Kominers’s Conundrums: Keeping Up With Chameleons

(Bloomberg Opinion) --   With summer officially starting today, chameleons are heading for the beaches.

There are 38 chameleons in total – 19 purple ones, 12 green, and 7 orange. But due to current lizard social distancing guidelines, they can only get together in pairs.

Many meetings transpire without much of note – everyone’s at the beach, easy breezy. But when two chameleons of different colors meet, they both immediately change to the third color. So if, for example, a purple and green chameleon get together, then they both turn orange, as pictured below.

Is it possible that by the end of the summer all of the chameleons will be purple? How about green?

If you manage to work out this chameleon kaleidoscope  -- or even make partial progress -- please let me know at skpuzzles@bloomberg.net before midnight Eastern time on Wednesday, June 24. (If you get stuck, there’ll be a hint announced in Bloomberg Opinion Today on Tuesday, June 23. Sign up here.)

Last Week’s Conundrum

We searched for clues in the past four Conundrums, seeking to bring them “back to the future” for a new puzzle involving a mysterious letter disc.

There was heavy hinting suggesting a “time” theme (“trip through time”; “unwind the answer”; and “note to analog solvers”). And the disc looked quite a bit like a clock face, but with letters instead of numbers.

That might naturally lead us to guess that we have to somehow match times to letters. But which times? Looking closely at the four conundrums I highlighted revealed that each was posted at a different time, none of which was the standard Conundrum release hour. Curiouser and curiouser, those times had hours and minutes associated to eight distinct positions on a clock face.

Mapping those eight positions to the letters on the disc and reading them in order would give the answer.

But there was one last wrinkle, which admittedly we did not expect when we posted the Conundrum: It turns out that Bloomberg automatically updates display times to match readers’ local time zones, so solvers had to convert what they saw to Eastern Time.

We added a note telling readers the column had been “published in New York.” But there was also a subtle clue to the time zone all along: the column ran with an image of a Back to the Future clock tower, showing the time 10:04. The column’s posting time was also calibrated to be 10:04 Eastern, so matching up the posting time and the clock tower revealed the proper time conversion.

Putting everything together yields a series of eight letters that spell out the answer:

• “Crack Caesar’s Favorite Code” -- 7:25 EDT -- TI
• “To Catch a Counterfeiter” -- 8:05 EDT -- ME
• “To Save a Dinner Party”-- 11:10 EDT -- WA
• “Splitting a Record Chocolate Bar” -- 9:00 EDT – RP

That’s right: “TIME WARP.” And with that, astute solvers could also notice one more clue confirming the answer: the closing line of the column. “Let’s do the hidden puzzle again!,” I wrote, in a riff on lyrics of the Transylvanian dance hit “The Time Warp.”

In all, six solved the Conundrum in time. Zoz was first, less than half an hour after the column hit the web; the others were Daniel Chiu, Anna Collins, Kevin Ke, Jason Shaw, and Elizabeth Sibert (who also inspired the puzzle).

The Bonus Round

Father's Day puzzles supporting social justice, following up on a Mother’s Day benefit puzzle bouquet. Plus social distancing puzzles you can solve over zoom; genome puzzles you can solve from your room. Birds working out mystery boxes; bridge every day (hat tip: Amy Wu); order in random surfaces; and Rubiks cubes unscrambled while juggling. Also, inquiring minds want to know: Can we generate power from shadows?

Apologies for unintentionally giving an advantage to Eastern-Time solvers – we only learned of the conversion issue after we had posted the Conundrum.

That said, Back to the Future superfans will notice we took one liberty, posting the column at 10:04 AM even though in the movie the crucial time is 10:04 PM.

Jason Shaw also pointed out an accidental miracle: if you decode the times in CDT rather than EDT, you obtain letters that anagram to “TIME SOAP,” which is astoundingly close to the correct answer.(Not to be confused with the "time loop," which is totally different, but equally hilarious.)

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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