Question

Rahul has just made a $3 	imes 3$ magic square, in which, the sum of the cells along any row, column or diagonal, is the same number N. The entries in the cells are given as expressions in x, y, and Z: | $3x+4y$ | $2x$ | $2x+y+z$ | | $2x^2$ | $4y$ | $y^2+z$ | | $y+z$ | $3x+2z$ | $z-1$ | Find N?

Accepted Answer

B. Equating sums of rows and columns: Sum of row 3 = $y+z + 3x+2z + z-1 = 3x+y+4z-1$. Sum of col 2 = $2x + 4y + 3x+2z = 5x+4y+2z$. Equating diagonal 1 sum: $(3x+4y) + 4y + (z-1) = 3x+8y+z-1$. Solving these simultaneous equations gives $x = 2$, $y = 3$, $z = 7$. Substitute $x=2, y=3, z=7$ into row 1: $(3(2)+4(3)) + 2(2) + (2(2)+3+7) = 18 + 4 + 14 = 36$. Hence, $N = 36$.

Magic Square Algebraic Sum

Explanation

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