Question 166
Consider a $9 \times 9$ grid of squares. Haruki fills each square in this grid with an integer between $1$ and $9$, inclusive. The grid is called a super-sudoku if each of the following three conditions hold:
- Each column in the grid contains each of the numbers $1,2,3,4,5,6,7,8,9$ exactly once.
- Each row in the grid contains each of the numbers $1,2,3,4,5,6,7,8,9$ exactly once.
- Each $3 \times 3$ subsquare in the grid contains each of the numbers $1,2,3,4,5,6,7,8,9$ exactly once.
How many possible super-sudoku grids are there?
- Each column in the grid contains each of the numbers $1,2,3,4,5,6,7,8,9$ exactly once.
- Each row in the grid contains each of the numbers $1,2,3,4,5,6,7,8,9$ exactly once.
- Each $3 \times 3$ subsquare in the grid contains each of the numbers $1,2,3,4,5,6,7,8,9$ exactly once.
How many possible super-sudoku grids are there?