lifebeyondfife

You're correct, the horizontal and vertical flips for the square, are already accounted for in the wreath product. And I miscounted the products themselves. Up to 1.2*10^12 symmetries.

The exponential number of symmetries present in sudoku problems, means that once you've found one valid instance, you've actually found up to 9! * 3!^4 * 8 which are exactly the same.

The numbers themselves are all interchangeable, so you have 9! combinations: 362,880.

Columns 1-to-3 are all interchangeable, as are 4-to-6, and 7-to-9. On top of this, these blocks of columns (1-to-3, 4-to-6, 7-to-9) are all interchangeable. Read about wreath products in group theory to know more. Each of the above symmetries are 3!, combined to yield 3! * 3! = 36 combinations. As well as the columns though, the rows have the same property, so those can be combined too: 36 * 36 = 1,296.

Finally, there are the symmetries of a square. Combining all rotations and flips yields a further 8.

In total, sudoku has 3,762,339,840 symmetries. Owing to the starting state of the sudoku puzzle being incomplete, the orbit of the set of points (more group theory) will be smaller than 3 billion, but it provides an efficient method of recreating many more puzzles with the same property. In this case, human complexity.

When I worked at Skyscanner, we'd volunteer at events where high school kids would be shown tech stuff. We'd setup Raspberry Pis with Minecraft on them and show them some basics of running Python scripts to alter the world (with the conclusion being programmatically create loads of dynamite blocks and explode them). Then at the end of the session, give every kid their own Raspberry Pi.

It was interesting reaching the occasional child who assumed this kind of thing wasn't for them.

Only US citizens are permitted to deploy code to the US government production servers, or look at the telemetry from those servers.

(I'm a UK citizen, based in the UK, and I have local colleagues supporting products that are deployed to both commercial .com, and US .gov domains. They deploy to .com themselves, but another team based in the US deploy to .gov)

The pandemic is ongoing, but despite its lasting impacts e.g. hybrid or remote is the norm, many things are back to normal. One thousand days out, how are things for you?