# Generating Pythagorean Triples, Palindromic-Type Pandigital Patterns, and Magic Squares

This work brings how we can generate Pythagoren triples and Magic square using some interesting tables. These Pythagorean triples again generate Palindromic-Type Pandigital Patterns and Magic Squares. The first table generates 9 blocks, the second table generates 99 blocks, the third table generates 999 blocks, and so on. In case of magic square these are … Continue reading Generating Pythagorean Triples, Palindromic-Type Pandigital Patterns, and Magic Squares

# Block-Wise Construction of Magic and Bimagic Squares of Orders 39 to 45

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

# Different Digits Magic Squares and Magic Sums Number Patterns

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

# 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 25 to 36

# Block-Wise Construction of Magic and Bimagic Squares of Orders 12 to 24

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

# Magic Rectangles in Construction of Block-Wise Pan Magic Squares

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

# Magic Crosses

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

# Block-Wise Equal Sums Magic Squares of Orders 6k

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

# Perfect Square Sum Magic Squares

This paper shows how to create magic squares with a perfect square number for the total sum of their entries. This has been done in two ways: Firstly, by using the sum of consecutive odd numbers, and secondly, by using the sum of consecutive natural numbers, and secondly, by using consecutive natural numbers. In the … Continue reading Perfect Square Sum Magic Squares

# Pythagorean Triples and Perfect Square Sum Magic Squares

This work brings the idea how we can achieve prefect square sum magic squares using primitive and non primitive Pythagorean triples . By perfect square sum magic square, we understand that the total sum of entries of a magic square is a perfect square. The work is divided in two parts, one on primitive triples and another on non primitive … Continue reading Pythagorean Triples and Perfect Square Sum Magic Squares

# Magic Square Type Extended Rows Palprimes of Order 5×5, 7×7 and 9×9

This work brings magic square type palindromic primes (palprimes) numbers of order axa, in such a way that rows, columns and principal diagonals are all palprimes along with extended row of rows. This kind of palprimes are named as  "magic square type palprimes" or "palprime distributions" of order axa. This work is limited to palprime distributions of … Continue reading Magic Square Type Extended Rows Palprimes of Order 5×5, 7×7 and 9×9

# Magic Squares with Perfect Square Number Sums

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

# Multi-Digits Magic Squares

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