Question

A semi-magic 3x3 square is the square with the sum of numbers in each row, column, and one of the diagonals equal to the same number. (The diagonal that goes from the left top corner to the bottom right corner does not have the same sum of the numbers.) Complete each semi-magic square.

a) 3 5 7, 1 5 9, 7 5 3
b) 2 7 6, 9 5 1, 4 3 8
c) 8 1 6, 3 5 7, 4 9 2
d) 4 9 2, 3 5 7, 8 1 6

Answer 1

A semi-magic square is a square with the sum of numbers in each row, column, and one of the diagonals equal to the same number. We need to check if the sums are equal for each semi-magic square. Option b) and d) satisfy the condition.

Step-by-step explanation:

A semi-magic square is a square with the sum of numbers in each row, column, and one of the diagonals equal to the same number. To complete each semi-magic square, we need to check if the sum of the numbers in each row, column, and diagonal is equal.

a) Sum of row 1: 3 + 5 + 7 = 15. Sum of row 2: 1 + 5 + 9 = 15. Sum of row 3: 7 + 5 + 3 = 15. So, the sum is equal in each row. However, the diagonal from top left to bottom right does not have the same sum.

b) Sum of row 1: 2 + 7 + 6 = 15. Sum of row 2: 9 + 5 + 1 = 15. Sum of row 3: 4 + 3 + 8 = 15. The diagonal from top left to bottom right has a sum of 2 + 5 + 8 = 15, which is also equal.

c) Sum of row 1: 8 + 1 + 6 = 15. Sum of row 2: 3 + 5 + 7 = 15. Sum of row 3: 4 + 9 + 2 = 15. The diagonal from top left to bottom right has a sum of 8 + 5 + 2 = 15, which is equal.

d) Sum of row 1: 4 + 9 + 2 = 15. Sum of row 2: 3 + 5 + 7 = 15. Sum of row 3: 8 + 1 + 6 = 15. The diagonal from top left to bottom right has a sum of 4 + 5 + 6 = 15, which is equal.