Sudoku

Sudoku is a well$-$known puzzle in which given a matrix of size $99$ with certain cells filled by

numbers, the goal is to fill the matrix such that each column, row, and $33$ submatrix contains

numbers $1$ through $9$ exactly once.

Problem $2.(40$ points$)$ Mathematically formulate general Sudoku puzzle for $99$ matrix. Also,

consider an example of your choice of Sudoku puzzle over $44$ matrix, and rewrite your

formulations for this example. $[$Note that this formulation can have integer$/$binary variables.$]$