How many hotheaded academics does it take to solve a riddle?
I don’t know what the best thing was about Jim Propp’s parties. They were a crystalline picture of the specialized, rarefied company I kept when I lived in Cambridge in the midnineties, parked on Mass. Ave. halfway between Harvard and MIT. Profs, postdocs, and assorted academic keepsakes from the cream of Boston academia all piled into Jim’s Victorian four-square house in Somerville for an evening of … well, we never quite knew what the evening would bring.
Technically, these were “word game” parties. Each was planned around a series of intellectual challenges arranged around the house more or less like evil wizards, ax-wielding dwarves, or more mundane impediments in a typical game of Dungeons & Dragons. You’d team up with a couple friends (or the pretty redhead who was probably dating one of your professors, if you could), and make your way from room to room, solving bits and pieces of puzzles that—if you were lucky—you could string together for the grand solution. The prize was bragging rights until the next party, six months down the line.
In any case, it all began with the invitation. Twice a year, a mysterious envelope would appear. I remember the first one I received: a single sheet with nothing but a swirling Spirograph flower on one side, and the letters RSVP below it. Where, when, and how were left to the recipient, presumably after he or she had coaxed the secret out of the cryptic drawing.
Another time, the invitation was a short story, beginning something like “‘I can’t believe what a prick Jim is!’ she said, throwing the invitation on the floor.” It self-referentially detailed an argument by a young couple who had received one of Jim’s invitations; they were exasperated that he expected them to divine the details of the party from his little story. At the bottom, as always, it just said “RSVP.”
Of course, if you couldn’t solve the puzzle, there was always a last resort: you knew the puzzle was from Jim, so you could admit defeat and simply ask him when and where the party was.
The party itself was a smorgasbord of puzzles. You could wander through the house, solving them in any order as you mingled, flirted, and nibbled on hors d’oeuvres, but you really had to try to solve all of them. The reason was this: Jim wasn’t content simply to think up a half dozen unrelated mind benders for us to pound our heads against. There was something larger hidden behind the curtain—solutions for the individual puzzles were merely clues that needed to be strung together to solve a larger puzzle that we didn’t even know existed.
Case in point: Jim’s now-famous Self-Referential Aptitude Test (the SRAT), a puzzle that featured in one of his parties before I fell into his orbit. The test was composed almost entirely of questions whose answers depended on answers for other questions, beginning with
1. The first question whose answer is B is question
(A) 1, (B) 2, (C) 3, (D) 4, (E) 5
2. The only two consecutive questions with identical answers are questions
(A) 6 and 7, (B) 7 and 8, (C) 8 and 9, (D) 9 and 10, (E) 10 and 11
and getting more convoluted and twisted as it went.
Eventually, though, with enough patience—and perhaps a degree in constraint-satisfaction programming—you’d come up with a self-consistent solution and breathe a sigh of relief. But then what? How did solving this puzzle help you unearth, let alone solve, the master puzzle that was still hidden in the evening?
What’s really on my mind is a particularly brilliant, if comically miscalculated, puzzle, intended to be the icebreaker at one of the last of Jim’s parties that I attended.
When the guests arrived at the front door that evening, we were each required to take a name tag. Not a peculiar requirement in itself, given that most of us were strangers who knew Jim from only one of his many disjoint social circles. But what was peculiar was that each name tag already had on it a puzzling (there’s that word again!) collection of words and letters.
One tag had, for example, “Cretaceous,” “Run,” “Carbon,” and the letter “M.” Another had “Spring,” “Pius II,” “Uranium,” and “P.” Yet another: “Pride,” “Jurassic,” “Hamlet,” and “A.”
Alone or in pairs, they made little sense, but this clever crowd quickly picked out the nature of the puzzle. What we had here were overlapping strands of partial orderings. Some people had geological periods on their tags; they needed to be arranged in chronological order. Same with the popes and Shakespeare’s plays. Elements had to be ordered by atomic weight. But others weren’t so obvious. “Summer” comes before “Fall” (as does “Pride”, we discovered), but where does the circle of seasons wrap around?
Complication number one: the sequences were carefully spread out, so there was no guarantee you’d have a direct overlap with any particular person. I couldn’t tell if Susan’s tag (“Triassic,” “Walk,” “Macbeth,” “L”) should be before mine (“Benedict I,” “Nitrogen,” “Hoover,” “A”) without discovering the mutual constraint imposed by Richard’s tag (“Cretaceous,” “Run,” “Carbon,” “M”).
That just left the matter of the letters, the only element common to everyone’s tag. It was clear to everyone, then, that the letters must spell out the secret message. But here was another problem: because the tags had been cleverly designed to make pairwise comparisons difficult, it wasn’t straightforward for people to sort themselves by looking at their neighbors. We actually needed an algorithm.
Fortunately for us, a good fraction of the attendees were mathematicians and computer scientists, and understood sorting algorithms better than they understood some of the subtler aspects of personal hygiene. Unfortunately, they were, again, predominantly Harvard and MIT professors, longing for that moment when their particular skills would be called on in an emergency, when they could just once utter that coveted phrase in a loud, authoritative but calm voice: “Stand back, everyone—I’m a computer scientist.”
This would have been a brilliant opportunity, had there been but one such savior lurking in our midst. We would have stood there, willing minions, as he directed us through the dance of his polylogarithmic merge-sort algorithm: You there: step forward and work your way down the line. You, in the pink sweater, now it’s your turn. And so on.
But as cruel Fate would have it, there were at least a dozen such computational mavens waiting in the woodwork, each with their own algorithm to direct, and none willing to abdicate his long-dreamt-of moment in the sun. And so one would direct an innocent partygoer to switch places with her neighbor, immediately causing another to howl that the first was scrambling his already-sorted section of list.
And the computer scientists weren’t the only ones at fault. The English professors may not have known squat about algorithms, but they sure as hell knew they weren’t going to be ordered to do-si-do by scruffy kids half their age with mismatched shoes.
And so things came off the rails. Voices were raised and veiled threats flew, involving tenure and the possibility of anonymous reviews. I don’t think anyone actually threw a punch, but there were plenty of innocent bystanders cowering in the corner. I don’t actually know how long the game went on—they say that time dilates in train wrecks and other disasters—but it was probably close to an hour, and the party was clearly over before it had ever really gotten started. Spouses grabbed coats and tugged their irate academicians, in full protest, to the door. (“But we’ve almost gotten it solved!” “No, dear, you’ve almost gotten punched in the nose.”)
One of the remaining guests, unencumbered by a spouse, seized on this moment to throw his plan into action. Starting with the pretense that departing guests needed to leave their tags in his custody, he quickly fleeced the remaining partygoers of their tags, too. Many came off before their wearers had the chance to raise objections, and our young turk retreated to the back of the room, facing a crowd that was hostile, but still vaguely curious whether the puzzle could be solved.
Unattached, the cards could be sorted more quickly, so we reined in our acrimony, giving him a few minutes to try his hand at sorting out the riddle that had so spectacularly ruined not only this party, but possibly friendships and careers.
Slowly it took form, and slowly, the irony of the message that appeared before us sank in. It was a quotation from Grantland Rice, one that we all knew, and all knew far better than we had when the evening had begun:
“He marks—not whether not whether you won or lost, but how you played the game.”
David Pablo Cohn is a flight instructor, folk musician, travel blogger, and former Google Research Scientist.