A $\textit{Sudoku square}$ is a $9 \times 9$ grid filled with nine symbols (such as the numbers from 1 to 9) in such a way that each row, column, and the nine $3 \times 3$ subsquares (shown above) contain each symbol exactly once. In a $\textit{Sudoku puzzle}$, the square contains some entries (called $\textit{clues}$), and the goal is to complete the Sudoku square. In the classical setting, the clues are chosen such that there is only one way to complete each square. You may try your luck with the two Sudoku puzzles above (caveat: If you've never played a Sudoku puzzle, watch outthese squares are addictive).
We will work on two problems regarding Sudoku squares:
1. How many Sudoku squares are there?
2. What is the minimum number of clues that yield a unique solution to a Sudoku puzzle?
These are hard questions. In fact, (1) was answered only in 2005 (the number of Sudoku squares is $6\text{,}670\text{,}903\text{,}752\text{,}021\text{,}072\text{,}936\text{,}960$), and (2) remains open (it is conjectured that the minimum number is 17). So we will simplify the problems and work with $4 \times 4$ Sudoku squares. Experiment with questions (1) and (2) in the $4 \times 4$ case.
nid);
while ($data = db_fetch_object($authorresult)) {
$authorfirstname = $data>firstname;
$authorlastname = $data>lastname;
$authors = $authorfirstname . ' ' . $authorlastname;
print $authors; ?>
nid);
if (mysql_num_rows($refresult) > 0 ) { ?>
nmcreferenceid;
$referenceauthor = $data>author;
$referencetitle = $data>title;
$referenceurl = $data>url; ?>
0 ) {
print '
Reference Author 
Reference Title 
Reference URL 



';
} ?>