Python program to fit all possible tiles into a 4x4 grid, where each tile side either has a door or not.

sorceress.py

#!/usr/bin/python3


class Piece:
  def __init__(self, mask):
    self.up = bool(mask & 1)
    self.down = bool(mask & 2)
    self.left = bool(mask & 4)
    self.right = bool(mask & 8)

  def line(self, i):
    if i == 0:
      return ' %s ' % ('|' if self.up else ' ')
    if i == 1:
      return '%s+%s' % ('-' if self.left else ' ', '-' if self.right else ' ')
    if i == 2:
      return ' %s ' % ('|' if self.down else ' ')

Piece.EMPTY = Piece(0)


class Grid:
  def __init__(self, rows, cols):
    self.rows = rows
    self.cols = cols
    self.cells = [[None for col in range(cols)] for row in range(rows)]

  def get(self, row, col):
    if row < 0 or row >= self.rows or col < 0 or col >= self.cols:
      return Piece.EMPTY
    return self.cells[row][col] or Piece.EMPTY

  def set(self, row, col, piece):
    self.cells[row][col] = piece

  def __str__(self):
    lines = []
    for row in range(self.rows):
      for i in range(3):
        line = []
        for col in range(self.cols):
          line.append(self.get(row, col).line(i))
        lines.append(''.join(line))
    return '\n'.join(lines)


def solve(pieces, grid, row, col):
  if row >= grid.rows:
    print(grid)
    return 1

  count = 0
  for i in range(len(pieces)):
    piece = pieces[i]
    if piece is None:
      continue
    if (piece.left == grid.get(row, col - 1).right and
        piece.up == grid.get(row - 1, col).down):
      pieces[i] = None
      grid.set(row, col, piece)
      if col == grid.cols - 1:
        next_row = row + 1
        next_col = 0
      else:
        next_row = row
        next_col = col + 1
      count += solve(pieces, grid, next_row, next_col)
      grid.set(row, col, None)
      pieces[i] = piece
  return count


count = solve([Piece(i) for i in range(16)], Grid(4, 4), 0, 0)
print('%d solutions found' % count)

            
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