The first time I saw a phone solve Sudoko was an app called Sudoko Grab which uses a artificial neural network. Wha? Given a picture of the puzzle, the app turns it into black and white and finds the grid (computer vision) then overlays the identified numbers over the live video feed (augmented reality).
Then, to solve the puzzle, it uses a toy model of how the brain works (this is the artificial neural network bit). Just a simple one - it only needs to do some maths - but it figures out what numbers should go where so they all obey the rules of the game. A toy model of the brain (the artificial neural network bit) is used to identify the numbers, and the puzzle is solved with yer more regular code. (Thanks Christian N for the correction!)
These's some hard math going on here. Cutting edge technology interests me only so-so when it's in high-end military tech. And then a little bit more when it shows up in games and toys (games and toys are automatically incentivised to pursue new shit, so they're good signals). But it gets super interesting when it's used for trivial things, but it means that it has become a commodity that large numbers of people can deploy, and that everyday platforms are powerful enough to run it. The interesting thing about Sudoku Grab is that the app is about puzzle solving, not showing off the algorithms, and that the iPhone - a regular, everyday device, widely deployed (ahem, in a certain social milieu) - is capable enough to do it. Hard math for trivial things.