Question
Complete the following magic square by supplying the missing numbers:
✓
Answer
In magic square the numbers in each vertical, horizontal, and diagonal row add up to the same value.
Sum of diagonal elements $= 2 + 12 + 7 + 17 = 38$
Now, Missing element in the first column $= 38 - (2 + 9 + 14) = 38 - 25 = 13$
Missing element in the first row $= 38 - (2 + 15 + 16) = 38 - 33 = 5$
Missing element in the second row and fourth column $= 38 - (5 + 10 + 17) = 38 - 32 = 6$
Missing element in the second row and third column $= 38 - (9 + 12 + 6) = 38 - 27 = 11$
Missing element in the fourth row and third column $= 38 - (16 + 11 + 7) = 38 - 34 = 4$
Missing element in the third row and third column $= 38 - (13 + 7 + 10) = 38 - 30 = 8$
Missing element in the fourth row and second column $= 38 - (14 + 4 + 17) = 38 - 35 = 3$
Hence, the complete magic square is
Sum of diagonal elements $= 2 + 12 + 7 + 17 = 38$
Now, Missing element in the first column $= 38 - (2 + 9 + 14) = 38 - 25 = 13$
Missing element in the first row $= 38 - (2 + 15 + 16) = 38 - 33 = 5$
Missing element in the second row and fourth column $= 38 - (5 + 10 + 17) = 38 - 32 = 6$
Missing element in the second row and third column $= 38 - (9 + 12 + 6) = 38 - 27 = 11$
Missing element in the fourth row and third column $= 38 - (16 + 11 + 7) = 38 - 34 = 4$
Missing element in the third row and third column $= 38 - (13 + 7 + 10) = 38 - 30 = 8$
Missing element in the fourth row and second column $= 38 - (14 + 4 + 17) = 38 - 35 = 3$
Hence, the complete magic square is
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