On Jigsaw Sudoku Puzzles and Related Topics Bachelor Thesis

Using memoization and various other optimization techniques, the number of dissections of the n × n square into n polyominoes of size n is computed for n ≤ 8. On this task our method outperforms Donald Knuth’s Algorithm X with Dancing Links. The number of jigsaw sudoku puzzle solutions is computed for n ≤ 7. For every jigsaw sudoku puzzle polyomino cover with n ≤ 6 the size of its smallest critical sets is determined. Furthermore it is shown that for every n ≥ 4 there exists a polyomino cover that does not allow for any sudoku puzzle solution. We give a closed formula for the number of possible ways to fill the border of an n × n square with numbers while obeying Latin square constraints. We define a cannibal as a nonempty hyperpolyomino that disconnects its exterior from its interior, where the interior is exactly the size of the hyperpolyomino itself, and we present the smallest found cannibals in two and three dimensions.