Solve Sudoku puzzles in O(N²) time

JavaScript Sudoku Solver.js

function sudoku(puzzle) {
    while (!isSolved(puzzle)) {
        for (x = 0; x < 9; x++) {
            for (y = 0; y < 9; y++) {
                puzzle[y][x] = digit(puzzle, x, y);
            }
        }
    }

    return puzzle;
}

function digit(puzzle, x, y) {
    if (puzzle[y][x] !== 0) return puzzle[y][x];

    var row = puzzle[y];
    var column = columnArray(puzzle, x);
    var grid = gridArray(puzzle, x, y);
    
    var knowns = row.concat(column, grid);
    
    var possibilities = [1, 2, 3, 4, 5, 6, 7, 8, 9].filter(function(item) { return knowns.indexOf(item) === -1; });

    return possibilities.length == 1 ? possibilities[0] : 0;
}

function columnArray(puzzle, idx) {
    return puzzle.map(function(row) { return row[idx]; });
}

function gridArray(puzzle, x, y) {
    x = Math.floor(x / 3) * 3;
    y = Math.floor(y / 3) * 3;
    
    var arr = [];
    
    for (i = x; i < x + 3; i++) {
        for (j = y; j < y + 3; j++) {
            arr.push(puzzle[j][i]);
        }
    }
    
    return arr;
}

function sum(arr) {
    return arr.reduce(function(a, n) { return a + n; }, 0);
}

function winningRow(arr) {
    return sum(arr.map(function(num) { return Math.pow(2, num - 1); })) == 511;
}

function isSolved(puzzle) {
    return puzzle.filter(function (row) { return !winningRow(row); }).length === 0;
}

Intriguing.

Why did you use condition like sum(arr.map(function(num) { return Math.pow(2, num - 1); }))? So why this sum should be 511?

Why did you use condition like sum(arr.map(function(num) { return Math.pow(2, num - 1); }))? So why this sum should be 511?

Because [1, 2, 3, 4, 5, 6, 7, 8, 9].reduce((memo, i) => { memo += Math.pow(2, i - 1); return memo })