[QUIZ] Perl 'Easy' Quiz of the Week #2005-03-04

IMPORTANT: Please do not post solutions, hints, or other spoilers
        until at least 60 hours after the date of this message.  
        Thanks.

Since nobody has posted a quiz for a while, here's mine. For a change
from word puzzles, here's a number puzzle...

Sudoku (or Su Doku) is a Japanese puzzle game. The field is a 9x9 grid,
which is subdivided into nine 3x3 blocks. Each grid square must contain
a number in the range 1-9; each number must occur exactly once within
each 3x3 block, within each (full) column, and within each (full) row.
A few numbers (24 or 28, in the examples I've come across) are given as
hints, in a pattern that exhibits some rotational symmetry (like many
crosswords).

More details and an example can be found at
http://www.puzzle.jp/letsplay/sudokurule-e.html (or by googling for
"sudoku"). For convenience I'll copy their example here:

+==+==+==++==+==+==++==+==+==+
|  |  |6 ||  |  |  ||  |  |1 |
+--+--+--++--+--+--++--+--+--+
|  |7 |  ||  |6 |  ||  |5 |  |
+--+--+--++--+--+--++--+--+--+
|8 |  |  ||1 |  |3 ||2 |  |  |
+==+==+==++==+==+==++==+==+==+
|  |  |5 ||  |4 |  ||8 |  |  |
+--+--+--++--+--+--++--+--+--+
|  |4 |  ||7 |  |2 ||  |9 |  |
+--+--+--++--+--+--++--+--+--+
|  |  |8 ||  |1 |  ||7 |  |  |
+==+==+==++==+==+==++==+==+==+
|  |  |1 ||2 |  |5 ||  |  |3 |
+--+--+--++--+--+--++--+--+--+
|  |6 |  ||  |7 |  ||  |8 |  |
+--+--+--++--+--+--++--+--+--+
|2 |  |  ||  |  |  ||4 |  |  |
+==+==+==++==+==+==++==+==+==+

Your objectives:

(1) Write a program to check the correctness of a solution.

(2) Write a solver. (There are several of these on-line already.)

(3) Write a random puzzle generator.

At the time of posting I have done (1) and (2) in Perl...

Roger