Scrooge McGrinch and the Four Elves (a Christmas Puzzle)

E. Scrooge McGrinch

In the hour before the sun peeked around the mountain, a green, green figure clumped up the hill, dysphoria washing over him yet again. Scrooge McGrinch felt misunderstood. His shrink explained he suffered from hereditary hormonal imbalance, festiphobia (a fear of holidays) and affluenza (a love of money). As the 7^th generation following the historic marriage of Ebenezer Scrooge Jr and Ethylene Glycol MacGrinch, his skin still bore the same pigment as an eight-dollar bill.

[For our vast audience of molecular biologists, see DAT1, DRD2, and SOD1-/- in ‘Condition Green’, Morley et al, JAM, 2022.]

Then he heard a racket, a cacophony of four voices, and his spirits leaped in joy. Off the trail, caught in an avalanche of snow, were wedged his sworn nemeses, a quartet of bratty elves who made his pitiful life miserable.

Four Awful Elves

Boozy, Doozy, Floozy, and Woozy had awakened at 4:30, giggling and chuckling. The lads chortled at the notion of joyriding the village’s most recent resident, Bolderdash, understudy for the nine celebrity reindeer. In the dark of the mudroom, they pulled on boots, mittens, and stocking caps. Emboldened by a generous slug of wintergreen schnapps, they headed toward the barns.

Bolderdash was not thrilled to be shaken and awakened when a bridle slipped over his nose. The brightly lit factory and rail yard swarmed with activity at that early hour, so the jackanapes led their captive reindeer into the dark before climbing aboard.

They cantered down the tracks of the Polar Express and galloped into the night. At the edge of the plateau near Kringle International Airport, a landing FedEx cargo plane zoomed overhead, startling Bolderdash. He balked. He had had enough. In a fit of pique, he bucked and skidded to a halt at the edge of a precipice.

Four little figures flew over a cliff and landed up to their chins in deep snow, fortunate they didn’t set off an avalanche. They found themselves trapped in cold white stuff, unable to move. Meantime, Bolderdash sulkily stalked back to the barns, hoping for a little more sleep before roll call.

The Problem and the Proposal

A half hour passed until Scrooge McGrinch stumbled upon the naughty elves. He said, “You… You in the red hat. What are you miscreants doing?”

The elves appeared confused. Two wore red hats and two wore green hats. “In the dark, O Verdant One, we grabbed toques without noticing the colors. None of us can see what we’re wearing.”

“You brats wear colorful hats, but you don’t know the hue, do you?” said McGrinch. “Let’s play a little game.”

Scrooge McGrinch wasn’t a mean man… Well, okay, he was mean in multiple senses of the word, but he wasn’t entirely heartless. Following a modicum of smug enjoyment, he said, “If anyone can figure out the color cap you’re wearing, I’ll rush to Ski Patrol to dig you out, else I’ll call your parents and they won’t be happy.”

The elves shivered. “We’ll give it a try, Your Viridescence.”

McGrinch grimaced. “Fine. Here are the rules.”

The Puzzle

1. Four elves in a row are immovably buried up to their chins in snow.
2. Their names and positions are Boozy₁, Doozy₂, Floozy₃, and Woozy₄.
3. Two wear red hats, two wear green, but no elf knows what color he wears.
4. Each elf can see only the elf or elves directly ahead.
5. Woozy is separated by an impenetrable snowdrift.
6. None can glimpse their own hat, nor do colors reflect off the snow.
7. Elves are not permitted to discuss what they see.

Solution after the break.

And so Scrooge McGrinch promised to rescue them if any elf correctly identified the color hat he was wearing, otherwise they faced the humiliation of begging the Big Elf’s help. Which elf might deduce his hat?

Dickens and His Ghosts

One of my co-workers asked the other day, Which is your favorite Christmas story? I said, the original, meaning the Nativity. I've always loved the Christmas Eve church service, the lessons and carols. The narrative from Luke, "Now it came to pass in those days, there went out a decree from Caesar Augustus, that all the world should be taxed."
Thinking about it, though, I realized that there's a lot to choose from, and the chiefest of these is A CHRISTMAS CAROL. It was a personal favorite of Dickens, and he performed it both publicly and for his family year after year, playing all the parts, taking all the voices, acting out every flourish. He was quite the spell-binder, by most accounts - his children loved it - and it must have been something to see. The story itself has amazing durability, and survives almost any adaption. (One of my own personal favorites is the animated Disney version.) What accounts for its staying power?

Well, first of all, it's a ghost story. There are four of them, remember. Most of us would say three. But the first to visit is Scrooge's dead partner, Marley, and he sets the tone, foretelling the spirits who are to come, past, present, and future. Dickens, then, shows his hand, he lets us know what to expect, even if he doesn't reveal all his cards, Like any skillful conjurer, Dickens uses a succession of reveals, each effect providing a shiver of recognition.

And it's a story of redemption. We suspect Scrooge will save himself, of course, but most of the fun comes from his adventures along the way, not his getting there. It's his resistance to the pull of his own feelings that gives the story its tension. If we were absolutely sure he'd give in to his better nature, we'd be looking behind the curtain. We pretend to be surprised, every time. It's more satisfying that way.

I think there's also a hidden force behind A CHRISTMAS CAROL. Dickens was always very aware of social injustice, and his age saw a lot of it. Children at risk, from poverty, from sickness, is one of the currents in the story. Dickens' own humiliation, when he was a boy, his father in debtors' prison, and the hated blacking factory (which experience figures in both COPPERFIELD and OLIVER TWIST, too), his long-lasting sense of victimhood. A CHRISTMAS CAROL is sentimentally effective because it's at first terrifying.

Lastly, the story's subversive. We sympathize with Scrooge, in some sense. Christmas has become a sort of pathology, all that crappy music on the radio, and the cheesy sales promotions. Who isn't a little gleeful to see it disdained? On the other hand, Dickens had a big part in making Christmas what it is today. It was the Victorians who created our Christmas, although they emphasized a generosity of spirit and the "context of social reconciliation" (the historian Ronald Hutton), not its commercial aspects.

So, in keeping with the season, let's say God Bless Us, Every One, and a Merry Christmas to you all.