# Minimum Perfect Square Sum Bordered and Block-Wise Bordered Magic Squares: Orders 3 to 47

There are many ways of writing magic or bordered magic squares, where the sum of entries is always a perfect square. In one of the possibility, the magic sums are such that they satisfy uniformity property. Another way is to write magic squares generated by Pythagorean triples. Based on these idea, we can always write magic squares or bordered magic squares where the sum of entries is always a perfect square. Still, these sums are not minimum. There is a third way to write magic squares or bordered squares such that we get minimum perfect square sum of entries. This what we have done in this work with bordered and block-wise bordered magic squares. In case of even order magic squares, we can always write \textbf{block-wise bordered} magic squares with equal sum sub-blocks. In case of odd order magic squares, we can write them as block-wise bordered magic squares, but with different sub-blocks sums. This work is for the orders 3 to 47. Recently, author applied this idea of perfect square sum of entries to write area representations of magic squares. The whole work is written in two parts. See the links below for download:

Below are examples of bordred and block-wise bordred magic squares of orders 3 to 47 with minimum perfect square sum of the entries.