New York Times, Tuesday, September 10, 2024

The theme in this puzzle really blew my mind.

TL;DR version:

• ~275,000 terms in my dictionary (Jeff's XWordInfo Dictionary)
• ~3.5 quadrillion possible sets of three terms (~275,000 choose 3)
• 19 sets obeying the constraint (every consonant, one time)
• 4 sets that could be laid out symmetrically

Longer version:

Themes are often found by whittling a large set of terms (say 200-300k) down to a smaller subset using some constraint. Loose constraints may allow hundreds of theme entry possibilities, whereas tight constraints may allow only 10 or so. The constraint in this puzzle was about as tight as I've ever seen them come.

For starters, my pool of candidates wasn't the 275k terms in my dictionary, but rather all possible sets of three terms that could be made from this dictionary. So instead of checking 275k terms, I needed to sift through ~3.5 quadrillion sets (275,000 choose 3). How? Python, hash tables, tricks, 3 minutes of data crunching... and voila! With a pool of ~3.5 quadrillion candidate sets, you'd think either no solution set exists, or conversely, many exist... Nope. I was stunned to find only 19 sets that satisfied the constraint, and of these, only four that could be laid out symmetrically with the revealer.

That's four tiny needles in one giant haystack (or maybe… a Sour Patch Kids stack?)

Bonus Puzzle Set:

This set didn't make the cut for symmetry reasons:

EXSQUEEZEME + THEJOYOFCOOKING + ?

Happy puzzling!

Hint: On-site worker?

Answer (Backwards): REPOLEVEDBEW

"Find three entries from a word list that, between them, include every consonant exactly once." That's an interesting software challenge. If I were still conducting interviews at Microsoft, I'd use it as a whiteboard design problem.

Of course, I had to try myself, looking for sets of three such entries from Jeff's list, counting Y as a vowel. (Daniel Bodily counted it as a consonant.) Most results include weird words like pyrzqxgl or six-pack bezique, but here are a few I found:

• fax equipment • glazed over • whack jobs
• flapjack • TV quiz show • mixing board
• have a good trip • Wolfman Jack • squeeze box
• privatized • qualifying exam • whack jobs

Because I loved I Claudius and I got to see the star in person in a play at the Barbican, I also like:

• exemplifying • TV quiz show • Derek Jacobi.

As you can see, TV quiz show and whack jobs are nearly as useful as six-pack bezique. (That's a sentence that has never before been written in the history of the English language.)