The image contains a magic square puzzle where the sums of each row, column, and diagonal must be identical. Some values are already filled in, and the task is to complete the square.

Let me analyze the square and solve it step by step.

Observations:

1. First Square (Top)

   • The magic sum is the same for all rows, columns, and diagonals.
   • Filled values:
     Row 1: -9, -3, 1
     Row 2: Unknown
     Row 3: 5, Unknown, -7

2. Second Square (Bottom)

   • The magic sum is labeled as -12.
   • Filled values:
     Row 1: -7, Unknown, -1
     Row 2: -4, 2, Unknown
     Row 3: Unknown

Let me calculate the missing values for both squares. numpy as np

Top square, magic square variables

top_square = np.array([ [-9, -3, 1], [0, 0, 0], # Unknown row to solve [5, 0, -7] ])

Bottom square, magic sum = -12

magic_sum = -12 bottom_square = np.array([ [-7, 0, -1], [-4, 2, 0], [0, 0, 0] ])

Solving top square

Row 1 sum = -9 + (-3) + 1 = -11

Row 3 sum = 5 + (-7) + x = -11, solve for x

row3_missing = -11 - (5 - 7) top_square[2, 1] = row3_missing

Now solve Row 2 (Middle Row)

Magic sum for rows/columns: -11

Middle column: -3 + x + 0 = -11

col2_missing = -11 - (-3 + row3_missing) top_square[1, 1] = col2_missing

Middle row: x + y + z = -11

-3 already solved, solve for left and right

middle_row = -11 - (col2_missing + 1) top_square[1, 0] = middle_row + col2_missing # fill

Solving bottom square rows Solve the remaining entries in the bottom square based on the given magic sum (-12)

Row 1: -7 + x + (-1) = -12 -> solve for x

bottom_square[0, 1] = magic_sum - (-7 - 1)

Row 2: -4 + 2 + x = -12 -> solve for x

bottom_square[1, 2] = magic_sum - (-4 + 2)

Column 1: -7 + (-4) + x = -12 -> solve for x

bottom_square[2, 0] = magic_sum - (-7 - 4)

Row 3: Solve last two missing entries (x + y = -12)

Col 2: x = -7 + (row totals)

bottom_squareHere are the solutions so far:

First Square (Top):

1. The missing values in the top square are partially calculated. I need to double-check some missing logic to fill the middle value row .