New York Times, Wednesday, May 5, 2021

We've been friends through high school and college, and over the years we've bonded over math, crosswords, computer science, and puzzlehunts. We're excited to be making our New York Times debut!

When thinking of a theme, our inner math nerd shone through, and we wondered if we could use clue numbers in an unconventional way. After a few iterations, we came up with what seemed like a crazy idea involving famous mathematical sequences. While we were excited about the concept, we had no idea if there was a grid that worked, and it's practically impossible to find one by hand.

In the end, we had to write a comically complicated program that generated feasible grids, and then checked a few hundred candidates manually until we found the grid you see in today's puzzle (you can read more on this blog post). It isn't perfect—it's heavy on three-letter words and has a few cheater squares—but we were happy with the outcome. We also considered sequences like CUBE, POWEROFTWO, PERFECT, and COMPOSITE but none of them ended up in the final puzzle.

Filling out the grid was a real challenge, because we couldn't add or remove black squares without breaking our theme. That being said, we were pretty happy with the diversity and quality of our resulting fill given these constraints.

It took me a while to fully grasp this concept, but once I did, the technician in me was so curious to drill down and see how this was EVEN possible. Look at FIBONACCI, for example. It's not referring to only its clue number, 34. The A square is numbered 55 (which is part of that answer) is also a FIBONACCI number!

Each of PRIME (2 23), SQUARE (9 25), FIBONACCI (34 55), ODD (39 43), EVEN (44 48) worked with exactly two examples. I appreciate the consistency.

The solver in me found it more a curiosity than an a-ha, but it is a novel concept.

Themes based around numbers are challenging to work with since any change in black square layout cascades through the entire puzzle. There was a lot of flexibility for where each of the five answers (plus NUMBER) went, but it's still an impressive feat. Imagine the nightmare: start with FIBONACCI, get the numbers correct. Place SQUARE, get those tuned in — aargh, that messed up FIBONACCI's numbers! Rinse and repeat (to infinity and beyond).

I had a difficult time finishing, the NAVI / IMGUR crossing feeling near impossible. I'm sure all the kids are rolling their eyes (and praying that us geezers don't get on IMGUR, or they'll have to move onto the next thing). Even though I'm an alpha nerd and have seen the MCU movies many times, I couldn't pull SHURI out, and the crossings felt tough. Is it more or less esoteric than DORA MILAJE? The fact that I'd be able to drop that in without any crossings shows how subjective this all is.

I wish the theme clues had better expressed the concept, but I'm not sure of exact wording. Circling the relevant numbers, and saying [Like the two numbers circled within this grid entry]? Removing NUMBERS from the grid would have made things less confusing by eliminating a cross-reference, too.

Still, the constructor in me admired the novelty and level of technical difficulty, even if my solver side didn't experience as big an a-ha moment as I'd have liked.