BrainTeaser LogicalAndReasoning AMC10/12 Basic
2020


Problem - 4730

The $25$ integers from $-10$ to $14,$ inclusive, can be arranged to form a $5$-by-$5$ square in which the sum of the numbers in each row, the sum of the numbers in each column, and the sum of the numbers along each of the main diagonals are all the same. What is the value of this common sum?


The answer is $\boxed{10}$.

Consider the five rows in this grid. Each and every number is used once and this it is easy to see that the desired sum must equal the one fifth of the total sum. Therefore the result is $$((-10)+(-9)+\cdots + 13 +14)\div 5 =\boxed{10}$$

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