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

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

## 87th Day of Year – 28.03.2021: Colored and Selfie Fractions Patterns

References: Inder J. Taneja, Colored Patterns With 2021 On a Board of 9×9, https://inderjtaneja.com/2020/12/26/colored-pattern-with-2021-on-a-board-of-9×9/Inder J. Taneja, Crazy Representations of Natural Numbers – The 10958 Problem, https://inderjtaneja.com/2018/11/16/crazy-representations-of-natural-numbers-the-10958-problem/Inder J. Taneja, Factorial-Type Numerical Calender 2021, Zenodo, December 16, 2020, pp. 1-31, http://doi.org/10.5281/zenodo.4329889Inder J. Taneja, Selfie Fractions: Addable, Subtractable, Dottable and Potentiable, Zenodo, March 24, 2019, pp. 1-260, http://doi.org/10.5281/zenodo.2604531Inder J. Taneja, Pandigital Equivalent Selfie Fractions, Zenodo, April 02, … Continue reading 87th Day of Year – 28.03.2021: Colored and Selfie Fractions Patterns

## Different Digits Selfie Fractions: Four and Five Digits Numerators

The addable fractions are proper fractions, where addition can be inserted into numerator and denominator, and the resulting fraction is equal to the original. The same is true for other operations, such as, addition, subtraction, multiplication, potentiation, etc. These types of fractions, we call selfie-fractions. This work brings selfie fractions with single and/or multiple representations in different digits with all basic operations. The … Continue reading Different Digits Selfie Fractions: Four and Five Digits Numerators

## August 2020 in Numbers: Part 4 – Patterned Single Letter Representations

References: Inder J. Taneja. (2019). Single Digit Representations of Natural Numbers From 1 to 5000, Zenodo, January 14, 2019, http://doi.org/10.5281/zenodo.2538893.Inder J. Taneja. (2019). Single Digit Representations of Numbers From 10001 to 15000, Zenodo, January, 26, 2019, pp. 1-510, http://doi.org/10.5281/zenodo.2550414.Inder J. Taneja. (2019). Single Digit Representations of Numbers From 15001 to 20000, Zenodo, January, 26, 2019, pp. 1-510, http://doi.org/10.5281/zenodo.2550440.Inder … Continue reading August 2020 in Numbers: Part 4 – Patterned Single Letter Representations

## Universal Magic and Bimagic Squares of Orders 3 to 32 Using 1 and 8

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

## 176th Day of Year: 25.06.19

References: Inder J. Taneja. (2019). Palindromic-Type Palindromes – I, Zenodo, January 15, 2019, pp. 1-99, http://doi.org/10.5281/zenodo.2541174 Inder J. Taneja. (2019). Palindromic-Type Non-Palindromes – I, Zenodo, January 15, 2019, pp. 1-117, http://doi.org/10.5281/zenodo.2541187 Inder J. Taneja. (2019). Amicable Numbers With Patterns in Products and Powers, Zenodo, March 05, 2019, pp. 1-25, http://doi.org/10.5281/zenodo.2583306

## Three Days With Upside-Down Digits: 0, 1, 6 and 9

References I.J. Taneja, Palindromic, Patterned Magic Sums, Composite, and Colored Patterns in Magic Squares. Zenodo, February 2, 2019, pp. 1-99, http://doi.org/10.5281/zenodo.2555741http://doi.org/10.5281/zenodo.2555741.

## Multiple-Type Pythagorean Triples Patterns

Pythagorean patterns are well-known in the literature of mathematics. This work brings patterns obtained by mutiplications with natural numbers to known patterns. It is done in two parts. One without final sum. Second with final sum. In some cases after multiplications, initial lines don't obey the pattern, but the rest part remains patterned. See below some … Continue reading Multiple-Type Pythagorean Triples Patterns

## 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

## Magic Squares

2017 I.J. TANEJA (2017), Magic Squares with Perfect Square Number Sums, Research Report Collection, Vol. 20, Article 11, pp.1-24, http://rgmia.org/papers/v20/v20a11.pdf. I.J. TANEJA (2017), Magic Square Type Extended Row Palprimes of Orders 5x5 and 7x7, Research Report Collection, Vol. 20, Art. 21, pp. 1-69, http://rgmia.org/papers/v20/v20a21.pdf. I.J. TANEJA (2017), Magic Square Type Symmetric and Embedded Palprimes of … Continue reading Magic Squares

## Recreation in Numbers

2018 I.J. TANEJA, Crazy, Selfie, Fibonacci, Triangular, Amicable Types Representations of Numbers, RGMIA Research Report Collection, 21(2018), Art. 3, pp. 1-140, http://rgmia.org/papers/v21/v21a03.pdf. I.J. TANEJA, Natural Numbers in Terms of Fibonacci and S-gonal Values - I, RGMIA Research Report Collection, 21(2018), Art. 6, pp. 1-115, http://rgmia.org/papers/v21/v21a06.pdf. I.J. TANEJA, Natural Numbers in Terms of Fibonacci and S-gonal … Continue reading Recreation in Numbers

## 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

## Intervally Distributed Magic Squares With Properties

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