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.
I counted one trillion or 9! * 3!^8 * 2 : the 8 because you have can choose 3 independent permutations of columns inside column blocks + 1 permutation of column blocks, plus same for rows. Then only one rotation should be counted, because flips are included in col/row permutations.
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.
I bought the 52x90 poster where each square is a week of your life. I've filled in significant events. It helps me ensure I keep working on making those events coming.
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.
was this by injecting from the pi to a capable Minecraft server? because exploding loads of TNT on a pi itself would run at a painful framerate, I presume
edit: actually mc renders locally so unless it was running at a really low resolution, I suppose it must have been painful
It mentions running on Wheezy, which from a bit of digging looks like the 2013-2015 version of Raspbian, based on the 3.x kernel. Wheezy is only listed for the 1/1+ and 2. https://minecraft.fandom.com/wiki/Pi_Edition lists it as being slightly stripped down from Alpha 0.6.1 of Pocket Edition.
Also a quote from 2016: "The original team has stopped supporting it and starting with 0.9 MCPE became a lot more ambitious technically, which also means that it became a lot harder to strip down to run on a Raspberry Pi. Actually, we finished removing all Pi related code to reduce complexity in 2015."
If your interest is simply in running MC on a Pi you're probably best off looking into Java Edition, though I have no idea how capable the hardware actually is graphics-wise. If you're more interested in MC on cheap hardware, you're probably better off with a cheap Windows machine and the Microsoft Store/Bedrock edition written in C++ for performance.
I'm not sure how impressed the average kid would be comparing dated, underpowered with current Minecraft
also, I never understood the meme but can it run Minecraft? since the game engine and mods can be pushed as far as you want on latest high-end hardware, and does struggle/gives bad playability on low-end hardware
that said they have made an outstanding effort to at least make the game run on potatoes, even if it looks less glamorous
I think the "can it run" bit is more with Doom, which runs on all sorts of absurd things (arguably including a lamp, but I don't think it counts if you actually have to mod it to add a display).
Minecraft on a Pi is insanely stripped down. So much so, you have to re-code some things with Python if you want to get closer to what actual Minecraft gameplay is like.
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?
I created a CloudFormation script specifically to do this (including CloudFront for CDN). Yes, there's reasonable complexity, but it's a trade-off of security and configuration. As others noted, the documentation is good, and this took me a weekend to write including learning CloudFormation from scratch.
Familiarity with S3, Route53, and CloudFront was a draw for me personally.
AWS is all about abstractions. Some of them are worth learning but increasingly there's a wall of options in AWS and, for me, it's not worth spending time staying on top of all of them. The few services needed for this setup are some of the most popular and will be there in the future.
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.