Category: Magic Numbers

During past years author worked with block-wise, bordered and block-bordered magic squares. This work make connection between block-wise and bordered magic squares. We started with block-wise bordered magic squares of orders 108 and 102. Based on these two big magic squares inner order magic squares multiples of 6 are studied. By inner order we understand that magic squares of orders 96, 90, 84, etc. Instead of … Continue reading Block-Wise Bordered Magic Squares Multiples of Magic and Bordered Magic Squares of Order 6

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

This work brings, magic squares of order 3 to 32 just with two digits in such a way that the magic squares are upside-down and mirror looking independent of magic sums. These types of magic squares we call as universal magic squares. This is done only with two digits 1 and 8. The work for … Continue reading Universal Magic and Bimagic Squares of Orders 3 to 32 Using 1 and 8

This short paper shows how to create magic squares in such a way that total sum of their numbers becomes a perfect square. This has been done in two ways: Firstly, Take the sum of odd numbers, and secondly, take the numbers in a sequential way. In the first case, for all orders of magic … Continue reading Magic Squares with Perfect Square Number Sums

In this work, magic squares are written in multi-digits formats. In some situations, different digits are considered according to order of magic squares. Magic squares related to combination with repetitions are also considered. In each case study is extended to palindromic magic squares. Full Work: Multi-Digits Magic Squares  

This work brings magic squares contructed based on intervally distributed numbers. It has been done in different form, such as, using pairwise mutually orthogonal Latins quares, self-orthogonal diagonalized Latin squares, block-wise compositions, etc. Work is divided in three parts: first from order 3 to 10, second from 11 to 20 and third from 21 to 25. … Continue reading Intervally Distributed Magic Squares With Properties