Category: Magic Squares

The idea of nested magic squares is well known in the literature, generally known by bordered magic squares. In this work, nested magic squares are studied in such a way that the magic sums are equal to the order of the magic square. The study include integer values. In some cases decimal entries with positive … Continue reading Bordered Magic Squares With Order Square Magic Sums

The idea of bordered magic squares is well known in the literature. In this work, bordered magic squares are constructed in such a way that the final magic sum of each bordered magic square is 2020. The work is for the orders 3 to 25. In each case, a symmetric result is found for the … Continue reading Fractional and Decimal Type Bordered Magic Squares With Magic Sum 2020

References: Inder J. Taneja, 2020 In Numbers: Mathematical Style – Revised, Zenodo, December 31, 2019, pp. 1-37,  http://doi.org/10.5281/zenodo.3596193. Inder J. Taneja, Representations of Letters and Numbers With Equal Sums Magic Squares of Orders 4 and 6, Zenodo, February 1, 2019, pp. 1-82, http://doi.org/10.5281/zenodo.2555287.

The idea of nested magic squares is well known in the literature, generally known by bordered magic squares. In this work, nested magic squares are studied for the consecutive natural numbers for the orders 5 to 25. Properties like, sub-magic squares sums, total entries sums, borders entries sums, etc. are studies. Final results lead us to symmetric properties. … Continue reading Symmetric Properties of Nested Magic Squares

The idea of nested magic squares is well known in the literature, generally known by bordered magic squares. Instead, considering entries as consecutive numbers, we considered consecutive odd numbers entries. This gives us perfect square sum magic squares. We worked with magic squares of orders 3 to 25. Finally, the result can be written in … Continue reading Nested Magic Squares With Perfect Square Sums, Pythagorean Triples, and Borders Differences

Reference: H. White, Borded Magic Squares, http://budshaw.ca/BorderedMagicSquares.html

This paper brings block-wise construction of magic squares of order 39 to 45. In order to construct these magic squares we applied the previous known magic squares of orders 3 to 14, except order 12. The order 22 is also used. In each case these are written again. Specially, in case of magic square of … Continue reading Block-Wise Construction of Magic and Bimagic Squares of Orders 39 to 45

Magic squares are generally constructed using sequential or concutive numbers such as 1, 2,..., n^2. Here in this work, we shall write magic squares using non consecutive different digits numbers. This work,  we have done for the magic squares of orders 5, 7, 8, 9 and 10. As commonly, the entries are not in a … Continue reading Different Digits Magic Squares and Magic Sums Number Patterns

This paper summarizes some of the results done by author in previous works on different ways are writing block-wise magic squares. The details can be seen in the links given below. The work is for the magic squares of orders 12 to 36, i.e., for the orders 12, 15, 16, 18, 20, 21, 24, 25, … Continue reading Block-Wise Construction of Magic and Bimagic Squares of Orders 25 to 36

This paper summarizes some of the results done by author in previous works on different ways are writing block-wise magic squares. The details can be seen in the links given below. The work is for the magic squares of orders 12 to 36, i.e., for the orders 12, 15, 16, 18, 20, 21, 24, 25, … Continue reading Block-Wise Construction of Magic and Bimagic Squares of Orders 12 to 24

The idea of magic rectangles is used to bring pan magic squares of orders 15, 21, 27 and 33, where 3x3 blocks are with equal sums entries,  and are semi-magic squares of order 3 (in rows and columns). The magic squares of orders 12, 18, 24, 30 and 36 are calculated, with the property that … Continue reading Magic Rectangles in Construction of Block-Wise Pan Magic Squares

The idea of magic rectangles is well known in literature. Using this idea we brought for the first time in history a new concept on magic crosses. The work is divided in two groups. One on orders (odd, odd) and another on orders (even, even). Within the orders (odd, odd), the work is on magic … Continue reading Magic Crosses

This work brings 26 letters from A to Z and 10 numbers from 0 to 9 in terms of blocks of pan diagonal magic squares of order 4. The construction is in such a way that each letter and number is formed by equal magic sums of magic squares of order 4. Similar kind of … Continue reading Letters and Numbers in Terms of Magic Squares of Order 4

In this paper, block-wise magic squares of orders 12, 18, 24, 30 and 36 are constructed. The construction is in a such way the each block is a magic square of order 6 with equal magic sums. Below are examples and link of download the complete work: Link for download the complete work: Block-Wise Equal Sums … Continue reading Block-Wise Equal Sums Magic Squares of Orders 6k

This work brings 26 letters from A to Z and 10 numbers from 0 to 9 in terms of blocks of magic squares of order 6. The construction is in such a way that each letter and number is formed by  equal magic sums of magic squares of order 6. Similar kind of work with  … Continue reading Letters and Numbers in Terms of Magic Squares of Order 6