Super-Magic Square

You must have heard of the magic square. And most of you must also be familiar with the solution. Here is an upgrade of the same problem – let’s call it super-magic square.

But first for those who are unaware of the magic square ……

Magic square is a 3 × 3 grid wherein one fills in 9 consecutive natural numbers, say 1 to 9 OR 2 to 10 and so on, one number to each cell, such that each row, each column and each diagonal adds up to the same value.

While in the above case, the numbers to be filled were given, in another variant of the same problem, the numbers to be filled is not given. Instead the problem is stated as ……

Fill in 9 distinct natural numbers, one in each cell of a 3 × 3 grid, such that each row, each column and each diagonal adds up to, say 33.

The only difference in this problem is that you need to figure out what numbers to put in the cell.

Now for the super-magic square

Fill in each of the first 16 natural numbers i.e. 1 to 16 in a 4 × 4 grid …

… such that …
… addition of the 4 numbers in each row …
… addition of the 4 numbers in each column …
… addition of the 4 numbers in each diagonal …
… addition of the 4 numbers in the 4 squares formed at top left, in the 4 squares formed at top right, in the 4 squares formed at bottom-left, in the 4 squares formed at bottom right …
… and the addition of the 4 numbers in the 4 squares formed in the center of the grid …
… are all equal.

Happy Solving.
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