Sudoku is a popular logic-based puzzle game that involves filling a 9x9 grid with digits so that each column, each row, and each of the nine 3x3 subgrids (also known as regions) contains all of the digits from 1 to 9 without repetition. The game typically provides a partially filled grid, and the player's objective is to fill in the remaining cells based on logical reasoning and deduction.The problem addressed by the Sudoku solver is to automate the process of solving Sudoku puzzles. This involves developing a software application capable of taking a partially filled Sudoku grid as input and determining the correct digits to fill in the remaining empty cells to satisfy the Sudoku constraints.

You are given the following Sudoku board obtained from sudoku.com. A Sudoku board is a 9 x 9 tablethat some of the cells are partially pre-filled with digits. A Sudoku board can also be partitioned intonine 3x3 boxes (highlighted with bold border). The goal is to fill the remaining blank cells in theSudoku board with new digits such that:• Every row of the Sudoku board contains every digit ranging from 1 to 9.• Every column of the Sudoku board contains every digit ranging from 1 to 9.• Every 3×3 box of the Sudoku board contains every digit ranging from 1 to 9.4 2 1 77 6 5 9 37 3 6 24 9 5 21 7 95 8 2 1 49 1 8 48 4 2 52 4 9 7 3à3 4 5 9 2 6 1 7 87 2 6 8 5 1 9 4 38 9 1 4 7 3 6 5 24 7 9 6 8 5 2 3 11 6 2 7 3 4 8 9 55 3 8 2 1 9 4 6 79 1 3 5 6 8 7 2 46 8 7 3 4 2 5 1 92 5 4 1 9 7 3 8 6Problem SolutionPlease describe verbally how to formulate this problem as states, actions, goal test and path cost (8marks

Determine if a 9 x 9 Sudoku board is valid. Only the filled cells need to be validated according to the following rules:Each row must contain the digits 1-9 without repetition.Each column must contain the digits 1-9 without repetition.Each of the nine 3 x 3 sub-boxes of the grid must contain the digits 1-9 without repetition.Note:A Sudoku board (partially filled) could be valid but is not necessarily solvable.Only the filled cells need to be validated according to the mentioned rules. Example 1:Input: board = [["5","3",".",".","7",".",".",".","."],["6",".",".","1","9","5",".",".","."],[".","9","8",".",".",".",".","6","."],["8",".",".",".","6",".",".",".","3"],["4",".",".","8",".","3",".",".","1"],["7",".",".",".","2",".",".",".","6"],[".","6",".",".",".",".","2","8","."],[".",".",".","4","1","9",".",".","5"],[".",".",".",".","8",".",".","7","9"]]Output: trueExample 2:Input: board = [["8","3",".",".","7",".",".",".","."],["6",".",".","1","9","5",".",".","."],[".","9","8",".",".",".",".","6","."],["8",".",".",".","6",".",".",".","3"],["4",".",".","8",".","3",".",".","1"],["7",".",".",".","2",".",".",".","6"],[".","6",".",".",".",".","2","8","."],[".",".",".","4","1","9",".",".","5"],[".",".",".",".","8",".",".","7","9"]]Output: falseExplanation: Same as Example 1, except with the 5 in the top left corner being modified to 8. Since there are two 8's in the top left 3x3 sub-box, it is invalid. Constraints:board.length == 9board[i].length == 9board[i][j] is a digit 1-9 or '.'.

You are a puzzle designer creating a Sudoku game. In Sudoku, each cell in a 9x9 grid must be filled with a digit from 1 to 9, with the constraint that each digit can only appear once in each row, column, and 3x3 subgrid. Which of the following accurately represents the variables, domains, and constraints in this CSP?a)Variables: Each cell in the 9x9 grid Domains: Digits 1 to 9 Constraints: Each digit must appear once in each row, column, and 3x3 subgridb)Variables: Digits 1 to 9 Domains: Each row, column, and 3x3 subgrid Constraints: Each row, column, and 3x3 subgrid can only have one digitc)Variables: Digits 1 to 9 Domains: Each cell in the 9x9 grid Constraints: Each cell can only have one digitd)Variables: Each row, column, and 3x3 subgrid Domains: Digits 1 to 9 Constraints: Each digit must appear once in each row, column, and 3x3 subgrid

Soduku can be defined as a puzzle in which missing numbers are to be filled into a 9 by 9 grid of squares which are subdivided into 3 by 3 boxes so that every row, every column, and every box contains the numbers 1 through 9. Which one of the following abilities, that humans have, can be detected in the activity of solving a soduku problem? A. process and manipulate symbols B. handle complex situations C. be creative and imaginative D. solve problems when important information is missing

You are given two grids of numbers a𝑎 and b𝑏, with n𝑛 rows and m𝑚 columns. All the values in the grid are 0, 1 or 2 You can perform the following operation on a𝑎 any number of times: • Pick any subrectangle in the grid with length and width ≥2. You are allowed to choose the entire grid as a subrectangle. • The subrectangle has four corners. Take any pair of diagonally opposite corners of the chosen subrectangle and add 1 to their values modulo 3. • For the pair of corners not picked, add 2 to their values modulo 3. Note that the operation only changes the values of the corners of the picked subrectangle. Is it possible to convert the grid a𝑎 into grid b𝑏 by applying the above operation any number of times (possibly zero)?