Mathematics of Sudoku

Sudoku, a number-placement puzzle, is a logic-based game consisting of 9x9 grids with 3x3 sub-grids. The objective of the game is to fill up all the grids so that each column and row, and each of the nine 3x3 sub-grids contain all the digits between 1 and 9. Thus there should not be repeated digits in each 3x3 sub-grids or each column and row.

An example of a completed Sudoku puzzle:

There would be empty grids in some of the grids in each puzzle given. The solver would then have to fill up the grids.

Try solving this: