Offtopic: Sudoku and Wordle

Tomorrow is a Cadence "global recharge day" and Monday is Presidents' Day in the U.S. So, as always, on the day before a break, I go off-topic.

One thing that has happened during the pandemic is that people have turned to online games as a way of entertaining themselves without leaving the house. There are only so many Netflix series that you can binge-watch before you want to engage your brain.

Wordle

The latest sensation is Wordle. It was only released last October but has millions of daily users. At the end of January, it was acquired by the New York Times. The price was not announced but the Times did say "the low seven figures". Nice return for what can't be that many lines of code. It was originally invented by software engineer Josh Wardle for his partner. The name of the game is a pun on his last name.

For the uninitiated: A green brick indicates that the letter is correct and in the exact location; a yellow brick indicates that the letter appears in the word but in a different place; and a gray or black brick indicates that the letter does not appear anywhere in the word. These analog brick layouts have been endlessly memed and have driven millions of tweets.

If you are of a mathematical inclination and want to see an analysis of optimal Wordle strategy using information theory, I highly recommend this Two Blue One Brown video:

If you watched that, there is a follow-up video that corrects some minor errors. One important effect is that the optimal first word changed from CRANE to SALET (which seems a bit too fake, but TRACE and CRANE are almost exactly as good).

Wordle is not really that unique. in the 1970s, at least in the UK, there was a game called Mastermind (nothing to do with the TV program of the same name that ran at the time) that did a similar thing using colored plastic pegs and a board.

Also, when I first arrived at Cambridge, the university's Titan and Atlas computers had a game called Moo. You had to guess a 4 digit number by proposing 4 digit numbers. Any number that was correct and in the right place was a bull, although unlike in Wordle you didn't know which digit. Any number that was correct but in the wrong place was a cow. So each guess would be scored and you'd get something like BBC as a score, meaning you had two digits correct and in the right place and one that was correct and in the wrong place. And, since there are 4 digits, one number that was simply wrong. There is even a Wikipedia page Bulls and Cows.

Sudoku

Another popular puzzle that has grown in popularity during lockdown in Sudoku. But not really the kind on the back of the paper, which are boring for two reasons. One, it is always the same set of rules, and two they are computer genererated so there is no clever route to the solve that has to be teased out.

The most popular Sudoku channel is Cracking the Cryptic. It has a weird name because they used to do crosswords and the occasional Sudoku. But as Sudoku has taken off, they now do two Sudoku solves per day (unlike Breakfast Bytes, including weekends), and occasionally throw in a crossword. And if you are interested in crosswords and want to see a solving tour-de-force, each month, Mark attempts (and usually succeeds) to solve the Times monthly puzzle...without a dictionary. Given that most of the words in the grid you will never have seen before, this is insane.

So who are the hosts of the channel?

Hi! We're Simon Anthony and Mark Goodliffe, two of the UK's most enthusiastic puzzle solvers. We have both represented the UK at the World Sudoku Championships and the World Puzzle Championships. We're also "cryptic crossword" aficionados. Mark is the twelve-time winner of The Times championship and Simon is the former record holder for most consecutive correct solutions to The Listener crossword. We hope we can help your puzzle solving while also introducing you to some of the world's best puzzles.

The two of them now run the channel as full-time YouTubers. But at the start of the pandemic, Mark was a CFO and Simon was a merchant banker (although he says he hated it so was glad to get out). There is obviously a whole team of backup people who test the puzzles, maintain the Patreon channel, and so on.

The type of normal Sudoku with no other rules is known as "classic". They do solve those sometimes, but only ones that have been handcrafted to make for an interesting solve.

But there are many variants, some of the common ones (there are lots more) being:

• Knight's Move: Same as classic, except any two cells that are a chess knight's move apart must cannot contain the same digit (there is also a King's Move version)
• Thermo: There are "thermometers" in the grid with a bulb at one end. The digits must increase along the thermometer.
• Arrow: There are circles with arrows leading out of them. The digits on the arrow must sum to the number in the circle.
• Killer: There are boxes in the grid with a small number in the top left. The digits in the box must sum to the total, and digits cannot repeat in the cage even if the normal rules of sudoku would alllow it
• German Whispers: There are lines in the grid. Digits on the line must differ by at least 5 from their neighbors. Some implications: 5 cannot appear on the line, and 4 and 6 can only appear at the ends of a line (because otherwise the digits on either side would have to be the same)
• As I said above, there are lots more
• Combinations: Adding several of these elements to the same puzzle

Many of these are extremely hard to solve (I can't do them!) and even Simon and Mark sometimes take over an hour. Often the biggest challenge is getting started and "breaking into" the puzzle. Often, the only way to get going is to color some of the squares to represent some deduction (like cannot be a 9) to reach a point where you can make the leap to fill in the first digit. Sometimes, the whole grid ends up being ambiguous and colored until the very end. Green and yellow might represent 3 and 6 but you don't know which way around they are until something late in the day allows you to finally decide.

Miracle Sudoku

If you want to watch the most popular video they have made, with 3.5M views. OK, it's not MrBeast level, but not bad for something so specialized. Mark sets up Simon by telling him he is not allowed to open the puzzle until he is recording. When he does, the grid contains just two digits, and Simon is convinced he is being trolled. "This can't possibly have a unique solution...but I can see a digit". It turns out that the additional constraints in the rules are enough for it to solve. Well worth 25 minutes of your time to see a puzzle of sublime genius.

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