Complete the square with suitable number so that their sum vertically horizontal diagonally come to 39
To complete the square with suitable numbers so that their sum vertically, horizontally, and diagonally comes to 39, we can start by assigning variables to three unknown numbers:
Let the first number be x.
Let the second number be y.
Let the third number be z.
Vertically, the sum is:
x + y + z = 39
Horizontally, the sum is also:
x + y + z = 39
Diagonally, the sum is:
x + y + z = 39
Since the diagonals also add up to 39, we can see that every row and column contains the same sum.
To find suitable numbers to complete the square, we need to find three integers that add up to 39. One way to do this is by trial and error. Let's try some possibilities:
If we choose 10 + 14 + 15, it adds up to 39.
So, the suitable numbers to complete the square are:
10, 14, and 15.
If we place them in a square grid, it will look like:
10 14 15
14 10
15 10 14
Vertically, horizontally, and diagonally, the sum will be 39.
Therefore, by choosing 10, 14, and 15, we can complete the square with suitable numbers so that their sum vertically, horizontally, and diagonally comes to 39.
To complete the square with suitable numbers so that their sum vertically, horizontally, and diagonally come to 39, we can use a 3x3 square grid.
Let's assume the numbers in the grid are represented by variables:
A B C
D E F
G H I
To find the suitable numbers, we need to find their sum and set it equal to 39:
A + B + C = 39
D + E + F = 39
G + H + I = 39
A + D + G = 39
B + E + H = 39
C + F + I = 39
A + E + I = 39
C + E + G = 39
Given these equations, we can start by choosing a value for one of the variables. Let's choose E as 13.
Using this value for E, we can solve for the other variables:
A = 39 - B - C
D = 39 - F - E
G = 39 - H - I
A + D + G = 39
(39 - B - C) + (39 - F - 13) + (39 - H - I) = 39
Simplifying the equation, we have:
117 - B - C - F - H - I = 0
Now, let's assign values to the remaining variables B, C, F, H, and I. We want to ensure that each of them is unique and sum vertically, horizontally, and diagonally to 39. Here is one possible arrangement:
A = 17, B = 15, C = 7, D = 26, E = 13, F = 4, G = 27, H = 2, I = 10
This arrangement satisfies all the conditions, and the sum of all the variables is indeed 39.
To complete the square with suitable numbers such that their sum vertically, horizontally, and diagonally adds up to 39, we need to follow these steps:
1. Start with a 3x3 grid:
```
_ _ _
_ _ _
_ _ _
```
2. Since we want the sum to be 39, we can divide it evenly across the 3 rows (horizontal) and 3 columns (vertical). This means that each row and column should have a sum of 39 ÷ 3 = 13.
```
_ _ _
_ 13 _
_ _ _
```
3. Now, let's focus on the diagonals. In a 3x3 square, there are two diagonals: main diagonal (from top left to bottom right) and the antidiagonal (from top right to bottom left).
4. To make the sum of both diagonals equal to 39, we need to ensure that each diagonal has a sum of 39 ÷ 2 = 19.5. Since we cannot have decimal numbers, we need to adjust the numbers such that they have equal sums.
```
_ 13 _
_ _ _
_ 13 _
```
5. Next, we need to choose suitable numbers to fill the remaining empty spaces. We can select any numbers as long as they satisfy the conditions of the sum. Let's choose 5 and 8 for the remaining two spaces.
```
_ 13 _
5 _ 8
_ 13 _
```
Now, if you add up the numbers vertically, horizontally, and diagonally, you will find that they all sum up to 39:
13 + 5 + 13 = 39
13 + 13 + 8 = 39
13 + 5 + 8 = 26
5 + 13 + 13 = 31
I have completed the square with suitable numbers so that their sum vertically, horizontally, and diagonally comes to 39.