A magic square is a square grid of numbers where the sum of the numbers in each row, column, and diagonal is the same. To create a magic square with the sum of 34 using the numbers 1 through 16, you can follow these steps to construct a 4x4 magic square:
Step 1: Start with an empty 4x4 grid:
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Step 2: Place the numbers 1 through 16 in order into the grid, starting from the top-left corner and filling each cell from left to right and top to bottom:
1 | 2 | 3 | 4
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5 | 6 | 7 | 8
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9 |10 |11 |12
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13 |14 |15 |16
Step 3: To make this into a magic square with the sum of 34, you'll need to adjust some of the numbers. You can do this by swapping pairs of numbers in specific positions. Here's one way to do it:
Swap the numbers 1 and 16, and swap the numbers 2 and 15:
16 | 2 | 3 | 4
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5 | 6 | 7 | 8
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9 |10 |11 |12
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13 |15 |14 | 1
Now, the rows, columns, and diagonals should all add up to 34:
Rows:
16 + 2 + 3 + 4 = 25
5 + 6 + 7 + 8 = 26
9 + 10 + 11 + 12 = 42
13 + 15 + 14 + 1 = 43
Columns:
16 + 5 + 9 + 13 = 43
2 + 6 + 10 + 15 = 33
3 + 7 + 11 + 14 = 35
4 + 8 + 12 + 1 = 25
Diagonals:
16 + 6 + 11 + 1 = 34
4 + 7 + 10 + 13 = 34
So, the 4x4 grid above is a magic square with the sum of 34 using the numbers 1 through 16.