solve.js

 
 var games = [
"4.....8.5.3..........7......2.....6.....8.4......1.......6.3.7.5..2.....1.4......",
"52...6.........7.13...........4..8..6......5...........418.........3..2...87.....",
"6.....8.3.4.7.................5.4.7.3..2.....1.6.......2.....5.....8.6......1....",
"48.3............71.2.......7.5....6....2..8.............1.76...3.....4......5....",
"....14....3....2...7..........9...3.6.1.............8.2.....1.4....5.6.....7.8...",
"......52..8.4......3...9...5.1...6..2..7........3.....6...1..........7.4.......3.",
"6.2.5.........3.4..........43...8....1....2........7..5..27...........81...6.....",
".524.........7.1..............8.2...3.....6...9.5.....1.6.3...........897........",
"6.2.5.........4.3..........43...8....1....2........7..5..27...........81...6.....",
".923.........8.1...........1.7.4...........658.........6.5.2...4.....7.....9.....",
"6..3.2....5.....1..........7.26............543.........8.15........4.2........7..",
".6.5.1.9.1...9..539....7....4.8...7.......5.8.817.5.3.....5.2............76..8...",
"..5...987.4..5...1..7......2...48....9.1.....6..2.....3..6..2.......9.7.......5..",
"3.6.7...........518.........1.4.5...7.....6.....2......2.....4.....8.3.....5.....",
"1.....3.8.7.4..............2.3.1...........958.........5.6...7.....8.2...4.......",
"6..3.2....4.....1..........7.26............543.........8.15........4.2........7..",
"....3..9....2....1.5.9..............1.2.8.4.6.8.5...2..75......4.1..6..3.....4.6.",
"45.....3....8.1....9...........5..9.2..7.....8.........1..4..........7.2...6..8..",
".237....68...6.59.9.....7......4.97.3.7.96..2.........5..47.........2....8.......",
"..84...3....3.....9....157479...8........7..514.....2...9.6...2.5....4......9..56",
".98.1....2......6.............3.2.5..84.........6.........4.8.93..5...........1..",
"..247..58..............1.4.....2...9528.9.4....9...1.........3.3....75..685..2...",
"4.....8.5.3..........7......2.....6.....5.4......1.......6.3.7.5..2.....1.9......",
".2.3......63.....58.......15....9.3....7........1....8.879..26......6.7...6..7..4",
"1.....7.9.4...72..8.........7..1..6.3.......5.6..4..2.........8..53...7.7.2....46",
"4.....3.....8.2......7........1...8734.......6........5...6........1.4...82......",
".......71.2.8........4.3...7...6..5....2..3..9........6...7.....8....4......5....",
"6..3.2....4.....8..........7.26............543.........8.15........8.2........7..",
".47.8...1............6..7..6....357......5....1..6....28..4.....9.1...4.....2.69.",
"......8.17..2........5.6......7...5..1....3...8.......5......2..4..8....6...3....",
"38.6.......9.......2..3.51......5....3..1..6....4......17.5..8.......9.......7.32",
"...5...........5.697.....2...48.2...25.1...3..8..3.........4.7..13.5..9..2...31..",
".2.......3.5.62..9.68...3...5..........64.8.2..47..9....3.....1.....6...17.43....",
".8..4....3......1........2...5...4.69..1..8..2...........3.9....6....5.....2.....",
"..8.9.1...6.5...2......6....3.1.7.5.........9..4...3...5....2...7...3.8.2..7....4",
"4.....5.8.3..........7......2.....6.....5.8......1.......6.3.7.5..2.....1.8......",
"1.....3.8.6.4..............2.3.1...........958.........5.6...7.....8.2...4.......",
"1....6.8..64..........4...7....9.6...7.4..5..5...7.1...5....32.3....8...4........",
"249.6...3.3....2..8.......5.....6......2......1..4.82..9.5..7....4.....1.7...3...",
"...8....9.873...4.6..7.......85..97...........43..75.......3....3...145.4....2..1",
"...5.1....9....8...6.......4.1..........7..9........3.8.....1.5...2..4.....36....",
"......8.16..2........7.5......6...2..1....3...8.......2......7..3..8....5...4....",
".476...5.8.3.....2.....9......8.5..6...1.....6.24......78...51...6....4..9...4..7",
".....7.95.....1...86..2.....2..73..85......6...3..49..3.5...41724................",
".4.5.....8...9..3..76.2.....146..........9..7.....36....1..4.5..6......3..71..2..",
".834.........7..5...........4.1.8..........27...3.....2.6.5....5.....8........1..",
"..9.....3.....9...7.....5.6..65..4.....3......28......3..75.6..6...........12.3.8",
".26.39......6....19.....7.......4..9.5....2....85.....3..2..9..4....762.........4",
"2.3.8....8..7...........1...6.5.7...4......3....1............82.5....6...1.......",
"6..3.2....1.....5..........7.26............843.........8.15........8.2........7..",
"1.....9...64..1.7..7..4.......3.....3.89..5....7....2.....6.7.9.....4.1....129.3.",
".........9......84.623...5....6...453...1...6...9...7....1.....4.5..2....3.8....9",
".2....5938..5..46.94..6...8..2.3.....6..8.73.7..2.........4.38..7....6..........5",
"9.4..5...25.6..1..31......8.7...9...4..26......147....7.......2...3..8.6.4.....9.",
"...52.....9...3..4......7...1.....4..8..453..6...1...87.2........8....32.4..8..1.",
"53..2.9...24.3..5...9..........1.827...7.........981.............64....91.2.5.43.",
"1....786...7..8.1.8..2....9........24...1......9..5...6.8..........5.9.......93.4",
"....5...11......7..6.....8......4.....9.1.3.....596.2..8..62..7..7......3.5.7.2..",
".47.2....8....1....3....9.2.....5...6..81..5.....4.....7....3.4...9...1.4..27.8..",
"......94.....9...53....5.7..8.4..1..463...........7.8.8..7.....7......28.5.26....",
".2......6....41.....78....1......7....37.....6..412....1..74..5..8.5..7......39..",
"1.....3.8.6.4..............2.3.1...........758.........7.5...6.....8.2...4.......",
"2....1.9..1..3.7..9..8...2.......85..6.4.........7...3.2.3...6....5.....1.9...2.5",
"..7..8.....6.2.3...3......9.1..5..6.....1.....7.9....2........4.83..4...26....51.",
"...36....85.......9.4..8........68.........17..9..45...1.5...6.4....9..2.....3...",
"34.6.......7.......2..8.57......5....7..1..2....4......36.2..1.......9.......7.82",
"......4.18..2........6.7......8...6..4....3...1.......6......2..5..1....7...3....",
".4..5..67...1...4....2.....1..8..3........2...6...........4..5.3.....8..2........",
".......4...2..4..1.7..5..9...3..7....4..6....6..1..8...2....1..85.9...6.....8...3",
"8..7....4.5....6............3.97...8....43..5....2.9....6......2...6...7.71..83.2",
".8...4.5....7..3............1..85...6.....2......4....3.26............417........",
"....7..8...6...5...2...3.61.1...7..2..8..534.2..9.......2......58...6.3.4...1....",
"......8.16..2........7.5......6...2..1....3...8.......2......7..4..8....5...3....",
".2..........6....3.74.8.........3..2.8..4..1.6..5.........1.78.5....9..........4.",
".52..68.......7.2.......6....48..9..2..41......1.....8..61..38.....9...63..6..1.9",
"....1.78.5....9..........4..2..........6....3.74.8.........3..2.8..4..1.6..5.....",
"1.......3.6.3..7...7...5..121.7...9...7........8.1..2....8.64....9.2..6....4.....",
"4...7.1....19.46.5.....1......7....2..2.3....847..6....14...8.6.2....3..6...9....",
"......8.17..2........5.6......7...5..1....3...8.......5......2..3..8....6...4....",
"963......1....8......2.5....4.8......1....7......3..257......3...9.2.4.7......9..",
"15.3......7..4.2....4.72.....8.........9..1.8.1..8.79......38...........6....7423",
"..........5724...98....947...9..3...5..9..12...3.1.9...6....25....56.....7......6",
"....75....1..2.....4...3...5.....3.2...8...1.......6.....1..48.2........7........",
"6.....7.3.4.8.................5.4.8.7..2.....1.3.......2.....5.....7.9......1....",
"....6...4..6.3....1..4..5.77.....8.5...8.....6.8....9...2.9....4....32....97..1..",
".32.....58..3.....9.428...1...4...39...6...5.....1.....2...67.8.....4....95....6.",
"...5.3.......6.7..5.8....1636..2.......4.1.......3...567....2.8..4.7.......2..5..",
".5.3.7.4.1.........3.......5.8.3.61....8..5.9.6..1........4...6...6927....2...9..",
"..5..8..18......9.......78....4.....64....9......53..2.6.........138..5....9.714.",
"..........72.6.1....51...82.8...13..4.........37.9..1.....238..5.4..9.........79.",
"...658.....4......12............96.7...3..5....2.8...3..19..8..3.6.....4....473..",
".2.3.......6..8.9.83.5........2...8.7.9..5........6..4.......1...1...4.22..7..8.9",
".5..9....1.....6.....3.8.....8.4...9514.......3....2..........4.8...6..77..15..6.",
".....2.......7...17..3...9.8..7......2.89.6...13..6....9..5.824.....891..........",
"3...8.......7....51..............36...2..4....7...........6.13..452...........8.."    
];

games.forEach(function(game){
  var start = Date.now();
  var board = solve(game);
  if(!board) return;
  display(board);
  var solved = search(board);
  var stop = Date.now();
  display(solved);
  console.log(game);
  console.log('solved in', stop - start, 'ms');
});

sudoku.js

var digits   = '123456789'
  , rows     = 'ABCDEFGHI'.split('')
  , cols     = digits.split('')
  , squares  = cross(rows, cols)

  , units    = ['ABC', 'DEF', 'GHI'].map(function(rs){
                  return ['123', '456', '789'].map(cross.bind(null, rs))
               }).reduce(concat)

  , unitlist = union([
                  cols.map(cross.bind(null, rows)),
                  rows.map(function(r){ return cross(r, cols) }),
                  units ])

  , peers    = zip(squares, squares.map(function(s){
                  return union(unitlist.filter(contains.bind(null, s)))
                    .filter(function(c){ return c !== s })
               }));


function solve(grid) {
  var chars = grid.split('').filter(function(c){
    return contains(c, digits + '0.')
  });

  if(chars.length !== 81) return false;

  var vals = zip(squares, squares.map(function(){ return digits }));

  return squares.some(function(s, i){
    return (contains(chars[i], digits)) ? !assign(vals, s, chars[i]) : false;
  }) ? false : vals;

}


function assign(values, s, d){
  return values[s].replace(d, '').split('').every(function(d2){
    return eliminate(values, s, d2);
  }) ? values : false;
}

function eliminate(values, s, d){

  if(!contains(d, values[s])) return values;
  values[s] = values[s].replace(d, '');

  if(values[s].length === 0) return false;
  else if(values[s].length === 1) {
    var d2 = values[s];
    if(!peers[s].every(function(s2){
      return eliminate(values, s2, d2);
    })) return false
  }

  return values
}

function search(board){
  if(!board) return false;
  if(squares.every(function(s){
    return board[s].length === 1;
  })) return board; // solved!

 var s = squares.map(function(s){ return {k: s, l: board[s].length} })
  .filter(function(p){ return p.l > 1 })
  .sort(function(a, b){ return b.l - a.l })
  .pop().k;

 var digits = board[s].split('');

 for(var i = 0; i < digits.length; i++){
   var res = search(assign(copy(board), s, digits[i]));
   if(res) return res;
 }

 return false;
}


function display(board) {
  var width = 1 + Math.max.apply([], squares.map(function(s){
    return board[s].length
  }));
  var seg = repeat('-', width*3);
  var line = [seg, seg, seg].join('+');
  console.log('\n'+ line);
  rows.forEach(function(r){
    console.log(cols.map(function(c){
      return center(board[r+c], width) + (contains(c, '36') ? '|' : '')
    }).join(''))

    if(contains(r, 'CF')) console.log(line);
  })
  console.log(line + '\n');
}

function repeat(str, times){
  return Array(times + 1).join(str);
}

function center(str, width) {
  var diff = width - str.length;
  str = repeat(' ', Math.floor(diff / 2)) + str;
  return str + repeat(' ', width - str.length);
}


function cross(A, B){
  var c = [];
  splat(A).forEach(function(a){
    splat(B).forEach(function(b){
      c.push(a+b);
    })
  })
  return c;
}

function splat(a){
  return Array.isArray(a) ? a : a.split('');
}

function union(arr) {
  return [].concat.apply([], arr);
}

function concat(p, c){
  return (p || []).concat(c)
}

function contains(v, a){
  return a.indexOf(v) !== -1;
}

function zip(A, B) {
  var obj = {};
  A.forEach(function(a, i){
    obj[a] = B[i];
  });
  return obj;
}

function copy(a){
  var o = {};
  for(var i in a) o[i] = a[i];
  return o;
}