Kominers’s Conundrums: A Word Chemistry Lab Needs Organizing

This past week was the Regeneron International Science and Engineering Fair, a worldwide competition among high school science whizzes, who present top-notch research in everything from botany to astrophysics.

I’ve been involved in the Fair for years — first as a student, and now as co-chair of the Mathematics category. Seeing the work of so many brilliant high school researchers — this year virtually — made me made me pretty nostalgic for the days when I was first learning science.

Back in high school I wasn’t working with neural nets or designing autonomous irrigation networks. But at least I was pretty good at balancing chemical equations — what’s known as “stoichiometry.”

Unfortunately, though, the truth is that I’ve long since forgotten most of my high school chemistry. So I came up with the next best thing: “Word Stoichiometry,” a wordplay game based around a chemistry motif.

We’re presenting seven different ways pairs of words that can “react” together to produce a new word. For example, in

ONE + STAG = ONSTAGE,

“ONE” and “STAG” react by inserting “STAG” right before the last letter of “ONE.”

We’ve put that together with six other example reactions — but for the others, you’ll have to figure out the patterns yourself.

  • ONE + STAG = ONSTAGE
  • NICHE + RACER = NICER
  • ELEPHANT + DELETION = ED
  • YEATS + STEWARD = YARD
  • NETS + RATE = EASE
  • AIMS + RANT = AIRMAN
  • RUN + UP = RUNDOWN

Once you’ve worked out how word chemistry works, we have seven new equations for you to solve — each using a different one of the seven reaction mechanisms just described.

If you find the (ahem) solution to each of these equations, that should precipitate a bit of further thinking: combining the resulting words together will give a clue to the formula for a particular brain food, which is well-known in part for its chemical makeup. That scrumptious snack is this week’s answer.

  1. BRED + PLANETARIUM = ?
  2. ESAU + SLIP = ?
  3. TWO EQUATION TK
  4. SOIL + DUMB = ?
  5. INTRA + NIGHT = ?
  6. BAD + LANCE = ?
  7. BREAK + SLOW = ?

Solving these equations might take a bit of trial and error because some of the reaction mechanisms could be applied to multiple ones of them. But there’s only one way to ensure that each reaction mechanism is used precisely once — at least if we want all the resulting words to be Scrabble-legal

And of course if you get stuck, you can always put the puzzle down for a bit and come back to it periodically.

If you figure out how to fuse these word molecules — or if you even make partial progress — please let us know at skpuzzles@bloomberg.net before midnight New York time on Thursday, May 28.

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 Conundrums email list!

Programming note: The next Conundrums will run on May 30.

Previously in Kominers’s Conundrums…

We sought to make sense of an ancient commodities trader’s tablet, which had been discovered by Conundrums archaeologist Paul Kominers.

Solvers were told that “the currency of the day was gold coins, and one egg was worth one gold coin.” The other market rates were explained through a confusing series of trading options, and even the identities of the other commodities were obscured through bizarre idioms.

The top-line idioms weren’t too difficult to figure out — especially because we provided the number of letters in each:

  • CURLY NEW ENGLAND FERN (10) = FIDDLEHEAD
  • BLEATING ANIMAL (4) = GOAT
  • TART YELLOW FRUIT (5) = LEMON
  • BALLPARK LEGUME SNACK (6) = PEANUT
  • COMMON BEACH FIND (5) = SHELL
  • DINNER SEASONING (4) = SALT
  • MARK KURLANSKY BOOK (3) = COD
  • ENGAGEMENT RING SPARKLER (7) = DIAMOND
  • HEN FRUIT (3) = EGG
  • BUILDING MATERIAL (4) = WOOD
  • ROMAN PARTY WRAP (4) = TOGA

After working those out, it was clear that “Got forty BLEATING ANIMAL (4)? That plus three HEN FRUIT (3) will buy you five ENGAGEMENT RING SPARKLER (7).” meant 40 GOAT + 3 EGG was worth the same as 5 DIAMOND.

You could then, for example, combine that expression with the following two:

  • Alternatively, you can get one ENGAGEMENT RING SPARKLER (7) in exchange for four ROMAN PARTY WRAP (4) plus four BLEATING ANIMAL (4). (1 DIAMOND = 4 TOGA + 4 GOAT)
  • And if you’re short on BLEATING ANIMAL (4), you can get four of them for one ROMAN PARTY WRAP (4). (4 GOAT = 1 TOGA)

These together yielded that 1 DIAMOND = 20 GOAT, meaning that 40 GOAT + 3 EGG = 100 GOAT, so 1 EGG = 20 GOAT, meaning that each GOAT was worth 1/20 of a gold coin. (And similarly, 1 TOGA was worth 1/5 of a gold coin.)

Further algebra made it possible to work out the other exchange rates. Then, solvers had to match the commodity types with alternate definitions provided in the trader’s goods manifest. GOAT, for example, corresponded to “Once-in-a-generation champion” (aka the “Greatest Of All Time”), and the ancient trader had 40 to trade in, which would’ve been worth 2 gold coins.

The full matching from commodities to exchange rates — and the associated conversion into gold coins — is shown in the table below.

But solvers weren’t quite done there: the answer to the puzzle was “what the trader expected to get out of all the items after trading them in for gold coins,” and we had hinted that “once you’ve figured out what our trader was going to cash out each set of items for, you might have to ‘cash in’ somehow to find the final answer.”

The last step of the puzzle was to look at the position in each commodity’s name that was indicated by the number of gold coins in the trader’s converted stash — so in the case of 40 GOAT, worth 2 gold coins, the associated letter would be an “O.” Putting those letters together in order spelled out the trader’s reward — one more commodity pun: “A TON OF DOUGH.”

Kominers’s Conundrums: A Word Chemistry Lab Needs Organizing

And for any solvers who weren’t exhausted by all of that trading, there was a bonus puzzle, as well: we asked, “What was our trader going to do after exchanging everything?” A surprisingly large number of solvers said “buy bitcoin pizza!” But while that sounds tasty, it wasn’t the intended solution.

The clue “exchanging everything” suggested looking at the exchange rates — and if you mapped those rates into the alphabet in order (with “1/19” as “S,” “1/5” as “E,” and so forth), you could see that our trader’s long-run plan was to “SETTLE CATAN.”

Zoz* solved first, followed by Ross Rheingans-Yoo, Dan Rubin & Jennifer Walsh*, Zarin Pathan, Lazar Ilic*, Nathaniel & Barb Ver Steeg, Noam D. Elkies, Elizabeth Grove, Sanandan Swaminathan, and Maya Kaczorowski*. The other solvers were Christopher J. Cifrino, Nicol Crous, Filbert Cua, Andre & Katrina Janiszewski, KG & Pax, Vikrant Kulkarni, Suproteem Sarkar, Nur Banu Simsek, Michaela Wilson, Dylan Zabell, and Rostyslav Zatserkovnyi.  (Asterisks indicate solvers who also figured out the bonus puzzle.) Cifrino noticed that “COD” wasn’t the only Kurlansky classic in our commodity list — he has also written on “SALT” and on oysters, which typically have a “SHELL.” And thanks especially to Eric Mannes for test solving!

The Bonus Round

This column is the 52nd edition of Conundrums! We’ve hidden a commemorative Easter egg somewhere in the text — can you find it?

After that, try constructing an unbiased coin from a biased one; or this mathematically notorious hat puzzle. Raising penguin chicks; “Windows of the World” (hat tip: Stefanie Stantcheva); group theory and crystal symmetries (hat tip: Shengwu Li); and “A Curious Golfer, a Lawn Mower and a Thousand Hours in Lockdown” (hat tip: Ellen Dickstein Kominers). Plus inquiring minds want to know: What if Alderaan had a huge mirror?

 

I also serve on the National Leadership Council of Society for Science, the nonprofit organization that runs the Fair. And I put together a series of Conundrums for this year's Fair attendees; you can check them out here.

Although if that was his plan, it's possible the trader should have kept his GOAT.

Many solvers interpreted the goal of the puzzle as just figuring out the total number of gold coins the trader could cash in for; since apparently the intended answer extraction strategy was unintuitive, we counted turning in the right number of coins (31) as a full solve.

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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