Puzzles vs puzzle analysis

I like solving puzzles. If a crossword puzzle or a Sudoku or a KenKen or a Wordle drifts by, I'll often freeze in my tracks and not leave until I've finished solving it.

My wife and I play "collaborative hard Wordle": we solve the puzzle together, discussing our potential guesses and agreeing on the next one to try, and we play in "hard mode", meaning that each subsequent guess must also obey all of the results of the previous guesses. If a previous guess had a green K in position 2, then all our subsequent guesses must also have a K in position 2; and if a previous guess had a yellow K in position 2, then all our subsequent guesses must have a K, but in some other position.

My dad liked puzzles too, particularly word puzzles such as English-style cryptic crosswords, and he, too, would often become mesmerized by a particular puzzle and not raise his head til he'd solved it.

But he didn't seem so interested in solving a particular Sudoku or KenKen; instead, he was drawn to understanding the underlying combinatorics. His notebooks contained pages and pages of thoughts about notations to describe and analyze a Sudoku.

Of course, there are lots of people who feel this way: Wikipedia's page on Mathematics of Sudoku gives you a great introduction.

And when I play Sudoku, I love to try to improve my play by using multi-step deductive logic techniques such as the strategies covered on SudokuWiki.

Instinctively, I feel like there is a qualitative difference between word puzzles and numeric puzzles. Wordle and cryptics are somehow fundamentally different than Sudoku. And I wonder if my dad felt that way too. At least, he never seemed to show an enormous interest in the mathematics of Wordle. I couldn't even get him interested in the "ask the bot" tool that does some basic probabilistic analysis on the guesses that you made.

He just liked finding the word.

But there are definitely ways to abstractly study the combinatorics of Wordle; for example, here's Playing every game of Wordle simultaneously .

One very important aspect of word puzzles is that they can contain humor and subtlety that are totally missing from, say, Sudoku. For example, many crossword-type puzzles include double entendres and homophones and hidden words and other sorts of word play.

Or consider vowelless crosswords . These plug into your solver's brain along some other sort of dimensional axis, letting you enjoy how it is that you actually recognize a word in the face of things like typos.

I applaud the people who are thinking abstractly about word puzzles, but their analyses don't really seem so interesting to me, and I suspect my dad would have thought so, too.

For now, I'll stick to simply solving a single Wordle, and leave the strategy theory to others.