How Combinatorics Is Useful in Sudoku?
Here is a detailed examination on How Combinatorics Is Useful in Sudoku.
While solving the sudoku puzzle you can only use each number one time in the square, column, and row. Columns and rows are not limited by the thicker boundaries of the square (also sometimes called a region.) They run from the top of the puzzle to the bottom of the puzzle (as pictured in blue above). The same is true of rows.
What makes a Sudoku different from a normal Sudoku?
Ordinary Sudokus (proper puzzles) have a unique solution. A minimal Sudoku is a Sudoku from which no clue can be removed leaving it a proper Sudoku. Different minimal Sudokus can have a different number of clues.