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Kominers’s Conundrums: A Fly Walks Into a Debate

Scott Duke Kominers
·5 mins read

(Bloomberg Opinion) -- This week’s Conundrum -- a version of a classic brainteaser that I pulled together with the help of game theorist Shengwu Li -- concerns a strange occurrence at a vice presidential debate. Any resemblance to actual people or events is purely coincidental.

Imagine, if you will, a vice presidential debate where the candidates are so intensely focused on the issues that they don’t notice when a fly lands on one of their heads.

Faced with an awkward distraction and unsure of how to proceed, the moderator makes a snap decision, blurting out, “There’s a fly on your head!!” It’s not clear, however, whom the moderator is addressing.

The candidates, of course, are mortified -- just shy of the kind of deep embarrassment that makes for viral video clips and GIFs. If either of them becomes certain that the fly is on his or her head, then that candidate will blush deep crimson.

But the candidates are still focused on the debate, and so they only get to glance at each other once per debating round. Do either or both of them blush in the end? And if so, after how many rounds?

And there’s one more follow-up question for our most dedicated solvers:

Would the answer be different if each candidate would try to bluff through the whole thing, and only blush if they become sure not only that they have a fly on their head, but also that everyone else in the room is certain they know they have a fly on their head? (Otherwise they have plausible de-fly-ability!)

If you knock this fly out of the park -- or if you even make partial progress -- please let us know at skpuzzles@bloomberg.net before midnight New York time on Thursday, October 15. If it’s useful to refer to the candidates by names in your solution, feel free to use random-sounding ones like “Parris” and “Hence.”

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.

Programming note: Next week, Conundrums will run on Sunday, October 18. 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 …

In our cartoonish acrostic, readers had to identify cartoon characters from the rather poor social media profile descriptions Donald wrote for them. We didn’t actually say where the characters were from, but heavy cluing suggested Disney. First, the column told a story about “Walt” having assigned “Donald” the task. Plus there were a number of oblique references and links to Disney songs in the text.

And indeed, each of the 15 profiles referred to a unique Disney character, from many different cartoon eras:

Caped hero known for “getting dangerous” -- DARKWING DUCK Definitely not a llama -- KUZCO Eats eggs and decorates with antlers -- GASTON Forgetful fish; found Nemo -- DORY Kid Hamlet -- SIMBA Klepto monkey -- ABU Little guy with top hat who recorded company theme song -- JIMINY CRICKET Loves pie, but should stay away from apples -- SNOW WHITE Necessity bear -- BALOO Scrooge’s pilot -- LAUNCHPAD MCQUACK Smiley feline who appears to be purple -- CHESHIRE CAT Space-age pretty boy; falls with style -- BUZZ LIGHTYEAR Speechless to set foot on land -- ARIEL The green caballero -- JOSÉ CARIOCA Toymaker with lifelike work -- GEPPETTO

After identifying the characters’ names, the next challenge was to fit them into the grid we provided. Most of them could only go in one place, but figuring out the right locations for a few of them required some careful unscrambling.

With the names in their proper places, the yellow column in the middle spelled out “How Walt characterized the whole operation:” A MICKEY MOUSE JOB -- meaning both “a fiasco” and a task he should have assigned to Mickey instead of Donald.

Zoz solved first -- just 12 minutes after the Conundrum hit the web -- followed by Michael Branicky, Lazar Ilic, Elizabeth Sibert, Anna Collins, Eric Berlin, and John Owens. The other 26 solvers were Xiao Chen, Filbert Cua, Hannah Dickey & William Herbst, Matt Dickstein, Martha Elias, Ginevra Ghezzi, Laurent Granger, Marissa R. Harrell, Phil Hu, Paul Kominers, Sam Lazarus & Patty Smith, Kristen Listor, Winston Luo, Jeannie McKinney, France Pinzon, Ross Rheingans-Yoo, Adam & Erin Rosenzweig, Suproteem Sarkar (who submitted an all-emoji solution), Simone Sellette, Jenna Shrove, Catherine Sibert, Spaceman Spiff, Karen Staebler, Nancy & Murray Stern, Skylar Sukapornchai and Sanandan Swaminathan.(1)

The Bonus Round

Global Math Week, happening now (hat tip: Ellen Kominers); help NASA find alien worlds. The best virtual tours of national parks and zoos. Comparing starship sizes; new traveling salesperson records (but you’ve got to know the territory!); an infinite tile pattern that never repeats; and paintings of animals their artists had never seen. Jabberwocky animated; Jabbawockeez dancing. Plus inquiring minds want to know: Why do mirrors only flip things horizontally?

(1) Thanks also to Jennifer Walsh for advising on the puzzle!

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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