Effective Knuth's algorithm for the Exact Cover problem and its application to difficult puzzles

Many of us have played and certainly know Sudoku or Polyomino puzzles. The latter, since its introduction by Solomon Golomb, has aroused the interest of mathematicians in the field of science and recreation. Numerous games - such as Tetris or Ubongo - puzzles and unsolved problems are based on these delightful elements which are created by joining along the edges of many non-overlapping unit squares...