place the numbers 11,12,13,14 and 16 in the square boxes in such a way that in a line is always same
To place the numbers 11, 12, 13, 14, and 16 in the square boxes in such a way that in a line is always the same, you need to arrange them in a square grid where each row, column, and diagonal adds up to the same sum.
First, let's calculate the expected sum. Since there are five numbers, the sum of all the numbers should be (11 + 12 + 13 + 14 + 16) = 66.
Now, we need to determine the locations for each number:
Let's start by placing 16 in the central square, as it will be part of the diagonals, rows, and columns. We'll represent empty squares with a blank space:
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| | | |
| | 16 | |
| | | |
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Now, let's arrange the remaining numbers around 16. To ensure that each row, column, and diagonal adds up to 66, we need to consider the following:
1. The diagonal containing 16 needs to have a sum of 66. In this case, the sum of the diagonal would be 16 + ? + ?. So, we need to find two numbers that add up to 50 (66 - 16). The only combination that works is 11 and 39, as 12, 13, and 14 could not be used since they would give a sum lower than 50.
So, let's place 11 and 39 in the locations adjacent to 16 on the diagonal:
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| | | 39 |
| | 16 | |
| 11 | | |
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2. Now, we need to find the remaining locations for the numbers 12, 13, and 14, ensuring that their sum with 16 in each row, column, and the diagonal is equal to 66.
To achieve this, let's start with the row and column that already have 16:
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| | ? | 39 |
| ? | 16 | ? |
| | ? | |
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The numbers we need to place in the second row and column should add up to 50 (66 - 16). The only combination that works is 14 and 36.
Let's update the grid:
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| | 12 | 39 |
| 36 | 16 | 14 |
| | 13 | |
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3. Finally, let's determine the location for the remaining number, 12, in the bottom row. To achieve the same sum in each row, column, and diagonal, the number we need to place should be 66 - (39 + 13). Hence, 66 - (39 + 13) = 14.
The final arrangement is:
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| 14 | 12 | 39 |
| 36 | 16 | 14 |
| 13 | 11 | 16 |
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In this arrangement, each row, column, and diagonal adds up to 66.