Combinatorics and Constraint Satisfaction | 10 Minute Read
There are approximately 6.67 sextillion valid 9x9 Sudoku grids. However, most of these are symmetrical rotations or digit swaps of the same fundamental puzzles. The actual number of 'essential' grids is much smaller, but still vast enough that you will never play the same game twice on RatzBrain.
A fascinating mathematical discovery concluded that a Sudoku grid must have at least 17 initial clues ('givens') to have a unique solution. Puzzles with fewer than 17 clues are mathematically guaranteed to have multiple valid solution states, which breaks the logic of the game.