Magic Square Puzzles

Magic Square puzzles

Magic Square Order 3

Magic Square puzzles also called as word squares dates back to 650 BC or earlier where Chinese and especially Arab mathematicians after the invasion of Indian Subcontinent learned Indian mathematics. It included aspects of Astronomy as well. It was used in Vedic Mathematics, in rituals, astronomical calculations. It was then later used by Illusionists and Magicians in Arab.

By definition, it is a square of integers (positive) i.e. arrangement of n +ve integers in a square of side n such that all rows, colums and diagnols contain all distinct numbers and the sum is same for all. An example of side 3 is as follows where each column, row and diagnol produces a sum of 15.

The constant sum is what is called as the Magic Constant or Magic Sum.

It is important to note that the magic constants are different for different magic square. Here is the list of some magic constants.
For Magic Square size (order) 3 , magic constant is 15
For 4, its 34
For 5, its 65
For 6, its 111
For 7, its 1260 and so on.

0, 1, 5, 15, 34, 65, 111, 175, 260, 369, 505, 671, 870, 1105, 1379, 1695, 2056, 2465, 2925, 3439, 4010, 4641, 5335, 6095, 6924, 7825, 8801, 9855, 10990, 12209, 13515, 14911, 16400, 17985, 19669, 21455, 23346, 25345, 27455, 29679, 32020, 34481, 37065, 39775

It is further interesting to note that they follow a sequence which follows
f(n) = n*(n^2 + 1)/2

For further details of this sequence click here

Just for fun, here is one of order 12, magic constant 870

Magic Square Order 12 Sum 870 thinkwitty.com