solves a blocks puzzle

blocks.js

window.addEventListener('load', function(e) {
  var pieces = [
    [ 28, 6 ],
    [ 28, 14 ],
    [ 21, 18 ],
    [ 10, 7 ],
    [ 32, 11 ],
    [ 14, 4 ],
    [ 28, 7 ],
    [ 21, 14 ],
    [ 21, 18 ],
    [ 17, 14 ],
    [ 21, 14 ],
    [ 32, 10 ]
  ];

  window.setTimeout(function () {
    var grid = makeArray(56,56,0);

    var ans = permute(grid, pieces);

    console.log(ans);
  }, 0);

}, false);

function permute(grid, remaining) {
  //console.log(remaining.length);

  var start = openCorner(grid);

  if (start === null) return '';
  
  for(var r = 0; r < remaining.length; r++) {
    var a = remaining[r];
    var next = remaining.slice(0);
    next.splice(r, 1);

    if (tryPaint(grid, start, a, 1)) {
      var got = permute(grid, next);
      if (got != null) {
        return ', (' + a[0] + ', ' + a[1] + ') @ (' + start[0] + ', ' + start[1] + ')' + got;
      }
      tryPaint(grid, start, a, -1);
    }

    var b = [ a[1], a[0] ];

    if (tryPaint(grid, start, b, 1)) {
      got = permute(grid, next);
      if (got != null) {
        return ', (' + b[0] + ', ' + b[1] + ') @ (' + start[0] + ', ' + start[1] + ')' + got;
      }
      tryPaint(grid, start, b, -1);
    }
  }

  return null;
}

function tryPaint(grid, start, size, delta) {
  if (56 < start[0] + size[0] ||
      56 < start[1] + size[1])
    return false;

  for (var x = start[0]; x < start[0] + size[0]; x++)
  for (var y = start[1]; y < start[1] + size[1]; y++) {
    var w = grid[x][y] + delta;
    if (w < 0 || 1 < w) 
      return false;
  }

  for (var x = start[0]; x < start[0] + size[0]; x++)
  for (var y = start[1]; y < start[1] + size[1]; y++) {
    grid[x][y] += delta;
  }

  return true;
}

function openCorner(grid) {
  for (var x = 0; x < 56; x++)
  for (var y = 0; y < 56; y++) {
    if (grid[x][y] === 0) 
      return [ x, y ];
  }

  return null;
}

function makeArray(w, h, val) {
  var arr = [];
  for(i = 0; i < h; i++) {
    arr[i] = [];
    for(j = 0; j < w; j++) {
      arr[i][j] = val;
    }
  }
  return arr;
}