(Bloomberg Opinion) -- Life is like a hurricane sometimes. When that happens, I like to take refuge in puzzles. Solving a challenging Conundrum can help focus your mind and perhaps even carry you off to a whole new world for a bit.

So here’s a Conundrum that may sound cartoonishly corporate at first, but I promise: It will actually bring you to a place free from worries, where there’s magic everywhere:

Walt asked Donald to put together new social media profiles for some of his team members – but he wasn’t too pleased with what Donald came up with.

Can you determine whom these taglines are describing, and fit their names into the grid below? Once you do, you should be able to figure out how Walt characterized the whole operation – and that is this week’s answer.

• Caped hero known for “getting dangerous”
• Definitely not a llama
• Eats eggs and decorates with antlers
• Forgetful fish; found Nemo
• Kid Hamlet
• Klepto monkey
• Little guy with top hat who recorded company theme song
• Loves pie, but should stay away from apples
• Necessity bear
• Scrooge’s pilot
• Smiley feline who appears to be purple
• Space-age pretty boy; falls with style
• Speechless to set foot on land
• The green caballero
• Toymaker with lifelike work (GEPPETTO)

We’ve included the character count for each row, and filled one in to help you get started. If you’re having trouble, maybe dig a little deeper into that individual’s background.

If you go the distance – or if you even make partial progress – please let us know at skpuzzles@bloomberg.net before midnight New York time on Thursday, October 8.

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 full name with your answer.

Programming note: Next week, Conundrums will run on Sunday, October 11. If you have opinions about the optimal release day/time for the column, please let us know at skpuzzles@bloomberg.net.

Previously in Kominers’s Conundrums …

For our 24th edition, we played the “24” game, seeking to make 24 out of six different sets of integers. Every mathematical operation under the sun was fair game, and readers came up with some really clever solutions.

The numbers 2, 3, 8, 8 could actually be solved in many ways using just the standard arithmetic operations (e.g., (3/2) × (8 + 8) = 24), but Charlie Hyde, Renee Wu, and several others found an elegant solution using exponentiation: 8 + 8 + 2^3 = 8 + 8 + 8 = 24.

Winston Luo identified the unique arithmetic solution for 1, 3, 4, 6: 6/(1 –3/4) = 6/(1/4) = 24. Many other solvers noted an easier answer that uses exponentiation: 1^3 × 4 × 6 = 24. Ross Rheingans-Yoo observed that 1 × BB(3) + 4 + 6, where BB is the busy beaver function.(2)

The numbers 3, 4, 9, 10 are in some sense surprisingly difficult: there are no solutions with just standard arithmetic operations. But as Teodor Ionita-Radu  and Ryan Wigley showed, it’s much easier if you allow factorials: 3! × 4 × (10 – 9) = 6 × 4 × 1 = 24, and (((10 – 9) × 4!)/3!)! = 4! = 24. Alternatively, you could solve it using exponentiation, as Michael Carlile & Flat did: (10 – 4)^3/9 = 6^3/9 = 216/9 = 24.

Spaceman Spiff figured out the unique arithmetic solution for 4, 4, 10, 10: (10 × 10 – 4)/4 = 96/4 = 24. Others such as Kenny Zhu used the tens to get rid of one of the fours so they could write 24 as 4!: (10 – 10) × 4 + 4! = 0 + 4! = 24.

For 2, 2, 2, 64, Dean Ballard, Bob Day, and many others noticed the intended trick of making a 6 by taking a base-2 logarithm of 64: Log2(64) × 2^2 = 6 × 4 = 24. But procrastidigitation and Noam Elkies came up with creative alternate solutions involving fractions, factorials and roots:

Most solvers simply reduced 1, 2, 5, 24 to 24 multiplied by 1 to a power. I may be biased, but I prefer my own overkill solution, which like the solution just above uses both a factorial and a root:

We also posed two bonus challenges.

First, we asked whether you could combine all 24 of the integers we gave to make 24 once more.

Laurent Granger and Suproteem Sarkar came up with similar solutions here: Take the 24 from the last set, and then multiply that by 1 raised to a gigantic power constructed from all the other numbers:

Then, we asked whether anyone could make 24 from 2, 13, 15, and 72, which my editor had said was too difficult for the main Conundrum.

Michael Branicky and several other solvers came up with an answer using the floor function, which gives the greatest integer less than or equal to a given number: 24 = 72/(2 + Floor(15/13)). Zoz instead used the sum of prime factors function; Phil Hu and Jeremy Hurwitz found solutions using trigonometric functions; Sanandan Swaminathan and several others used modular math; Filbert Cua used the decrement operator; and Noam Elkies gave answers using the Tribonacci numbers and the gamma function.(4)But in fact, none of these were the answer I had found: I was using the Euler “totient function,” which counts the number of positive integers less than a given integer that share no factors with that integer other than 1. Totient(72) = 24, so 24 = Totient(72) × (15-13)/2.

Michael Branicky solved first, followed by Noam Elkies, Lazar Ilic, Suproteem Sarkar, Elizabeth Sibert, and Zoz. The other 25 solvers were Dean Ballard, Michael Carlile & Flat, Filbert Cua, Robert Day, Laurent Granger, Peter Haupt, Phil Hu, Jeremy Hurwitz, Charlie Hyde, Teodor Ionita-Radu, Kevin Ke, Winston Luo, Alex Ognev, Robbie Ostrow, Ryan Phua, Matthew Prins, procrastidigitation, Tom Rankin, Ross Rheingans-Yoo, Spaceman Spiff, Sanandan Swaminathan, Ryan Wigley, Renee Wu, and Kenny Zhu; plus over 300 people solved “3, 4, 9, 10” on Instagram.(3)

The Bonus Round

An awesome interactive domino game from Hevesh5! Fat Bear Week; an ode to crosswords; paradox-free time travel; whiskey hunters; and physics majors pwning golf (hat tip for the preceding two: Ellen Kominers). How to fold a bunny (hat tip: Robin Houston); a persistence of memory puzzle (hat tip: Eric Berlin); and the PostCurious puzzle/game roundup. Deep learning making music; a new way to generate primes; lost languages in one of the world’s oldest libraries. And inquiring minds want to know: will computers win the International Mathematical Olympiad one day?

(1) Rheingans-Yoo in fact came up with a solution for each set of numbers that used the numbers in the order we presented them!

(2) For example, 24 = 2 + 15 + (Tribonacci(13) / 72).

(3) Robbie Ostrow came up with a strategy for generating any number from any set of numbers, but we'll be keeping that one secret pending future 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.

©2020 Bloomberg L.P.