Question

Make a 4×4 magic square with consecutive numbers with a difference of 4 in each number.
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100 points​

Answer 1

Answer:

Example 1

 As usual we are going to make a magic square with the first natural numbers, the magic sum of  first 16 natural numbers  is 34. Going  by our formula. 



AP: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16



STEP– 1

Draw 4 x 4 square grid and put small ‘dots’ in the boxes along both diagonals. Start counting from the topmost left and fill the un dotted boxes with the respective terms. Although the dotted boxes are counted the term corresponding to that box is not written there and the adjacent box is filled in the order.( Here the crossed cells are not filled even though they are counted with numbers written in it,)



STEP– 2

Now start filling from the lower most right cell, the boxes are counted using the same AP towards left. The dotted boxes are then filled with the numbers corresponding to that box.

Alternate Method. The same result can be obtained if we fill all the cells in the order with out putting any vacant cells along the diagonals and then reversing the filling in these diagonals.

Here the Magic Sum

a)  Along Rows     =     34                   b)  Along Columns    =      34                     c)  Along Diagonals         =   34        

Answer 2

Answer:

There are 3 magic carpets and each has these properties: Any 4x4 square contains the numbers 0-15. Any 4 squares in a horizontal line add up to 30. Any 4 squares in a vertical line add up to 30.