They are difficult. As I'm not a native English speaker, I didn't know many of the obscure words or usages, so I actually played these games from a purely computational perspective. I discovered early on that there were a lot of at least NPC problems in them. As my English improved (partially thanks to these games), intuitions began to help me take shortcuts, as if I had become a nondeterministic Turing machine.
There is a theory that for a puzzle game to interesting it has to be NP-hard. Something about how otherwise your brain is too good a latching onto the "trick" and the game is boring.
the rubiks cube is in P space, but has a large state space
towers of hanoi is also in P-space, has a trick to latch onto, and is still popular - though maybe this strays from being interesting and is popular for different reasons
I do wordle, strands and, when available (once a week) I do the midi.
Wordle and strands together usually take less than 5m. The midi ranges from 3m30 (my best time) to ~12m (my worst).
Not done Letterbox, Pips and Tiles, but I figured that all their puzzles are at the same level of difficulty.
It's interesting, to me, that (from my reading of the paper, which was very quick) they they consider it hard/easy based on a sort of brute-force attempt to find all the answers.
For clarification, these results mean the problems are difficult when some aspect of the problem size grows (e.g. dictionary size, alphabet size, ...). For example for letter boxed, the size of the square can vary, so can the alphabet size and dictionary of words. See Table 1.
It is not really meaningful to talk about the computational complexity of most problems exactly as they are published in NYT, or they end up trivially in P, since the problem description length is bounded by finite English letters, fixed board size, finite English dictionary etc.
If you enjoy the NYT games but want something new too, check out The Daily Baffle at https://dailybaffle.com. There's a range of word and logic puzzles that NYT lovers should appreciate.
I do Wordle, Pips, Strands, Connections & Sudoku. Of all of them, I find Connections definitely the hardest, even without the occasional US cultural references that I miss.
Just Connections, Wordle, and Mini for me (in that order), with the occasional Crossword (tend towards a barbell strategy of just doing maybe Mon, Tue, Sun to get the quick hits and a real challenging puzzle).
Also experience the odd difficulty due to Americanisms, but can't really fault a puzzle coming from something called the New York Times for that. I do however think the puzzle setting for Connections is inferior to The Wall from Only Connect, where they got the idea from. If you haven't seen that yet it's definitely worth a watch (it gets harder as as a season progresses).
I think the hardest part of connections is that there are intentionally overlaps between most (if not all) of the categories. When my wife and I would do them daily, she would steadfastly refuse to make a single guess until she was fairly confident in the entire solution because in practice it was hard to be sure of the current four for a given category even with high confidence of what the category is. (I agreed with her but in practice have both less patience and more trouble figuring out certain categories, so I would often guess and either take a few misses before figuring it out or sometimes completely fail).
Connections are the only one that can't be solved by either a regexp grep against /usr/share/dict/words or an LLM query. I was actually surprised how poorly LLMs fared against it---I thought they'd be better at associating peripheral connections.
I do World, Strands, Connections, and occasionally pips and the spelling bee. I used to be a big fan of the minis but you have to be logged in to do them now :(
Wordle, Connections, Spelling Bee, and Pips (All modes) for me. Wordle is fun but Pips is very satisfying. Pips medium can sometimes be more difficult than hard one.
I'm honestly a bit surprised that strands has managed to stick around as long as it has in the current form. The way "hints" work especially mystifies me; I don't really get why someone would want an entire word given to them more than maybe once total just from being able to guess completely unrelated words that are in the puzzle.
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[ 4.5 ms ] story [ 35.0 ms ] threadtowers of hanoi is also in P-space, has a trick to latch onto, and is still popular - though maybe this strays from being interesting and is popular for different reasons
Wordle and strands together usually take less than 5m. The midi ranges from 3m30 (my best time) to ~12m (my worst).
Not done Letterbox, Pips and Tiles, but I figured that all their puzzles are at the same level of difficulty.
It's interesting, to me, that (from my reading of the paper, which was very quick) they they consider it hard/easy based on a sort of brute-force attempt to find all the answers.
It is not really meaningful to talk about the computational complexity of most problems exactly as they are published in NYT, or they end up trivially in P, since the problem description length is bounded by finite English letters, fixed board size, finite English dictionary etc.
Statistically, approximately zero people play Letter Boxed and Tiles.
Also experience the odd difficulty due to Americanisms, but can't really fault a puzzle coming from something called the New York Times for that. I do however think the puzzle setting for Connections is inferior to The Wall from Only Connect, where they got the idea from. If you haven't seen that yet it's definitely worth a watch (it gets harder as as a season progresses).
If you like puzzles this will brighten your day.
https://youtu.be/yKf9aUIxdb4