what is missing number for magic square for 22, 111,72, 131
To find the missing number in a magic square, we need to understand the properties of a magic square. A magic square is a square grid of numbers, where the sum of each row, column, and diagonal is the same. In this case, we have a 4x4 magic square with the given numbers: 22, 111, 72, and 131.
To find the missing number, we first need to calculate the sum that each row, column, and diagonal should have. Since it is a 4x4 magic square, the sum will be equal to the sum of all the numbers divided by 4. Let's do the calculations:
Sum of all numbers = 22 + 111 + 72 + 131 = 336
Sum of each row, column, and diagonal = 336 / 4 = 84
Now we can check each row, column, and diagonal to find which one is missing the number.
Checking the rows:
Row 1: 22 + 111 + 72 = 205
Row 2: ? + ? + ? = 84 (missing numbers)
Row 3: 131 + ? + ? = 84 (missing numbers)
Row 4: ? + ? + ? = 84 (missing numbers)
Checking the columns:
Column 1: 22 + ? + 131 = 84 (missing number)
Column 2: 111 + ? + ? = 84 (missing numbers)
Column 3: 72 + ? + ? = 84 (missing numbers)
Column 4: ? + ? + ? = 84 (missing numbers)
Checking the diagonals:
Diagonal 1: 22 + ? + ? = 84 (missing numbers)
Diagonal 2: 131 + ? + ? = 84 (missing numbers)
From the calculations, we can see that both Column 1 and Diagonal 1 are missing the number. Now we need to find what number, when added to the existing numbers, will give us a sum of 84.
Column 1 missing number: 84 - (22 + 131) = -69
Diagonal 1 missing number: 84 - (22 + 72) = -10
Therefore, the missing numbers for Column 1 and Diagonal 1 are -69 and -10, respectively.