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\(\begin{array}{| *5{@{}c@{}|}} \hline \qquad & \qquad & \qquad & \textcolor{red}{\heartsuit} & \qquad \\ \hline & 74 & & \qquad & \\ \hline & & & & 186 \\ \hline & & 103 & & \\ \hline 0 & & & & \\ \hline \end{array}\)

It is possible to place positive integers into the vacant twenty-one squares of this \(5 \times 5\) grid so that the numbers in each row and column form an arithmetic sequence. Find the number that must occupy the vacant square marked by the \(\textcolor{red}{\heartsuit}\).

 Feb 1, 2019
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See the solution here:  https://artofproblemsolving.com/wiki/index.php/1988_AIME_Problems/Problem_6

 Feb 1, 2019

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