Kominers’s Conundrums: Overstuffed Bears Seeking Stability
(Bloomberg Opinion) -- It’s time for one of the most adorable holidays of the year: Fat Bear Week, where people all around the world help identify the fattest bear at Brooks River in Katmai National Park, Alaska. It’s an elimination tournament, with March Madness-style brackets — and there’s still time to get in on the action.
These bears really do become rather rotund — previous champions have had estimated weights upwards of 1,400 pounds. And while surveying bears’ weights might sound a little bit ridiculous, it’s actually really important for judging the overall health of the bears, who don’t eat or drink during winter hibernation.
At the moment, the bears are snacking as much as they can in hopes of winning the title. Our Conundrums Bear Brigade found a new floating pier to catch salmon off of, but unfortunately it’s a bit topsy-turvy. The pier is shaped like an equilateral triangle, and to keep it from flipping over, the bears will have to walk out from the center and balance their weight across the three points.
We've pictured each of our bears along with their weight. Can you separate them into three equal-weight teams? Then you can take the next step: Single out the first letter in the name of each bear and shift it forward in the alphabet by the number of bears in its team. Then, and only then, you should be able to spell out an eight-letter phrase that tells us what’s running through all these adowable bears’ heads while working on this math problem.
And you might find an Easter egg at the end once you’ve solved the main puzzle: Hidden somewhere is what the winner of Fat Bear Week becomes.
If you figure out how to bring the bears to their all-you-can-eat feast — or if you even make partial progress — please let us know at email@example.com before midnight New York time on Thursday, October 21.
Programming note: Conundrums will be hibernating next week, and returning on October 17.
Last Week’s Conundrum: There’s Still Time to Solve!
Previously in Kominers’s Conundrums…
We turned famous quotes into jigsaw puzzles by mixing up their words. Solvers had to sort out the proper sequence, and find one extra word in each.
The quotes were as follows, with the extra words indicated in bold:
- a ago all and and and are brought conceived continent created dedicated equal fathers forth four in liberty men nation new on our proposition score seven that the this to years [Abraham Lincoln] = FOUR SCORE AND SEVEN YEARS AGO OUR FATHERS BROUGHT FORTH ON THIS CONTINENT, A NEW NATION, CONCEIVED IN LIBERTY, AND DEDICATED TO THE PROPOSITION THAT ALL MEN ARE CREATED EQUAL.
- a between but cards nothing of pack you're [Alice] = YOU'RE NOTHING BUT A PACK OF CARDS!
- and animals be comfortable difference fur good in its keep let looks on only original own owner skin theirs your [Tim Howard] = FUR ONLY LOOKS GOOD ON ITS ORIGINAL OWNER. BE COMFORTABLE IN YOUR OWN SKIN, AND LET ANIMALS KEEP THEIRS.
- accomplish accomplished and are basically claim crowded extra first group have is less of people people people the there things things to two types who who [Mark Twain] = THERE ARE BASICALLY TWO TYPES OF PEOPLE. PEOPLE WHO ACCOMPLISH THINGS, AND PEOPLE WHO CLAIM TO HAVE ACCOMPLISHED THINGS. THE FIRST GROUP IS LESS CROWDED.
- an army extraordinary its marches on stomach [Frederick the Great] = AN ARMY MARCHES ON ITS STOMACH.
- are buy crazy earth fool greed is is no on one sir that there thneed who with would you [The Lorax] = SIR! YOU ARE CRAZY WITH GREED. THERE IS NO ONE ON EARTH WHO WOULD BUY THAT FOOL THNEED!
- eye jest little not or religion the with with [George Herbert] = JEST NOT WITH THE EYE OR WITH RELIGION
- nevermore ordinary quoth raven the [Edgar Allan Poe] = QUOTH THE RAVEN "NEVERMORE."
- all almost alone and and beauty being can come describe eternity ever experienced for for for have have is joy knowledge little me mine more much mystical nature need no not of of of powerful really say suddenly that that the the there those those to unexpected who who with words [Jane Goodall] = FOR THOSE WHO HAVE EXPERIENCED THE JOY OF BEING ALONE WITH NATURE THERE IS REALLY LITTLE NEED FOR ME TO SAY MUCH MORE; FOR THOSE WHO HAVE NOT, NO WORDS OF MINE CAN EVER DESCRIBE THE POWERFUL, ALMOST MYSTICAL KNOWLEDGE OF BEAUTY AND ETERNITY THAT COME, SUDDENLY, AND ALL UNEXPECTED.
- be be is not or question that the the to to [Hamlet] = TO BE, OR NOT TO BE, THAT IS THE QUESTION.
and between difference extra extraordinary is little ordinary that the
Unscrambling that quote gave “THE DIFFERENCE BETWEEN ORDINARY AND EXTRAORDINARY IS THAT LITTLE EXTRA,” which matched up with repeated references to “extra” words. The quote is attributed to Jimmy Johnson, and his name was the answer.
There was a bonus puzzle as well — we had hinted that hidden somewhere was “a clue to what is in some sense the most quotable answer possible.” We added, “you might have trouble seeing it at first — but don’t forget that classic quotes sound best when read aloud.”
The phrase “at first” hinted that you should look at the first words of the different quotes, but that looked like gobbledygook:
FOUR YOU’RE FUR THERE AN SIR JEST QUOTH FOR TO.
As suggested, the trick was to read these words aloud to obtain the instruction, “For your further answer, just quote 4 2.” The bonus puzzle solution was “42,” which is quite quotable indeed — many say it’s the answer to everything.
Zarin Pathan* solved first, followed by Noam D. Elkies, Andrew Garber, Iolanthe Stronger, Zoe Schaefer, Ellen & William Kominers, Eric Wepsic*, Maya Kaczorowski, Sanandan Swaminathan*, Nancy & Murray Stern, Robbie Stern, Warren Sunada-Wong, Paul Kominers, Luke Harney*, Ellen Xu, Yannai Gonczarowski & Elee Shimshoni*, Rostyslav Zatserkovnyi, Ross Rheingans-Yoo, Lazar Ilic, Zoz*, and Benjamin Salop. (Asterisks denote those who also solved the bonus puzzle.) And thanks especially to Zoe DeStories for test-solving!
There’s also a bit more to postmortem on our “guess four-sixths of the average” competition from several weeks ago. You might have heard of “imaginary numbers” which are kind of like regular numbers except they go off on a different axis? We had a few “imaginary” submissions to our competition from solvers who sent in numbers by email rather than filling out the official form. We’re sorry we missed these — and while it’s not clear how we would have adjudicated them in the contest rules, one of those submissions (9,480 from Zoz) was actually the second-closest to the target among all the numbers we received.
Additionally, Elkies pointed out that the winning number, 9,216, is especially mathematically elegant, as it is 96^2 = 2^10 × 3^2. He also noted that it was surprisingly large — and it’s possible we’ve found the reason why. Further post-Conundrum investigation uncovered a conspiracy among the columnist's own family members to target numbers in the 20,000-32,000 range. They didn’t win, but they did push the numbers up a bit — dropping their entries would have reduced four-sixths of the average by about 1000, elevating michael mogan and Lazar Ilic onto the podium alongside the winners we listed.
The Bonus Round
Relive the opening of Disney World; tour The Imagineering Lab at the Mona Gallery; or just turn Magic: The Gathering into Uno. Non-attacking chessboard Queens; a crypto-trading hamster (hat tip: Zoe DeStories); “a psychedelic landscape highway”; and “Giant Tortoises at Full Speed.” The “melting face” emoji (hat tip: Ellen Dickstein Kominers); giant penguin fossils; and ruining a puzzle proposal (hat tip: Paul Kominers). Plus inquiring minds want to know: Where are all the aliens?
You can actually watch them catch fish in real-time here.
You might have been able to get to this sequence a bit quicker by noticing that the words appeared in alphabetical order, just like in the other jigsaws – and this implied some constraints on what the extra words in each jigsaw could have been.
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.
Lara Williams manages Bloomberg Opinion's social media channels.
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