OO Javascript Sudoku Solver solving the hardest puzzles.

SudokuSolver.js

class SudokuSolver {
  constructor(board) {
    this.board = board;
  }

  solve() {
    const index = this.board.indexOf('0');
    if (index === -1) return this.board;

    for (let possibility = 1; possibility < 10; possibility++) {
      this.board = this.setCharAt(this.board, index, possibility.toString());
      if (this.validBoard(index)) {
        if (this.solve()) return this.board;
      }
    }
    this.board = this.setCharAt(this.board, index, '0');
    return false;
  }

  validBoard(index) {
    return !this.invalidRow(index) &&
      !this.invalidCol(index) &&
      !this.invalidBox(index);
  }

  invalidRow(index) {
    const row = Math.floor(index / 9);
    const start = row * 9;
    const end = start + 9;

    for (let checkIndex = start; checkIndex < end; checkIndex++) {
      if (this.invalidCell(checkIndex, index)) return true;
    }

    return false;
  }

  invalidCol(index) {
    const col = index % 9;

    for (let colStart = 0; colStart < 80; colStart += 9) {
      if (this.invalidCell(colStart + col, index)) return true;
    }

    return false;
  }

  invalidBox(index) {
    const colStart = Math.floor((index % 9) / 3) * 3;
    let rowStart = Math.floor(index / 27) * 27;

    for (let i = 0; i < 3; i++) {
      for (let col = colStart; col < colStart + 3; col++) {
        if (this.invalidCell(col + rowStart, index)) return true;
      }
      rowStart += 9;
    }

    return false;
  }

  invalidCell(checkIndex, index) {
    return index !== checkIndex && this.board[index] === this.board[checkIndex];
  }

  setCharAt(str, index, chr) {
    if (index > str.length - 1) return str;
    return `${str.substr(0, index)}${chr}${str.substr(index + 1)}`;
  }
}

const boards = [
  '000000012000000003002300400001800005060070800000009000008500000900040500470006000',
  '020050700400100006800003000200008003040020500000600010002090000090000005704000900',
  '000000003001005600090040070000009050700000008050402000080020090003500100600000000',
  '120300004350000100004000000005400200600070000000008090003100500000009070000060008',
  '100000002090400050006000700050903000000070000000850040700000600030009080002000001',
  '000000039000001005003050800008090006070002000100400000009080050020000600400700000',
  '120300000400000300003050000004200500000080009060005070001500200000090060000007008',
  '003006080000100200000070004009008060030040001070200000300005000005000600980000050',
  '100000009006700020080000400000075030005002000060300000090000800600040001002500060',
  '009000400070300020800060007100800006000010070000056000300005001040000090002000700',
  '000000000000003085001020000000507000004000100090000000500000073002010000000040009',
  '000090050010000030002300700004500070800000200000006400090010000080060000005400007',
  '400030000000600800000000001000050090080000600070200000000102700503000040900000000',
  '708000300000201000500000000040000026300080000000100090090600004000070500000000000',
  '307040000000000091800000000400000700000160000000250000000000380090000500020600000',
  '000000008003000400090020060000079000000061200060502070008000500010000020405000003',
  '000000010400000000020000000000050407008000300001090000300400200050100000000806000',
  '000000012000035000000600070700000300000400800100000000000120000080000040050000600',
  '100000002090400050006000700050304000000060000000058040002000600030009080700000001',
  '000001020300040500000600007002000001080090030400000800500002000090030400006700000'
];

for(let i = 0; i < boards.length; i++) {
  let solver = new SudokuSolver(boards[i]);
  console.log(solver.solve());
}