What about Sudoku?
Ok, this is the rule, just one:
each row, each column and each little square 3x3 must contain all the digits from 1 to 9!
The number of valid Sudoku solution grids for the standard 9×9 grid was calculated by Bertram Felgenhauer in 2005 to be 6,670,903,752,021,072,936,960 (sequence A107739 in OEIS). This number is equal to 9! × 722 × 27 × 27,704,267,971, the last factor of which is prime. The result was derived through logic and brute force computation.
Well, the following is a sample from Wikipedia.org:

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