Four people sit in a train compartment in which two seats face two seats. Each person, therefore, sits next to one person, across from another, and at the diagonal from a third. Two of these people are men, and two are women. Each person has a different profession, each wears a hat of a different color, and each has a different country of origin.
- The person sitting neither across from nor directly next to the man wearing the green hat has a PhD in mathematics. His dissertation, a summary of advances in the field of automated deduction, was largely plagiarized from a series of papers his advisor recommended even though he, the advisor, had never read them. His work requires no specialized knowledge or expertise.
- The woman sitting next to the German is not wearing a green hat or a blue hat or a white hat or a black hat or a yellow hat or a gray hat or a purple hat. She wonders why it's so hot in here.
- The dentist is not a real dentist, but few people know this. Among the people who do know it is the Cuban, who would not be here if not for that knowledge and all that it represents, if not for the problems associated with the work the dentist does when not pretending to be a dentist, if not for his crimes, if not for the expectation (both professional and moral) that she should eliminate the threat embodied by the dentist.
- The American believes she passes easily for a German. The trick of it, she says, is to adopt an unyielding affection for inconsequential products of German manufacture. Toothpaste, for example, and fabric softener. Though in truth, there is no real call for the American to feign connection to that country or those people. Her maternal grandmother was German and her mother lived outside Köln (as she insists on calling it) for a few short years as an infant, but these facts are inconsequential. She often feels a kind of disdain for behaviors and attitudes that she considers unique to her compatriots, and she confesses to her closest friends that it's a snobbery she wishes she could avoid. She sometimes apologizes to her students for her Teutonic thoroughness. They nod or smile but have no idea what she means.
- The woman wearing the purple hat (who is uncomfortable with a purple hat, who finds that a purple hat makes her conspicuous when she ought to be nondescript) has the explicit instruction to find and eliminate the man sitting directly in front of her, knee to knee. The information she was given indicates that the man has no suspicion of her, but the way he stares and refuses to look away makes her wonder if something or someone might have clued him in, tipped him off, spilled the beans.
- The Serbian isn't a programmer, practically speaking, but something closer to an office manager.
- The man in the brown hat hates the words currently in vogue related to legal relationships between men who love men and women who love women. Especially in English, and particularly in the United States, where he spends a fair bit of his time, even if he would prefer not to. He hates the very sound of phrases like "domestic partnership" and "civil union." He hates just as much, the word "cohabitation." But more than these, he feels a literal shiver anytime he hears the word "lover," the way it reduces a person to his or her sexual relationship to another. He hates it no matter how it gets applied, or to whom. It has become his primary example when asked to explain why the English language pales next to his native tongue.
- The person in the red hat knows nothing of mathematics and nothing of spies and spying, and nothing of government secrets sold for personal profit. But she knows a thing or two about cigar smoke and feels nothing short of contempt for those who produce it, or, as is the case with the man to her left, those who hold unlit cigars in their mouths as though to brag about the awful thing they mean to do just as soon as they find a match or lighter. It's just so hot in here, and she worries that any moment now the man might just light up, and she feels a sudden longing for the smoke-free environments that are among of the virtues of her homeland. She waves a train timetable at her face, an improvised fan, and wonders if the windows of trains like this one can be opened.
- The Serbian hates German fabric softeners but doesn't know it. What he knows is that the woman sitting across from him, too close to him, stinks of something chemical and awful.
- The German smokes a cigar (holds an unlit cigar in his mouth, wishes he were smoking it, longs for a drag) and believes that his life is filled with spectral presences. He wonders if the people sharing this train compartment have physical form or only appear to. He wonders, particularly, about the woman sitting in front of him, how calmly, unflinchingly, patiently she sits there. It's not human, the German thinks, to be so calm and so unflinching. There's something about her that isn't right. It might be her hat, which matches nothing else about her. Why lavender, the German wonders. Or is it violet? And why does it remind him of the dead and dying?
- The spy has much in common with the non-dentist. She too pretends to be someone she is not. She too lives under multiple layers of deceit and subterfuge. She is known as many things to many people and worries, constantly, that she might one day lose the sense of order she has worked so hard to maintain. She worries, that is, that she might one day lose the thread of things.
- The person sitting at the diagonal from the woman wearing the purple hat has a chocolate bar that will not be shared with anyone. The quality of that chocolate is greater than any to be found on the entire North American continent.
- The non-female, non-spy, non-non-dentist often confuses the phrases "discrete mathematics" and "discreet mathematics." To date, no one has corrected the error. In truth, she knows virtually nothing of mathematics, but because of a quirk in the university policies for naming positions, she is often mistaken for the head of the programming section of the computer engineering department. Too often, she is compelled to explain that she is not the head of programming, but the head of programs. It would make more sense to call her a chair or a coordinator, but the university insists that those titles are reserved for academic units.
- The man who is not wearing a brown hat is also not wearing a green hat. He is, instead, holding his green hat, spinning it end over end, running his fingers on and around its brim, inspecting it, considering it. The hat is a new one, size 21 and 7/8 inches, which is, by most standards, small or medium small. The size of a man's head is no indication of his intelligence, everyone knows that, but the man not wearing a brown hat can't help but wonder if what everyone knows is really a reliable guarantee. He wonders if his intelligence is lacking and if the size of his head is a clear indication of that fact. He wonders, too, if the size of his head, irrespective of what it may or may not actually say about his intelligence, might incline people, such as the people in this train compartment, to assume some deficiency on his part. Do they think I'm slow? he wonders. Do people think me a fool? Does this woman sitting in front of me think me an idiot? And why not? What would tell her otherwise?
- The person sitting across from the person not currently wearing a green hat has not seen her mother in more than six years. They parted, that last time, on polite terms, but she carries the sense that something unfinished between them must, sooner or later, be seen to and accounted for. Her mother, she knows, must wonder where she is and why she doesn't call and why her letters have gone unanswered. The explanation is simple, but the woman sitting across from the person not really wearing a green hat is obligated (professionally, morally) to say nothing, to explain nothing. She carries some guilt for what she's done to her mother even if she's trained herself against demonstrations of that guilt. She knows which questions on which tests are designed to determine whether or not she is the kind of person who might feel and subsequently be swayed by the kind of guilt she carries with her. She is not that kind of person. She refuses to be that kind of person. But still, at times like these, her resolve seems more brittle than it once was.
- The programmer speaks six languages and has adopted, as a result, a peculiar accent that leads others, especially strangers he interacts with in the village of his birth, to wonder aloud where's he's from. They have wondered, with delighted grins, what brings him here, to this part of the world, to such a place. They have wondered, based on his accent, if he might not be vacationing from Germany or some place farther north. But why here, they ask, so far into the hills, so far from the cities?
- The woman in the red hat would like very much to drift off for a few minutes. She fears, though, that were she to do so, she might sleep right through her stop, which is, she thinks, one of the next two or three. It's hard to say. More importantly, she worries that if she were to slip away for a moment, her head might nod and her hat might fall off, and then where would she be? Because the hat is the sign she gave to the man who promised to meet her, and if she weren't wearing the hat, how in the world would he know that she was she? She couldn't be more sure that without this hat she'd blend in all too easily. But when she suggested a red hat, she thought it would be a more distinguishing feature. She never expected to find herself among so many hat-wearing people. Here in this train compartment, for example, 100% of the people are wearing—or at least holding—hats, and not just ordinary brown and black ones (though there is one of those), but also green ones and purple ones, every bit as conspicuous as hers. What if the man should see this other woman, this woman sitting at the diagonal from her, and forget for a moment that it was a red hat he was after? What if that man were to take this other woman by that arm and traipse off across Europe with that other woman and her purple hat?
- The Cuban is not and never has been married. The American was engaged once, briefly. The Serbian is not married and does not see reason to expect otherwise, given the state of things. The German is twice divorced and has four children, one from his first marriage, two from his second, and one that neither of his wives knows anything about.
- The German has never been mistaken for anything but a German. But he often wakes at night and feels a strange sense that he isn't at home, that he has, instead, been transported by unfriendly forces to a place that only looks familiar. He fears that these forces have only yet shown him a small portion of their power and that any day now he might wake to discover the full, unmitigated force of so much spite. Despite the heat, the thought gives him a chill. He needs, more than anything, a bit of fresh air. He leans toward the woman on his right and whispers, conspiratorially, that he would like to switch seats with her. Excuse me, the woman says. He looks at the woman as though they both know all too well that she heard him plainly the first time. I'm sorry, she says, with a hint of panic in her voice, but no. The German shrugs his shoulders and stands. At the very least, he says, perhaps I could ask you to watch my hat for a moment. He passes through the compartment door and into the main corridor of the train. His hat remains in his now empty seat.
- The Cuban waits exactly 20 seconds and then follows after the German, leaving in the train compartment the programmer, the head of programs, and a green hat.
I'd largely forgotten how much I loved deduction puzzles as a kid until my own son came home from school with a sheet of clues about some neighbors and the instruction to identify which man lived in a house of which color. I didn't set out to write an actual logic puzzle (good ones can be so incredibly difficult), but I kept thinking about the odd, impractical, convoluted narratives that emerge from them.