In the given magic square use numbers from 1 to 16 and fill in the blank boxessuch that the sum of numbers should be 34 however you add it. (That is from left tomight, top to bottom inclined etc.)Sum = 34​
Here is one possible solution for the magic square:
16 3 2 13
5 10 11 8
9 6 7 12
4 15 14 1
If you sum the numbers in any row, column, or diagonal, you will always get 34.
To solve the given magic square and fill in the blanks such that the sum of the numbers is 34, follow these steps:
1. Start by drawing a 4x4 grid with empty boxes.
| | |
---------------------
| | |
---------------------
| | |
---------------------
| | |
2. Assign numbers from 1 to 16 to the empty boxes, starting from the top-left corner and moving left to right, top to bottom:
| 6 | 7 | 10 |
---------------------
11 | | | 6 |
---------------------
| | | |
---------------------
| | | |
3. Now, we need to determine the values of the remaining empty boxes. Start with the middle row, second box:
| 6 | 7 | 10 |
---------------------
11 | 4 | ? | 6 |
---------------------
| | | |
---------------------
| | | |
4. To calculate the missing value, let's first check the sum of the known values in that row (11 + 4 + ? + 6):
21 + ? = 34
? = 34 - 21
? = 13
So, the missing value in the middle row, second box, is 13.
| 6 | 7 | 10 |
---------------------
11 | 4 | 13 | 6 |
---------------------
| | | |
---------------------
| | | |
5. Now, let's move to the last column, third box:
| 6 | 7 | 10 |
---------------------
11 | 4 | 13 | 6 |
---------------------
| | | ? |
---------------------
| | | |
6. To calculate the missing value, let's check the sum of the known values in that column (10 + 6 + ?):
16 + ? = 34
? = 34 - 16
? = 18
So, the missing value in the last column, third box, is 18.
| 6 | 7 | 10 |
---------------------
11 | 4 | 13 | 6 |
---------------------
| | | 18 |
---------------------
| | | |
7. Finally, let's determine the value of the bottom-right box:
| 6 | 7 | 10 |
---------------------
11 | 4 | 13 | 6 |
---------------------
| | | 18 |
---------------------
| | | ? |
8. To calculate the missing value, let's check the sum of the known values in that row (6 + 7 + 10 + 18):
41 + ? = 34
? = 34 - 41
? = -7
However, we cannot have a negative number in the grid. This indicates that the initial values assigned to the boxes may be incorrect or the given sum is not possible to achieve.
To recap, the given magic square cannot be solved using numbers from 1 to 16 with a sum of 34.