Into each row of a grid, Nigel writes the digits in order, starting at one of the digits and returning to 1 after 9. For example, one row might contain .
The grid is called gorgeous if each nine-digit number read along any row or column or along the diagonal from the top-left to the bottom-right corner or the diagonal from the bottom-left to the top-right corner is divisible by 9.
How many of the possible grids are gorgeous?
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Cayley Mathematical Olympiad (2024)
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