Learning from Sudoku Solvers (2007)

Trying to represent sudoku as an integer program leads to a natural way to represent the board: a 9x9x9 boolean grid where x and y are the board dimensions and z is the number in each square.

You end up with three symmetric constraints + the box constraint:

- The sum along any x, y, or z row is 1 (one of each number per row, one of each number per column, and one number per square)

- The sum of each 3x3x1 box slice is 1 (one of each number per box)

I really like the symmetry between the row sum constraints here. And it does pretty neatly align with the way many people solve Sudoku by writing little numbers in the squares to represent possible values before pruning impossible ones.

https://news.ycombinator.com/item?id=44220245 on the same topic was posted four months ago and has more substance than this short 2007 post.

There are plenty of posts out there on using Knuth’s dancing links as a fast sudoku solver. Has it fallen out of fashion?