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Omni-MATH / How many ways can one fill a 3×3 square grid with nonnegative integers such that no nonzero integer appears more than once in the same row or column and the sum of the numbers in e…

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problem

How many ways can one fill a 3×33 \times 3 square grid with nonnegative integers such that no nonzero integer appears more than once in the same row or column and the sum of the numbers in every row and column equals 7 ?
Plain-text mathematical notation (without MathML)
How many ways can one fill a 3×3 square grid with nonnegative integers such that no nonzero integer appears more than once in the same row or column and the sum of the numbers in every row and column equals 7 ?
Original LaTeX notation
How many ways can one fill a $3 \times 3$ square grid with nonnegative integers such that no nonzero integer appears more than once in the same row or column and the sum of the numbers in every row and column equals 7 ?

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