From there, you’ll need to make another logical leap and figure out how to “convert” each unit you’ve identified into a single letter. Putting those letters together in sequence will spell out this week’s answer, which is one way we might characterize the switch back to imperial units.
• 1.137 LITERS = 1 ___ (5)
• 1.36 KILOGRAMS = 3 ___s (5)
• 0.032 BUSHELS = 2 ___s (4)
• 335 INCHES (at MIT) = 5 ___s (5)
• 378 GALLONS (of wine) = 6 ___s (8)
• 0.444 CUBITS (of horses) = 2 ___s (4)
• 0.5 KILDERKINS = 1 ___ (6)
• 16.308 LIGHT-YEARS = 5 ___s (6)
• 2.333 DRAMS (to an apothecary) = 7 ___s (7)
• 1000 MILLIGRAMS (of precious stones) = 5 ___s (5)
We’ve indicated the number of letters in each unit name in parentheses after the blank; these numbers don’t count the “s” at the end of plural units, which we’ve filled in for you. We’ve also provided a few hints for cases where the proper interpretation might depend on the measurement context. Note also that we’ve rounded everything on the left side to three digits after the decimal place, which means that the two sides won’t always match up perfectly.
To get started with these, you first need to figure out what type of measurement each given unit represents. Then it often helps to divide out the multiples. For example, BUSHELS are a measure of capacity for dry goods. The puzzle asks: 2 of what unit equals 0.032 BUSHELS? Dividing both sides by 2, we see that corresponds to the question: What unit is equal to 0.016 BUSHELS? With a tiny bit of research, we can then discover that 0.016 BUSHELS (rounded up) equal 1 PINT. (And note that’s an imperial pint, rather than a US pint.(6))
That approach should get you started filling in our missing units, but don’t forget about that extra logical leap at the end! The final answer you’re looking for is a ten-letter phrase.
If you uncover the true weight of these measurements — or if you even make partial progress — please let us know at email@example.com before midnight New York time on Thursday, October 7.
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 if you’re enjoying these Conundrums, please sign up for our email list!
Last Week’s Conundrum: There’s Still Time to Solve!
Don’t forget to take a crack at our jigsaw quotes Conundrum if you haven’t already! As a reminder, the goal is to reassemble classic quotes from their “pieces,” such as this one from The Lorax:
• are buy crazy earth fool greed is is no on one sir that there thneed who with would you
(“Sir! You are crazy with greed. There is no one on earth who would buy that fool Thneed!” There’s one extra “is,” which is used in the solving the overall puzzle.)
And there’s a bonus puzzle too, which so far only a couple of solvers have managed to sound out.
Previously in Kominers’s Conundrums…
To commemorate the 64th edition of Conundrums, we played a classic math game: Guess four-sixths of the average.
The format was simple: Everyone submitted a number between 0 and 64,000, inclusive. The goal was to guess the number closest to four-sixths of the average of all the numbers.
Equilibrium logic in this game pushes towards low numbers: All the numbers are less than 64,000, so four-sixths of their average must be less than 42,667. But that means everyone should submit numbers less than 42,667, and four-sixths of that is 28,444. Iterating this logic might quickly convince you that the optimal number to submit is 0 or something very close to it.
Yet as we mentioned, it’s well known that in this game many people don’t play the equilibrium — they might send in their favorite numbers, or submit especially high numbers just for amusement. And indeed, our solvers did!
We received 86 submissions, led off by Joshua Gans, Lazar Ilic, Franklyn Wang & Cindy Yang, GiulioG, and David R. DeRemer (full list of entrants here). The distribution of entries in submission order was as follows:
Four people submitted the maximum value, 64,000.(1)Other than that, people mostly seemed to be trying to find something that looked like equilibrium balance: The next highest number submitted was 34,257, and the curve was fairly continuous from there, with a lot of weight on lower numbers.
The overall average was 13883.82, and four-sixths of that is 9255.883.
That means that Emanuel Schertz’s submission of 9,216 was by far the closest (highlighted in the bar chart above), followed by Ishan Khare (10,000), Michael Perusse (8,427.01), and Scott W. (8,384). Sanandan Swaminathan submitted the most interesting number we received: 64,000/e × 2/3 × 2/3 = 10464.126, which was also stunningly close to the right answer. GiulioG and Zarin Pathan submitted the answer to everything, “42.”(5)
And as a “captcha” of sorts, we also asked entrants to prove they weren’t robots by telling us the names of their favorite animals. The variation across this list was impressive. Dogs and cats unsurprisingly led the pack; there was then a four-way tie for third between capybaras, pandas, tigers, and my personal favorite, bears. Special shoutouts to Rostyslav Zatserkovnyi for “dilophosaurus”; M for “scimitar oryx”; Swaminathan (again) for “tauntaun”; Eric Wepsic for “okapi”; and Risa Puno for “Internet kittens.”(2)
Also, two belated thanks from the art heist Conundrum we presented the solution for last week: The Escape Game’s Theo Hoglund and Max Magura both served as test solvers, and Magura was additionally the voice on the Barclay Museum’s phone line!
The Bonus Round
Hurricane reports that sound like subtweets; “bouncy numbers”; kite geometry (hat tip: Milena Harned by way of Ken Fan); and “The Ern Malley hoax.” Matt Amodio breaks $1 million; a notorious unsolved number puzzle; small world photomicrography (hat tip: Ellen Dickstein Kominers); made-in-Nigeria boardgames; and “Hexagons are the Bestagons” (also hat tip: Ellen Dickstein Kominers)! Monowheels; a book barcode mystery (hat tip: David Kwong); and “An Oral History of ‘Batman: The Animated Series’” (hat tip: Paul Musgrave). Plus inquiring minds want to know: Why are street lights turning purple?
(1) You might want to use an index of measurement terms to help you out.
(2) If you get stuck on something, maybe try checking both US and imperial.
(3) We are omitting their names in order to save them from any tomatoes the other entrants might want to throw – although I don’t know whether to be proud or chagrined that one of them was one of my own students.
(4) We also appreciated the submission name “Iwill Notwin”; amusingly, this pseudonymous solver was actually pretty close to winning, with the entry 10666.667.
(5) Also LOL to the people who wrote “humans.”
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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