A semimagic square is an arrangement of integers in a square grid, where the numbers in each row or column adds up to the same number, which is called the magic sum.

Consider the \( 2 \times 2 \) square grid below.

\[ \begin{array} { | c | c | } \hline a & b \\ \hline c & d \\ \hline \end{array} \]

How many ways are there to fill each square with an integer from 1 to 10, such that the sum of each row and column is the same?

Details and assumptions

The integers may be used multiple times. For example, the square grid with all 1's satisfies the conditions.


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