Kominers’s Conundrums: Sizing Up a Stuntman’s Traffic Mess
(Bloomberg Opinion) -- Even during a pandemic, getting out of New York can be a traffic nightmare. This week, we'll be looking at a particularly bad scenario involving a lot of vacationers and one risk-loving motorcyclist:
There’s two hours’ worth of cars backed up while waiting cross the Verrazzano-Narrows Bridge on the way to the Jersey Shore from Brooklyn.
Then suddenly daredevil Evel Knievel rides up and jumps over all of them to cut in front. What’s the total delay he causes, added up across all the cars in line?
And if you’re feeling creative: What’s the right penalty for Knievel when the traffic cops catch up with him? (PG answers only, please!)
I learned this classic brainteaser from my friend and collaborator Alex Tabarrok. One of the things I love about it is that the puzzle comes with so little structure that it’s hard to believe that it has a solution at all. You don’t know how many cars are in line, for example, or whether they all move at the same speed.
But it turns out that you can still figure out the answer – and it doesn’t even require jumping through too many hoops!
You can assume that there’s no more theatrics once Knievel makes it to the front -- flashy motorcycle notwithstanding, he drives across the bridge just like a regular car. Also, there’s no rubbernecking: New Yorkers are so used to seeing wild things happen on the road that daredevils don’t have much impact on drivers' road speed other than extending the backup.
And that’s all you need. Do you dare to give it a try?
If you solve this stumper -- or even make partial progress -- please let me know at skpuzzles@bloomberg.net before midnight Brooklyn time on Wednesday, July 29. (If you get stuck, there’ll be a hint announced in Bloomberg Opinion Today on Tuesday, July 27. Sign up here.)
Last Week’s Conundrum
We sought to deconstruct six word pyramids to learn their secrets. Each one had five words that fit a pattern, and one that didn’t belong. Those odd-words-out could then be used to construct a seventh “meta” pyramid; the goal was to identify that pyramid’s misfit word.
As I hinted, the pattern in the first pyramid was relatively straightforward: All of the words except “COD” were palindromes -- i.e., they read the same way forward and backward:
The second pyramid was full of strange-sounding words like “MOUSER” and “BUGABOOM,” some of which (“ROY”; “IGGY”; “HARRIET”) looked likely to be names. In fact, all of them were names -- of Nintendo video game characters, that is. Five were villains (“bosses,” in game-speak) from different editions of the Super Mario franchise. The odd one out, NAYRU, was a goddess from the Legend of Zelda, with no role in Super Mario that I’m aware of -- hence the minor in-text clue that these words were “super unfamiliar.”
The third pyramid was full of chemical elements, and I hinted that solvers needed “divide one out from the others.” The trick was to look at atomic numbers: Boron’s is 5, which divides the atomic number of every element in the pyramid except “URANIUM.”
The next pyramid sounded a bit like late night at the Comedy Cellar: “MOP,” “SCHLOCK,” and plenty of “SCHMALTZ.” Lots of potential relationships between the words seemed possible. “ODOR,” for example, is a synonym of “STINK.” But this one wasn’t about the meanings of the words at all. Rather, as the “sound” clue in the text hinted, you needed to look at syllables: “ODOR” has two; each other word in the pyramid had only one.
The fifth pyramid featured words with repeated letters: “ZOO,” ”FREE,” “ROOTS,” and so forth. In all but one of the words, those repeated letters were vowels; “NESTEGGS” was the odd-word-out, with “GG.”
And the sixth may have been the hardest of all. At first glance, the words looked totally unrelated -- but at the same time there weren’t any letter similarities or wordplay clues in sight. The trick was that each word but one had a secondary meaning that’s a name for a group of animals: a “POD” of dolphins, a “RAFT” of otters, a “SLOTH” of bears, a “PRICKLE” of porcupines, and a “CAULDRON” of bats. The one word that didn’t fit the pattern was “VOYAGE.”
Once you'd solved the six different pyramids, you could put their answers together into the seventh:
But what to do with that? At first glance, it looked even more bizarre than the first six combined. What you needed to do was take a “meta” perspective and look across the words instead of thinking about them individually.
Reading down the first and last letters, all the words except one together spelled out “CONUNDRUMS,” making “VOYAGE” the odd word out -- and the answer to the full Conundrum.
And like the pyramids of Giza, this Conundrum left some mysteries for us to keep puzzling over: Michael Branicky observed that if you take “HARRIET” and “BORON” to be the answers to the second and third pyramids, then you get a different seventh pyramid for which “VOYAGE” is still the right answer – the other five words all contain a US state abbreviation as a substring:
Tamar Oostrom, meanwhile noticed an accidental layout miracle: if you left-align the meta-pyramid, then all but one of the words ("NESTEGGS") actually show up a second time as criss-crosses of the others. “URANIUM,” for example, crosses “NAYRU” and “VOYAGE:”
I have no idea how to estimate the precise probability of this happening, but it is definitely very low.
So were aliens involved? It’s possible.
The Bonus Round
Solve a world-class physicist’s “Puzzles to Unravel the Universe”; then test your geometric precision (hat tip: Nick Jaeger) and your pinball wizardry. Bear fixes traffic cone; bird counts to food; “American Hedgehog Warrior” (hat tip: Âriel de Fauconberg). Ritter Sport won the battle over square chocolate (although of course we did that first here at Conundrums). Plus inquiring minds want to know: What's the sound of a graviton?
As Michael Branicky and Spencer Kassimir pointed out, there was a minor spelling error: “HARRIET” from Super Mario Odyssey should have been spelled “HARIET.” We didn't correct this in the posted edition because it would have necessitated a major change – the two spellings have different numbers of letters – and it didn't seem to be confusing solvers.
Not to be confused with sloth bears.
See also this video of a porcupine eating corn on the cob.
And indeed, you didn't actually have to solve all six – in order for the answers to fit into a pyramid, they all had to be different lengths. That meant that once you had solved five correctly, the answer to the sixth could be identified just from its letter count.
Thanks also to Zoe DeStories and Adam Rosenfield, who test-solved part of the puzzle in advance.
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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