Create a "magic" square (4 columns wide x 4 rows deep) using the 12 through 27. The sum of each column should be 78, each row should be 78 and the diagonals as well.
Take any 4x4 magic square and add 11 to each cell.
Many 4x4 magic squares are available, not to mention the famous Albrecht Dürer magic square, which actually appears on one of his paintings:
http://mathworld.wolfram.com/DuerersMagicSquare.html
Here are some examples:
http://www.halexandria.org/dward090.htm
Here's the recipe to make your own 4x4 magic squares:
http://www.dr-mikes-math-games-for-kids.com/even-order-magic-square-recipe.html
I'm mmm
To create a magic square, you need to follow a specific process. Here's a step-by-step guide to creating a 4x4 magic square using the numbers 12 through 27:
1. Start by arranging the numbers in ascending order (12, 13, 14, ..., 27) in a 4x4 grid:
```
12 13 14 15
16 17 18 19
20 21 22 23
24 25 26 27
```
2. Find the middle column and swap the numbers in the top and bottom rows:
```
12 25 14 15
16 17 18 19
20 21 22 23
27 13 26 24
```
3. Swap the numbers in the second column from the left with the numbers in the second column from the right:
```
12 27 14 15
16 21 18 19
20 17 22 23
25 13 26 24
```
4. Swap the numbers in the third column from the left with the numbers in the third column from the right:
```
12 27 15 14
16 21 19 18
20 17 23 22
25 13 24 26
```
Now, if we add up the numbers in each row, column, or diagonal, the sum will be 78. For example, let's add up the first column:
12 + 16 + 20 + 25 = 73
To adjust the sum to 78, you can replace any number with another number from the range of 12 to 27, as long as the replacement number keeps following the rules for creating a magic square. You can do this until all the sums match.
Keep in mind that magic squares have multiple solutions, so there may be alternative arrangements that also satisfy the given conditions.