Kominers’s Conundrums: A Puzzle That Spins Until It Sparks
(Bloomberg Opinion) -- The second half of our end-of-summer remix is here, and just in time. This week, we’re combining our Conundrums on sequencing and famous face identification.
We’ve put together four sequences (mostly) comprised of faces; your goal is to figure out what comes next in each. But to make things a bit more challenging, we’ve also added two aspects of our pyramid puzzle: Each sequence has a single element that doesn’t belong. Plus, there’s one bizarre-looking sequence that’s made up entirely of chemicals.
It’s up to you to figure out which five boxes in each row are the real start of each sequence. But once you discover the pattern, it should be pretty easy to identify the red herrings – even if it’s hard to name them initially.
If you uncover the next elements in any or all of the sequences – or if you even make partial progress – please let us know at skpuzzles@bloomberg.net before midnight New York time on Wednesday, September 9. Answers don’t have to be submitted as pictures, of course – just stating who or what comes next is sufficient.
If you get stuck, there’ll be a hint announced in Bloomberg Opinion Today on Tuesday, September 8. Sign up here. To be counted in the solver list, please include your full name with your answer.
Previously in Kominers’s Conundrums …
In a mashup of our integer sequence and playlist puzzles, solvers had to identify nine famous sequences, and figure out which number was missing from each. After that, you had to combine those pieces of information by looking at the missing number’s position in the sequence name, yielding a single letter. Missing 3s in the “GOLOMB” sequence, for example, indicated the letter “L.”
But that might not have looked much like an answer until you remembered that the puzzle was a remix, implicitly cluing a relation to music: Lateralus is the name of a Tool song about and crafted around the Fibonacci sequence. (The mathematical rabbit hole on this song goes pretty deep – see the analysis here.) With that recognition, solvers could spot confirmatory clues in the Conundrum text, including Fibonacci references and the instruction to “use any tools at your disposal” (emphasis added).
Lazar Ilic solved first – extending his first-solver streak – followed by Kid Beyond, Noam Elkies, Alan Zhu & Shuli Jones, and Suproteem Sarkar. Others among the 20 solvers included Michael Branicky, Filbert Cua, Jeff Fossett & Evan Finkle, Dianhui Ke, Karl Mahlburg, Stephen O'Hora, Rithvik Rao, Elizabeth Sibert, Skylar Sukapornchai, Liz Wood, and Zoz.
The Bonus Round
Colby’s Curious Cookoff: an at-home, online puzzling smorgasbord. Design lessons from Magic: The Gathering; favorite Lego pieces; colorful manicure puzzles (hat tip: Eric Berlin); and deceptively simple math games (hat tip: Ellen Kominers). Reflections from the leader of a Neopets hacking syndicate; a Star Wars reference in The Legend of Zelda(!?); artificial intelligence can now play Diplomacy. The art of unnatural lighting; exploring 1911 New York (hat tip: Ben Golub). And inquiring minds want to know: How would anyone think of algebra?
What better way to ward off the end-of-summertime blues?
Awful pun, sorry!
The closing line, “If you manage to sort out the answer from among the infinite possibilities […]” was also a hidden reference to one of the song's lyrics.
Thanks also to Adam Rosenfield for consulting on the Conundrum draft!
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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