Kominers’s Conundrums: A Pyramid Scheme to Ponder

When solving puzzles, we often play the role of a detective. We start with a sequence of clues, and examine them closely to try to fill in what’s missing. That was the trick to last week’s playlist puzzle (see below) and the explicit goal of our numerical sequence and “missing dinner guest” puzzles several weeks ago.

This week, the goal is the opposite: We’re looking for patterns that can tell us what doesn’t belong.

I’ve created six pyramids of six words each. In each one, five of the words share a pattern; the sixth doesn’t fit. Your goal is to find these “odd-words-out” and assemble them into a seventh pyramid.

That last pyramid is what’s called a “metapuzzle” – a puzzle of puzzles, if you will. Like the others, it contains one word that doesn’t match the pattern of the other five. That last meta-misfit word is this week’s answer.

The patterns in these pyramids can take many different forms. To begin with, here’s one that is clearly related to the words’ letters, rather than their meanings:

Kominers’s Conundrums: A Pyramid Scheme to Ponder

Bizarre words like “SNELLENS” tend to be particularly revealing. They probably wouldn’t appear unless they were among the few words of the right length that match whatever the pattern is.

Of course, looking for unusual words doesn’t help much when all the words are super unfamiliar, as in our second pyramid:

Kominers’s Conundrums: A Pyramid Scheme to Ponder

Other times, all six words share a clear relationship. But that can make it hard to divide one out from the others:

Kominers’s Conundrums: A Pyramid Scheme to Ponder

Similarly, the words might sound vaguely related. Then you have to think carefully to find the one that doesn’t belong:

Kominers’s Conundrums: A Pyramid Scheme to Ponder

And other times, the pyramids might seem impossibly dense. Give these last two a try without any further commentary:

Kominers’s Conundrums: A Pyramid Scheme to Ponder
Kominers’s Conundrums: A Pyramid Scheme to Ponder

Once you’ve found all the words, don’t forget to assemble them into our “meta-pyramid,” and solve once more.

If you figure out which word doesn’t fit the meta  or if you even make partial progress  please let me know at skpuzzles@bloomberg.net before midnight New York time on Wednesday, July 22. (If you get stuck, there’ll be a hint announced in Bloomberg Opinion Today on Tuesday, July 21. Sign up here.)

Last Week’s Conundrum

I invited readers to tune into the Conundrums summer playlist. But unfortunately, each song title was missing a word. Once you filled those words in, they spelled out a simple clue phrase:

Of course, “WHO IS MORE GROOVY JOHN OR RING OH” doesn’t quite make sense until you read it aloud – hence the “listen closely!” clue in the Conundrum text. When you do so, you realize it’s asking for your take on one of the great debates of Beatlemania: “Who is more groovy, John or Ringo?”

Kominers’s Conundrums: A Pyramid Scheme to Ponder

The puzzle’s solution, then, was whichever Beatle you prefer.  

Taylor Vonk & Brendan Yang solved first, followed minutes later by Anna Collins, Zoz, and my mother, Ellen Kominers. Others among the 37 solvers included M. Scott Anderson, Andrew James Betts, Filbert Cua, Tony Free, Carney Hawks, Duncan Heidkamp, Ernie Hou, Ridge Montes, Stephen Ohora, Jay Oken, Jane Redicker, Max Sabor & Georgia Shelton, Jennifer Walsh, Liz Wood, and Michael Yin.

And what about the debate? Even though Ringo had “more period-appropriate facial hair” (thanks, Zoz!), John carried the vote, two-to-one. Brad Warkins was the only one to submit the answer “George Harrison.” As for me, I’m with my mom and several other solvers who voted the obvious choice: “Paul.”

The Bonus Round

Play literary puzzles by mail (hat tip: Ellen Kominers); or explore inner dimensions with paper and coasters (hat tip: Matt Dickstein). Selfie masks that look like your face (hat tip: Chris Peterson); the rest of the world finally notices “real or cake.” Random mazes; mesmerizing kinetic sculptures (hat tip: Elizabeth Sibert); Lego Super Mario (coming soon). The Where in the World is Carmen Sandiego cast reunion is this Friday. And inquiring minds want to know: What does social distancing have to do with number theory?

People who just sent in the clue phrase received a version of the reply, "Great question! What's your answer?”

Conundrums -- always at the cutting edge of pop-culture trends -- featured this delicious meme in our very first bonus round!

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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