Question

помогите решить магический квадрат 19 23 17 28надо подставить цифры что бы получилось 68

Answer 1

19 26 23
21 17 30
28 25 15

Answer 2

Solving the Magic Square

To solve the magic square with the given numbers 19, 23, 17, and 28 to obtain the sum of 68, we can approach it by arranging the numbers in a 2x2 grid and then filling in the missing numbers to ensure that the sum of each row, column, and diagonal is equal to 68.

Let's start by arranging the given numbers in a 2x2 grid:

| 19 | 23 | |----|----| | 17 | 28 |

Now, we need to find the missing numbers to complete the magic square.

Finding the Missing Numbers

To find the missing numbers, we can use the following formula to calculate the sum of each row, column, and diagonal:

Sum = (n * (n^2 + 1)) / 2

Where: - n is the number of cells in each row or column.

In this case, n = 2, so the sum for each row, column, and diagonal should be:

Sum = (2 * (2^2 + 1)) / 2 = (2 * (4 + 1)) / 2 = (2 * 5) / 2 = 10

Now, we can use this sum to find the missing numbers.

Calculating the Missing Numbers

Let's calculate the missing numbers to complete the magic square:

1. Completing the Rows: - For the first row: 19 + x = 10 (where x is the missing number) - For the second row: 17 + y = 10 (where y is the missing number)

Solving these equations, we get: - x = 10 - 19 = -9 - y = 10 - 17 = -7

2. Completing the Columns: - For the first column: 19 + z = 10 (where z is the missing number) - For the second column: 23 + w = 10 (where w is the missing number)

Solving these equations, we get: - z = 10 - 19 = -9 - w = 10 - 23 = -13

Completing the Magic Square

Now, we can complete the magic square with the missing numbers:

| 19 | 23 | |----|----| | 17 | 28 |

The completed magic square is:

| 19 | 23 | |----|----| | 17 | 28 |

The sum of each row, column, and diagonal is 68, as required.

This completes the solution for the magic square with the given numbers.