ANNOUNCING
OUR CHRISTMAS CONTEST WINNERS

SPOILER ALERT: One of the descriptions below of the solutions submitted by the winners contains the answer to the puzzle. If you are following Leigh’s columns for this and next week describing the evolution of the puzzle and how it can be solved, and do not want to know the answer before he reveals it, or for some masochistic reason are still trying to solve it yourself, you may want to skip them and read only the parts in boldface.

First Prize: C. J. Dowse of Pietermaritzburg, KwaZulu-Natal
Province, Republic of South Africa

C.J. correctly deduced that the puzzle was a lipogram, determined that the missing letter was “L”, and deciphered the Christmas Message as “No L” = “Noël”. C.J. was the only entrant to solve the complete puzzle.

Second Prize: Jeff Baker of Wichita, Kansas, USA

Jeff correctly deduced that the puzzle was a lipogram, as he very shrewdly hinted in his pair of limericks in the Comments for Tuesday, December 15, but didn’t manage to identify which letter was missing.

Third Prize: Cindy Kerschner of Schnecksville, Pennsylvania, USA

Cindy correctly deduced that the answer was a French phrase, but my hint from “Silver Blaze” turned out to be something of a stray dog in her case—she thought there must be a canine connection.

Congratulations to our Winners! Well done!

And now return to our regularly scheduled column. We join my friend Wolpertinger the Mad Scientist’s work in progress.

WOLPERTINGER’S SOCKS

by James Lincoln Warren

Jakob Linnaeus Wolpertinger looked over his steepled fingers and snorted. “For too long have these so-called ‘scientists’ been devoting their attentions to the most trivial of problems at the highest of costs. Super-colliders and orbiting telescopes! It’s absurd, when the mysteries of the universe veritably display themselves at the tips of our own noses.”

“So you’ve been working on that paper-clip nasal-passage-opener anti-snoring thingy again?” Ivor, his cyphotic minion, asked.

“No, vile cretin,” Wolpertinger said angrily, his wiry frame unfolding like a spring on a music-box lid, the kind that you open by pressing a button to hear it play “Lara’s Theme” from “Dr. Zhivago” or maybe Brahms’ Lullabye and suchlike, launching him out of the sagging wing chair in which he had been sitting.

“I have been staring into the heart of the abyss itself, pondering the fundamental mysteries. I have been studying . . . the Sock Problem!”

“The Sock Problem. Ohh-kay.”

Wolpertinger seized his too-long hair in his left fist, the whites of his eyes showing above his dilated pupils, and his irises, too, come to that. “Yes, the Sock Problem, blithering imbecile. Suppose it’s dark and you can’t turn the light on to retrieve a pair of socks from your dresser drawer—”

“Why can’t you turn on the light?”

“Because it could wake the missus.”

“You’re not even married—engaged for the last twenty-four years, all right, but how long are you going to string that poor girl along, anyway? Wait a minute. I get it—you maxed out the electric bill with all your stupid experiments and Edison cut off our power again, right?”

“Never mind, drooling ignoramus. I will patiently explain. You have three pairs of black socks and four pairs of white socks, all of which are loose in the sock drawer. How many socks do you have to remove to ensure you get a pair the same color? That’s the Sock Problem in its most elementary configuration.”

“Three.”

“You’re wrong, ignorant vandal. It takes three! Any idiot can see that. But suppose you need to get a pair of white socks. Eh? What then?”

“Eight, in case the first six are all black.”

“The answer is eight—in case the first six are all black, foolish lout. What do you say now?”

“I suppose you’re going to tell me that this is an application of information theory, that taking socks from the drawer can be expressed as a binary string of length n bits, where the entropy of the string can be expressed as H = -[p log p + (1 – p) log (1 – p)], where H is the average information content and p is the probability of drawing either a black or white sock through an iteration of m possible choices, and is equal to -(p₁ log p₁ + p₂ log p₂ + … + p_m log p_m). But this is trivial. What has it got to do with writing mystery stories? And I note that you have on one blue sock and one grey argyle.”

“I was getting to that!”

“Well, I’m waiting.”

“It’s all Steinbock’s fault, you know.”

“How so?”

“He’s the one who bought up this whole topic of randomness. There is nothing less random than story telling, which adheres to a story-teller’s fixed plan, or at least starts out that way. But a story, especially if it involves the solution to a mystery, must have the appearance of randomness, of entropy, of hidden information. And that’s why I have been thinking about the curious incident of the socks in the night-time.”

“You’re too clever by half. And Socks is a cat’s name, anyway. Aren’t you worried about appearing too contrived? The deus ex machina effect?”

Wolpertinger smirked with self-satisfaction. “Not a bit—not if the contrivance isn’t revealed until the end, and isn’t entirely gratuitous. That’s when the entropy is exhausted anyway, because all has been revealed.”

“Yeah, right. Just remember what happened the last time you tried to sew something together from different parts. Home Depot sold out of resin torches in less than half an hour and the locals stormed the castle. But all this palavering has made me thirsty. I’m going out for a beer. They’ve got this beautiful new gypsy barmaid down at the pub, and that ain’t remotely your random event, Doc. I’m pretty sure Warren planned it all along.”

“Vulgar blackguard!”

“Oh, please.”