  Over the last decade, Sudoku, a combinatorial number-placement puzzle, has
become a favorite pastimes of many all around the world. In this puzzle, the
task is to complete a partially filled $9 \times 9$ square with numbers 1
through 9, subject to the constraint that each number must appear once in each
row, each column, and each of the nine $3 \times 3$ blocks. Sudoku squares can
be considered a subclass of the well-studied class of Latin squares. In this
paper, we study natural extensions of a classical result on Latin square
completion to Sudoku squares. Furthermore, we use the procedure developed in
the proof to obtain asymptotic bounds on the number of Sudoku squares of order
$n$.
