Trying to solve a puzzle for which there is no solution

I grew up voraciously reading mystery novels, with Agatha Christie being my author of choice, with other mystery writers thrown in from time to time. She was a prolific writer and I suspect that I have read at least 90% of her output. Hence my ideas about the conventions of that genre have largely been shaped by her books.

One of the cardinal rules was that the author had to play fair by the reader. There had to be a rational solution to the mystery that fitted the facts that had been presented. No magic and supernatural elements were allowed. The author was allowed to plant fake clues to lead the reader astray (and we in fact expected it) but there could not be facts that contradicted the solution.

I extend this expectation to everything that constitutes a puzzle or mystery, such as mystery films.

I recently watched the 2005 French film Cache (the English title is Hidden) starring Daniel Auteuil and Juliette Binoche. It is a slow-moving suspense film. The central plot is that a family consisting of parents Auteuil and Binoche and their 12-year old son suddenly start receiving videotapes on their doorstep that seem to be taken from a hidden surveillance camera pointing at the front of their house and thus captures their comings and goings. Later on, the tapes arrive wrapped in paper that has crude drawings in crayon of blood spurting from the necks of people and chickens.

Needless to say they become worried by this stalking and the film is about the toll it takes on them as they try to figure out who is doing this to them and how and why, although Auteuil has reason to suspect that it is something that had its origins in his childhood.

The film never answers those questions and the viewer is left at the end trying to figure it out. Film critic Roger Ebert in an initial review highly praised the film and then later did an extremely close, almost frame-by-frame, analysis of it trying to solve the puzzle, and suggests various possible solutions but points out that none of them are satisfactory since every postulated one has problems in that some fact seems to contradict it. He says that the film director Michael Haneke seemed to delight in the fact that people could not solve the puzzle. Haneke even has a closing scene that is important but he shoots it in such a way that apparently over 50% of viewers missed entirely (as I did) a key interaction between two people, because they were at a distance and at the edge of the screen while other figures were moving around in the central foreground. Haneke was supposedly pleased that so many people missed it.

I found the film highly unsatisfying for those reasons. I enjoy solving puzzles. But human-created puzzles (crosswords, Sudoku, jig-saw, and the like) are constructed according to rules that guarantee a solution and only the skill of the puzzle-solver stands in the way of a solution. It is easy to construct a puzzle that has no solution but who would bother to attempt it?

It is similar to scientific research. With the puzzles of nature that form the basis of scientific research, one assumes that a solution must exist and that the only thing that prevents one from finding it is insufficient information or cleverness. One is certain that one is not being deliberately misled. Einstein expressed this sentiment famously as, “The Lord God is subtle but malicious he is not” but since religious people can never get it into their head that Einstein was using god as a metaphor, I prefer his alternative formulation of “Nature conceals her secrets because she is sublime, not because she is a trickster.”

Since books and films are human creations, the same rules should apply. In my opinion, if a film poses a puzzle, then it should contain a solution that can be figured out. It is not necessary that everything be nicely wrapped up and tied with a bow at the end. It could have alternative explanations that are each plausible, such as in Rashomon or a film could be constructed in a way that it is hard to reconstruct the sequence of events, as in Memento. Those are allowable and in some cases desirable if you want to leave people with the idea that sometimes we just cannot figure out the solution to a puzzle because of insufficient information.

It is also different with questions of meaning and motive because those are inherently ambiguous and possibly unknowable and people often do act out of contradictory motives. A film that leaves you guessing about the whys is fine. But to make the actual facts of the events such that no solution is possible seems wrong to me.

But a filmmaker should not insert facts that preclude anyone arriving at any answer at all because each one is confounded with a contradictory piece of information. To do so is to reveal the filmmaker as a ‘trickster’. I refuse to waste time trying to solve such fake puzzles and think of it as a betrayal of trust between the filmmaker and the audience. I suspect that Cache falls into that category though I am willing to be proven wrong. So while the film was interesting (and Binoche in particular gives a fine performance) it left me feeling dissatisfied and even cheated.


  1. says

    Just as annoying are movies which don’t have a logical connection between A and B. When the end comes, it’s “There’s the killer!” and he explains himself and his motivations, Scooby-Doo style (see: “The Bone Collector”, “Who Framed Roger Rabbit?”). The only connection throughout the movie is that the killer was a character present for most of the film.

    In good mystery movies, the clues are there but the audience may have missed them on first viewing, and that’s what makes films worth repeat viewing. I know it’s overused as an example, but “The Usual Suspects” did it brilliantly. The lighter is only noticeable as an artefact on second viewing, and the use of a different hand and manner in Verbal Kint seems like a mistake or Verbal’s ego taking over in telling the story, not a giveaway to the audience. Even torture porn movies like “Saw” do it better than most.

  2. Pierce R. Butler says

    “Je suis fucking avec ta tête,” is a perfectly à la mode message from French intellectuals: see Baudrillard, Foucault, et al.

  3. physicsphdstu says

    I preferred Poirot to Sherlock because of this very reason. This joke used to do the rounds during my school days : math problems and christie novels have no unnecessary clues 🙂 .

  4. Trebuchet says

    I’ve read ALL of Christie’s mysteries. Been a while since I read one, however. I used to buy used paperbacks of them for 10 to 25 cents. (It’s been a while!) I once read all eighty-some of them, one after the other, in order of publication.

    Christie did provide all the clues, but sometimes they were so obscure as to make it impossible for a typical reader to figure out. She first became famous after tricking the reader in The Murder of Roger Ackroyd. (I’ll omit the spoiler, go read it yourself!)

  5. mnb0 says

    “Michael Haneke seemed to delight in the fact that people could not solve the puzzle.”
    Yep, it’s a cheapo.
    I don’t mind unresolved mysteries though if the very point of the movie is that the mysterie remains unresolved. Excellent examples are Blow-up from 1966 and The Passenger (with Jack Nicholson at his very best) from 1975. Antonioni specialized in it.

  6. mnb0 says

    I wonder how quick fans of the Usual Suspects will find out?
    Because of Roger Ackroyd I knew within 45 minutes of that movie who Kayer Soze was.

  7. mnb0 says

    “The Usual Suspects did it brilliantly.”
    I’m afraid only for those not familiar with Roger Ackroyd.

  8. Reginald Selkirk says

    One of the cardinal rules was that the author had to play fair by the reader.

    Right. Which is one reason why I didn’t like Agatha Christie. I’ve only tried a few of her books, but they had some outlandish contrivances. A woman marries the same man for a second time and doesn’t realise it? I don’t think so.
    I have read and enjoyed almost all of the Nero Wolfe books by Rex Stout.

  9. zekehoskin says

    Okay, if this is turning into a thread about Agatha Christie, two things:
    First, she did NOT always play fair and rational. She wrote a few stories where it turned out to be magic.
    Second, she was possibly the most influential British author of her time, because instead of writing social commentary that only an intellectual would plow through, she put carefully calculated doses into mysteries that feel like pure entertainment.

  10. mnb0 says

    “carefully calculated doses”
    Yes, that’s why I like Christie much more than her colleague Dorothy Sayers. Without ever becoming explicit she painted a quite nasty picture of the English social elite of her time. Then after WW-2 she did the same with English rural life.
    It hasn’t been pointed out very often – so I’m happy that you are aware of it too – but Christie was a good chronicler of her time. The only colleague who could compete with her in that respect probably was Margery Allingham and then specifically Tiger in the Smoke.

  11. deepak shetty says

    One of the cardinal rules was that the author had to play fair by the reader.
    Yep I preferred Christie to Doyle for this reason . Perry mason’s also seemed to fall into the latter category.

  12. Peter B says

    Dr. Singham,

    This is at least somewhat OT. Delete if appropriate. I will not complain. (Your title made me post the box problem in my last paragraph.)

    I like math puzzles that appear to violate common sense such as

    -20 = -20
    16-36 = 25-45
    16-36+(81/4) = 25-45+(81/4)
    now factor . . .
    (4-(9/2))^2 = (5-(9/2))^2
    4-(9/2) = 5-(9/2)
    4 = 5

    The best part about this proof that 4=5 is the mental problem algebra students have in factoring expressions consisting entirely of numbers. That problem leads them away from the mathematical guerilla staring them in the face.

    But the puzzle that plagued me when I was 14 or 15 was a simple word problem. It stated that a 4-foot square box sitting on flat ground was pushed snug against a vertical wall. A 10-foot ladder touches the wall, the outside corner of the box and then the ground. How high up the wall does the ladder reach? Similar triangles and a^2 + b^2 = c^2 should be enough. Yet when I plugged in numbers nothing worked.

  13. Chiroptera says

    Heh. Your 4=5 paradox is a good one — I’ll have to write it down and remember it.

    The resolution is obvious to me, but it’s kind of unfair since I teach math for a living, and this puzzle relies on a common error that I have to constantly try to warn my students against.

  14. Mano Singham says

    That is a good paradox. These number paradoxes are usually caused by neglecting to take the negative root into consideration or dividing by a zero that has been hidden.

    Did you discover for yourself as you got older why the ladder problem has no solution?

  15. Peter B says

    Yes. It was the reason my younger self kept finding square roots of negative values. Younger me just knew there had to be a proper solution. The magazine – Pop Science I think it was – had this nice line drawing so it just HAD to work.

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