Kominers’s Conundrums: Can You Escape This Column?
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I have not been inside an escape room for quite some time, but I am very much looking forward to it. There’s something special about testing your wits against a succession of mysterious puzzles — typically, with the added challenge that you have to uncover those puzzles and their purpose for yourself. (And there’s the added intensity that comes from the fact that you’re stuck inside until the puzzles reveal the escape mechanism!)
Your mission — should you choose to accept it — is to escape this column. To do that, you’ll need to find and interpret three hidden “keys.” Each key is a pair of words, and putting those words together will reveal the way out. Once you find the escape path, it will lead you to a secret location, the name of which is this week’s answer.
Like with a classical escape room, everything in the column is fair game as a hiding spot — keys and the clues to uncovering them could be anywhere in the text, or even in other parts of the page like that big picture at the top. But watch out: There might be a few red herrings as well.
As a starting point, here’s a clue to the first key:
What to make of that? It’s pretty cryptic, and looks bizarre. But maybe there’s a complementary clue somewhere that could help bring a bit of order to the chaos?
Plus if you can’t find one of the keys, you shouldn’t panic — you can probably make your way out with just two of them, or even with one if you’re really clever about interpreting what it means.
Got the game? Then put on some thematic background music and dive in. Does anything look unusual or out of place? The clues and keys — and even the escape route — are right in front of you. Where, exactly? You’ll have to figure that out.
If you manage to make this great escape — or if you even make partial progress — please let us know at email@example.com before midnight New York time on Thursday, April 15.
If you get stuck, there’ll be hints announced on Twitter and in Bloomberg Opinion Today. To be counted in the solver list, please include your name with your answer. And don’t forget to sign up for our new email list. (Apologies to those of you reading in syndication — to solve this Conundrum, you’ll need to look at the version of the column posted at bloomberg.com/opinion.)
Programming note: The next Conundrums is scheduled to run on April 18.
Previously in Kominers’s Conundrums…
First the “watchdog” Tock (1 word, 5 letters) barked out the cryptic message, “11 PM! 9 AM! 8 PM! 3 AM! 8 AM!,” commenting that “If you really wanted to, I suppose you could divide up time any which way. And you could label it however you want […]. But the twenty-third hour is important here, and twenty-five and twenty-six aren’t.”
Converting to 24-hour time gave us “23! 9! 20! 3! 8!.” Then, looking at the corresponding letters in the alphabet yielded “W! I! T! C! H!” — leading to the answer “WITCH.”
Next, King Azaz (1 word, 5 letters) of Dictionopolis presented a word criss-cross puzzle by his brother, the Mathemagician of Digitopolis. As Azaz explained, the puzzle came with an indication that “even a word-lover can’t escape numbers completely” — and indeed, it turned out that each word in the grid contained the name of a number:
- When you win a championship, and then another, and then another — THREEPEAT
- This answer is hazy; try again later — EIGHTBALL
- A European bowling game with a diamond-shaped target — NINEPINS
- What a hobbit eats before luncheon, or when you might have an English Breakfast — ELEVENSES
- By an order of magnitude — TENFOLD
- Paper currency featuring the Lincoln Memorial, casually speaking — FIVER
Filling in the grid and reading the letters where the words crossed (“I’m so cross with him”) spelled out the answer “AISLE.”
Next a helpful-seeming, but nondescript man (2 words, 3 letters each) spoke about how “You can be many different things, depending on how you start out.” He next explained:
- “Some days when I get up in the morning, I feel like those droplets that form on leaves in the fall or spring — or perhaps like part of a Grateful Dead song.”
- “Other days, I feel more like the plant itself — coniferous, with highly poisonous berries, and featured in a song performed by Battlefield Band.”
Puzzling over these two descriptions, solvers realized that each corresponded to a three-letter word, and the only difference between those two words was the first letter: “DEW YEW.”
Next color conductor Chroma the Great (1 word, 4 letters) needed help with a digital instrument experiment. “I feel as though I’ve hexed myself,” he declared, trying to make sense of some bizarre-looking sheet music.
Each note turned out to be the code for a color, written in a hex triplet:
- ce2029 — FIRE ENGINE RED
- c8a2c8 — LILAC
- ffff00 — YELLOW
- 614051 — EGGPLANT
Then we learned of a trick King Azaz had played on the Mathemagician (1 “word,” 1 digit) of Digitopolis: He replaced the numbers on the royal blackboard with letters!
The Mathemagician presented the equation
ABCD * E = DCBA,
asking what digit “A” represents.
Recognizing each letter as a different base-10 digit (so they couldn’t all be “0,” for example), the equation has a unique solution:
2178 * 4 = 8712,
under which “A” corresponds to the answer “2.”
In the Mountains of Ignorance, the Terrible Trivium (1 word, 6 letters), presented an unnecessarily difficult trivia challenge. He would ask, for example, “Who’s the bumbling spy best known for chasing a moose and squirrel?”; a demon would answer, “that’s Boris”; and then Trivium would snarl “WRONG!!”
Yet of course Boris is the name of a bumbling spy best known for chasing a moose (Bullwinkle) and squirrel (Rocky) — so what could be going on?
Examining the clues closely revealed that each one had precisely two potential answers — as the puzzle hinted, the demons “don’t seem to know half as much as they think they do.”
Trivium, solvers inferred, must have been looking for the alternate answers (“Natasha” in the case of the clue above). This made it possible to figure out the “correct” answers to each question as follows:
- “Who’s the bumbling spy best known for chasing a moose and squirrel?” Trivium asks.
“Oh, oh — I know,” a demon shouts, “that’s Boris.”
“WRONG!!” Trivium snarls. (Correct answer: Natasha)
- “Who’s the Atlanta rapper who won his first Grammys for ‘Ms. Jackson’ and Stankonia in 2002?”
“You must mean Big Boi.”
“WRONG AGAIN!” (Correct answer: Andre 3000)
- “Now who was the Union commander in the United States’ Civil War?”
“NOPE!” (Correct answer: Ulysses S. Grant)
- “How about the sailor who got trapped on an island with a professor and movie star after a supposed three-hour tour?”
“WRONG!” (Correct answer: Gilligan)
- “The smuggler who travels a far-away galaxy in the Millennium Falcon?”
“NO! You’re awful at this.” (Correct answer: Han Solo)
- “Last question: Who’s the performer who hosted ‘Weekend Update’ and then starred in a successful seven-season-long sitcom?”
“Amy Poehler, obviously.”
“WRONG AGAIN!!" (Correct answer: Tina Fey)
Looking at the first letters in the correct answers spelled out the puzzle answer “NAUGHT,” which also fit with a second hint given in the puzzle text (“It sounds as if these demons know nothing”).
Finally, solvers arrived at castle of princesses Rhyme and Reason (2 words, 4 letters each) — with the demons shouting from outside.
- One group of demons chanted, “Sash! Pot knot bot lot! Lot bot! Brash not!”
- The second screamed, “Rash cot mash! Bot clot! Slash knot! Bash stash pot!”
To help you make sense of this, Rhyme said, “I’m pretty sure I can help you.” Next, Reason added, “I’m pretty sure I can help you after that.”
Solvers had to recognize that the demons’ cacophonous chants were comprised entirely of words that rhyme with either “dot” or “dash.” From there, treating the exclamation points as letter breaks made it possible to read each group’s chant as a word in Morse code; this yielded the answer “THIN KING.”
Having solved all seven of the individual puzzles, the final challenge was to put their answers together to identify “the single word that wraps up our story.” A helpful tollbooth operator suggested you might try saying the answers aloud — and indeed, you could read them together as
“WITCH AISLE DEW YEW FLYE 2 NAUGHT THIN KING”
Making sense of this required one last trip to the “Tollbooth” world. In the story, there is an island that characters find themselves whisked away to whenever they come up with an idea without thinking carefully first: “CONCLUSIONS.” A good word to “wrap up” with, that was the answer to the full Conundrum.
Zoz solved first, followed by Lazar Ilic, Ross Rheingans-Yoo, Noam D. Elkies, and Zarin Pathan. The other solvers were Darren Fink & Dina Teodoro, Bill & Ellen Kominers, Daniel & Patricia Miron, Andrea Spalding, Matthew Stein, Robbie Stern, Michael Thaler, Nathaniel & Barbara Ver Steeg, Eric Wepsic, Michaela Wilson, and Dylan Zabell. Pathan noted that there actually is a Conclusion Island in Alaska. My brother and I were especially pleased that our parents, Bill & Ellen Kominers, solved, since they are the ones who introduced us to the “Tollbooth” in the first place. Thanks also to Jeffrey Cohen and Yi-Hsin Lin for test-solving!
The Bonus Round
Taylor Swift’s new puzzle; History of magic; Iceland’s eruptions; Rather large sushi rolls; Delicate primes. “King of legal hypotheticals”; Everywhere the ship can get stuck; Young otters. Interesting numbers; Squares the same size? Lifting heavy objects with science; Engineering new woolly mammoths; Topology tricks; Tough tongue-twisters; Erdős’s coloring conjecture, now solved; Really useless machines. Plus inquiring minds want to know: where is the final key hidden?
These days, you can even play escape rooms in "Super Mario Maker!"
“ffff00” is also sometimes called “electric yellow”; luckily, by some miracle, “FLEE” turned out to work almost as well in the final puzzle solution as "FLYE."
The Morse code reference is why we also hinted that Norton Juster's other most famous work,The Dot and the Line, could provide insight as well. (Get it? "Dot" and "line"? We’re hilarious here at Conundrums.)
Another way to get at the idea of looking for homonyms for the individual answers was to remember that "The Phantom Tollbooth" features a character named the "Which," whom others in the story are careful not to confuse with the "Witch."
“CONCLUSIONS” also linked up with the confirmatory clue “jump to it” at the end of the Conundrum text, since in the novel, characters who end up on the island are said to be “jumping to Conclusions.”
This column does not necessarily reflect the opinion of the editorial board or Bloomberg LP and its owners.
Scott Duke Kominers is the MBA Class of 1960 Associate Professor of Business Administration at Harvard Business School, and a faculty affiliate of the Harvard Department of Economics. Previously, he was a junior fellow at the Harvard Society of Fellows and the inaugural research scholar at the Becker Friedman Institute for Research in Economics at the University of Chicago.
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