This blog from is really interesting.

It demonstrates how to build a Miracle Sudoku solver using Prolog, which is a logic programming language written in a declarative syntax. It’s incredible how concisely a solver for Sudoku puzzles can be written in that language!

What’s remarkable about these solvers is how they can tell you interesting facts about puzzles such as the Miracle Sudoku:

  • The minimal number of hints necessary to uniquely define a solution board is 2.
  • Boards with just 1 placed hint have 8 solutions, always – no matter which digit the hint is or where it’s placed.
  • There are many, many valid 2-digit hints. For example, there are 2320 ways to place a 1 and a 2 on the board which lead to a unique solution. Since there are only 72 unique solution boards, you’d run out of interesting solutions before you ran out of hints.