In this script, I develop a simple algorithm to solve any sudoku grid in a very fast manner. The algorithm follows four very simple principles:

• Principle 1: A cell has exactly one value.

• Principle 2: A row/column/box contains each value exactly once.

• Principle 3: If there is only one value available to fill a cell, fill the cell with it.

• Principle 4: If a value has only one location available in a row/column/box, write it there.

Despite its simplicity, the algorithm can solve most sudoku grids, even the most sparse ones!

Yet, for difficult grids, the algorithm can get stuck. When the algorithm is stuck, we need to guess the value of a cell. I updated the original algorithm so that, when it is stuck, it guesses the value of a cell and subsequently checks the validity of the obtained grid. This version of the algorithm solves even the most difficult grid after a few iterations.

This shows that, for most sudoku grids, applying these four simple (almost trivial) principles in a systematic way lead to a solution. When these principles are not sufficient, we just have to make one or two guesses. Who knew sudoku was so simple?