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Question
In a magic square given below each row, column and diagonal should have the same sum. Find the values of x, y, and z
| 1 | −10 | x |
| y | −3 | −2 |
| −6 | 4 | z |
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Solution
Column total = Row total = diagonal total
∴ 1 + y + (−6) = (−10) + (−3) + 4
y + (−5) = −13 + 4
y = −9 + 5
y = −4
So 1 + (−10) + x = y + (−3) + (−2)
−9 + x = (−4) + (−3) + (−2)
−9 + x = −9
x = −9 + 9
x = 0
Now x + (−2) + z = (−10) + (−3) + 4
0 + (−2) + z = (−13) + 4
−2 + z = −9
z = −9 + 2 = −7
z = −7
∴ x = 0, y = −4, z = −7
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