.

        Not very convincing, admittedly, as Mr. Garmisch could possibly obtain a theatre stub without spending the whole evening at the theatre… but that’s just as Simon Doyle could possibly wince and clasp his leg without being shot there, and just as Simon could possibly have an incompacitating injury at the time of examination by Dr. Bessner, but not at the time he was ostensibly shot by Jackie. So why should we consider Simon’s alibi “impossible” and Mr. Garmisch’s not? What difference is there between Mr. Garmisch’s claim of lack of opportunity and Dr. Bessner’s claims of Doyle’s incapacity, other than level of credibility? Is it possible they could both be false? Of course.

        Undoubtedly, Doyle’s alibi is reinforced by a greater number of points of substantiation. But both are claims of physical impossibility formed by individual arguments that are ultimately proven destructible.

        For there is a “continuum of credibility” between Mr. Garmisch’s alibi and Simon Doyle’s. If Mr. Garmisch had a witness that he was at the theatre the whole time, his alibi would seem stronger— though of course that alibi too could be faked (a lying witness, or a deceived one). Even a large group of witnesses deceived is a possibility (Think Lord Edgware Dies). Or there could be a filmed record of his attendance at the theatre (maybe a security camera), which could also conceivably be faked. And coming from the other direction, there is also the possible gradual weakening of a Doyle-type alibi (Van Dine has an example where a faked incapacity is similarly made real after the time of the crime, but neither the nature of the nature of the incapacity nor the reinforcements of deception are nearly as convincing). Delineating the point at which such an alibi shifts from “normal” to “impossible” presents us with the Sorites Paradox.

        My point is that whether the alibi is “My leg was shattered,” “I was at the theatre,” or “I was in outer space” the claim is the same: “it was physically impossible for me to be at the crime scene when the victim was killed.” So when does such an alibi become an “impossible alibi”? I’d suggest it is when the detective character (or other character of authority) deems that the claim is impregnable. One could say “when the reader deems it so,” but that doesn’t work…. there are those who see who through or doubt the Simon Doyle alibi right off, and an alibi can’t be simultaneously possible and impossible. Certainly there are “impossible” alibis that are doubted by many a reader, and yet, as I said before, every alibi is a claim of impossibility. So ultimately the judgment of a character within the fiction must serve as arbiter.

        That said, an “impossible alibi” doesn’t make an “impossible crime story.” I don’t think anyone considers Death on the Nile an impossible crime story, despite the apparent impossibility of either Simon or Jackie commuting the murders. That is because beyond them, there are still avenues of possibility. It is only when all avenues of possibility are apparently exhausted that a detective story becomes an impossible crime tale.

        Liked by 2 people

      • TomCat July 14, 2021 / 6:35 am

        Did you reread Death on the Nile before composing your comment? 😀

        I appreciate your comment and the thought you put into it, but I disagree for the reasons previously stated. We have very different ideas and qualifications of what makes, or rather what not makes, an alibi an impossible alibi. I don’t think everyone needs to have an alibi to have one, or two, alibis count as an impossibility nor does the reader anticipating (part of) the solution disqualify it as one, but fans are never going to agree on this subject. It’s such a hazy, ill-defined subcategory and even trying differentiate between two different types of alibis (one of them overlapping with the impossible crime) runs into problems and objections. Maybe it’s easier if we make the alibi problem, all of them, a subcategory of the howdunit.

        Liked by 2 people

  5. scottkratner June 30, 2021 / 11:23 am

    That all said, we don’t generally refer to the Christie you mentioned in code (why aren’t we naming it?) as an impossible crime tale, because the lack of opportunity for one or two characters will not qualify a story as such as long as their are still other possibilities open. THEY may not have apparently committed the crime, but others still could have. It is usually only when there is apparently no possibility that ANYONE could have committed the crime that we refer to it as an impossible murder (such as in the latter stages of And Then There Were None ).

    The exception to this is Isaac’s impossible alibi scenarios, where it is made clear that X is the culprit (often attested to by the author himself) and yet still it seems an impossibility.

    Liked by 2 people

    • TomCat July 2, 2021 / 6:17 am

      why aren’t we naming it?

      I brought it up before as an example of, what I believe is, an impossible alibi and people said it was to spoiler-ish to mention it in that context. They had a point. I remain it counts as an impossible alibi. Bar bs gur zheqreref jnf nccneragyl fubg va gur yrt naq gur bgure jnf chg gb orq jvgu n zbecuvar fubg naq n ahefr fgnaqvat thneq. So it doesn’t matter others could have done it. Gurer nyvovf znqr vg nccrne gurl jrer culfvpnyyl hanoyr gb unir pbzzvggrq gur zheqre. That’s an impossible alibi.

      Feel free to disagree. 🙂

      Liked by 1 person

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