Kominers’s Conundrums: A Pyramid Scheme to Ponder

(Bloomberg Opinion) -- 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:

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:

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

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

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

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:

Who's Zoomin' Who Love Is a Battlefield More Than a Feeling The 59th Street Bridge Song (Feelin' Groovy) Sloop John B Should I Stay or Should I Go? Ring Them Bells December, 1963 (Oh, What a Night)

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?”