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Kominers’s Conundrums: Splitting a Record Chocolate Bar

Scott Duke Kominers

(Bloomberg Opinion) -- Just before the lockdown, Chocolade atelier van Noppen set the world record for the biggest chocolate bar ever. It measured just over 26.8 x 14.3 meters, for a total of 383.24 square meters. You can watch them create it here.

That’s way too much chocolate for even Count Chocula,(1)but how would they go about dividing the bar in the most efficient way? That is the core question of this week’s puzzle, which is an old classic that economist Matthew Jackson recently reminded me of:

Let’s imagine that van Noppen’s chocolate bar were subdivided into a 2,680 x 1,430 grid of 38,324 individual decimeter-sized squares, separated by scoring lines like on an ordinary Hershey’s bar.

What’s the minimum number of breaks you need to split the bar into individual squares? (Each break needs to be along a scoring line. And you can only break one piece of chocolate at a time – no stacking pieces or sticking them together temporarily.) Bonus points if you provide a creative estimate of how long the breaking process itself will actually take.

There is an easy way to start solving this one with a strategy we’ve used before in this column: Start small. Imagine a 6 x 4 piece of chocolate, with five potential vertical breaks, and three potential horizontal ones:

If we start by breaking along the first vertical line, we end up with two pieces, one of which is 1 x 4 and the other of which is 5 x 4. We can then break either of those down further — for example, by splitting the 1 x 4 piece in the middle:

That said, it’s not obvious whether that’s the right sequence of breaks to start out with. And don’t forget that our Conundrum is a bit bigger than the example — almost 1,600 times bigger, in fact!

If you manage to break through to the answer — or even make partial progress — please let me know at skpuzzles@bloomberg.net before midnight Eastern time on Wednesday, June 10. (If you get stuck, there’ll be a hint announced in Bloomberg Opinion Today on Tuesday, June 9. Sign up here.)

Last Week’s Conundrum

Thanks to Sam’s unwise decision to leave his cat alone with a meticulously set dinner party table, a puzzle was born. The pet ran across the table and mixed up the place cards, each of which was made of individually cut letters. As Sam scrambled to unscramble them, he had the nagging feeling that one guest was left out.

Most of the letter jumbles didn’t look much as if they came from names — the first two, for example, were “DFGNLA” and “EYRM.” But if you squinted hard enough, you could spot that each collection of letters was close to the name of a character from Tolkien’s “Fellowship of the Ring.” 

Astute solvers might then have noticed other clues in the puzzle pointing in that direction: “Sam” was a nod to Samwise Gamgee — himself a member of the Fellowship. And at least according to “The Adventures of Tom Bombadil,” Sam Gamgee was known to have some experience with cats.

There were even a few clues outside the frame, such as my reference to the puzzle as the “middle” of a “fantastical tale,” highlighting “Middle-earth” and the fantasy genre.(2)

But there was a catch: if “DFGNLA” is supposed to refer to “GANDALF,” then it’s missing an “A” — and indeed, upon sorting out the letters, we see that precisely one letter is missing from each name:

GDFNLA → G(A)NDALF

EYRM → ME(R)RY      

SLOEGL → LEGOL(A)S

IMIL → (G)IMLI

FDOR → FR(O)DO

IOMBRO → BO(R)OMIR

PIPIP → PIPPI(N)

Reading out the missing letters in order spells out the answer “ARAGORN” — the last member of the Fellowship, who was “left out” in more ways than one since he also did not have a place setting.(3)

Melissa Shirley solved it first, barely an hour after the Conundrum hit the web; Iolanthe and Brad Stronger solved just minutes later. Others among the 24 solvers included Michael Branicky, Daniel Chiu, Hannah Ellery, Ali Haberman, Bryn Huxley-Reicher, Eric Mannes, Adam Rosenfield, Hollie Schmidt, Katya Sharma, Stephen Strenio and Bloomberg Opinion’s own Social Media Mage, Lara Williams.

Plus, special shoutouts to Zoe DeStories, who helped me come up with the puzzle concept.

The Bonus Round

Didn’t get your fill of chocolate above? Check out this infinite chocolate bar trick. Then play minigolf with a marble machine; peruse the history of Pac-Man; and/or piece together a 30-year-old video game byte by byte. Turn your cat photos into Impressionist portraits — or turn your house into a Seussical cat playground. Solve this fish puzzle. Plus inquiring minds want to know: How is ketchup made?

(1) Or as they say in The Eleventh Hour: “One mouse could never eat it all!”

(2) Not to mention that Tuesday’s hint included multiple oblique references to Sauron’s One Ring:“Do any of the [sets of letters] have a familiar ring? And as to that missing guest: would adding one more somehow bind the others together?”

(3) Did you know it's possible to spell out “ARAGORN” using one letter from each of seven different Fellowship members’ names? More news you can use, courtesy of Conundrums!

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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