References Inder J. Taneja, Single Digits Representations of Numbers from 1 to 20000, https://inderjtaneja.com/2019/01/01/single-letter-representations-of-numbers-from-1-to-20000/Inder J. Taneja, Single Letter Representations Of Natural Numbers, https://inderjtaneja.com/2017/08/19/single-letter-representations-of-natural-numbers/Inder J. Taneja, Power-Type Semi-Selfie Numbers and Patterns, Zenodo, July 16, 2019, pp. 1-130, http://doi.org/10.5281/zenodo.3338366

# Author: Inder J. Taneja

# 61st Day of Year: 02.03.22 – Single Digit, Single Letter and Semi-Selfie Representations

References Inder J. Taneja, Single Digits Representations of Numbers from 1 to 20000, https://inderjtaneja.com/2019/01/01/single-letter-representations-of-numbers-from-1-to-20000/Inder J. Taneja, Single Letter Representations Of Natural Numbers, https://inderjtaneja.com/2017/08/19/single-letter-representations-of-natural-numbers/Inder J. Taneja, Power-Type Semi-Selfie Numbers and Patterns, Zenodo, July 16, 2019, pp. 1-130, http://doi.org/10.5281/zenodo.3338366

# 60th Day of Year: 01.03.22 – Single Digit, Single Letter and Semi-Selfie Representations

References: Inder J. Taneja, Single Digits Representations of Numbers from 1 to 20000, https://inderjtaneja.com/2019/01/01/single-letter-representations-of-numbers-from-1-to-20000/Inder J. Taneja, Single Letter Representations Of Natural Numbers, https://inderjtaneja.com/2017/08/19/single-letter-representations-of-natural-numbers/Inder J. Taneja, Power-Type Semi-Selfie Numbers and Patterns, Zenodo, July 16, 2019, pp. 1-130, http://doi.org/10.5281/zenodo.3338366

# Single Digit and Single Letter Representations of 28.02.22

References: Inder J. Taneja, Single Digits Representations of Numbers from 1 to 20000, https://inderjtaneja.com/2019/01/01/single-letter-representations-of-numbers-from-1-to-20000/Inder J. Taneja, Single Letter Representations Of Natural Numbers, https://inderjtaneja.com/2017/08/19/single-letter-representations-of-natural-numbers/

# Block-Wise Bordered Magic Squares Multiples of Orders 4, 6, 8, 10, 12 and 14 – Summary

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. This page brings summary of results obtained by author as multiples of magic squares of orders 4, 6, 8, 10, 12 and 14. The mais property of this work is that in case bordered magic squares removing external borders, we still left … Continue reading Block-Wise Bordered Magic Squares Multiples of Orders 4, 6, 8, 10, 12 and 14 – Summary

# Block-Wise Bordered Magic Squares Multiples of 14

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 140 and 126. Based on these two big magic squares, the inner order magic squares multiples of 14 are studied. By inner orders we understand as the magic squares of orders 112, 98, 84, etc. … Continue reading Block-Wise Bordered Magic Squares Multiples of 14

# Block-Wise Bordered Magic Squares Multiples of 12

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 120 and 108. Based on these two big magic squares, the inner order magic squares multiples of 12 are studied. By inner orders we understand as the magic squares of orders 96, 84, 72, etc. … Continue reading Block-Wise Bordered Magic Squares Multiples of 12

# Block-Wise Bordered Magic Squares Multiples of 10

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 120 and 110. Based on these two big magic squares, the inner order magic squares multiples of 10 are studied. By inner orders we understand as the magic squares of orders 100, 90, 80, etc. … Continue reading Block-Wise Bordered Magic Squares Multiples of 10

# Block-Wise Bordered Magic Squares Multiples of 8

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 120 and 112. Based on these two big magic inner order magic squares multiples of 8 are studied. By inner orders we understand that magic squares of orders 96, 88, 80, etc. Instead of working … Continue reading Block-Wise Bordered Magic Squares Multiples of 8

# 100-Magic Squares of Order 42 With Numbers 00 to 99

During past years author worked with block-wise, block-bordered and block-wise bordered magic squares. Recently, author wrote block-wise and block-wise bordered magic sequares mutliples of 4, 6, 8, 10 and 12. Considering multiples of 6, we have two magic square with equal sums and equal digits blocks of order 6 resulting in magic square of order 42. Here we have 49 … Continue reading 100-Magic Squares of Order 42 With Numbers 00 to 99

# Crazy Representations of Natural Numbers Using Factorial From 200001 to 300000

In 2013-2014, author (click here) wrote natural numbers in increasing and decreasing orders of 1 to 9 using only basic operations. See below some examples: For more details and extension work by other see the following link: Inder J. Taneja, The Crazy Representations and 10958 Problem, https://inderjtaneja.com/2018/11/16/crazy-representations-of-natural-numbers-the-10958-problem/ The above study include the natural numbers till 30000. In … Continue reading Crazy Representations of Natural Numbers Using Factorial From 200001 to 300000

# Magic Squares of Orders 30, 36 and 40 With 22

Order 30 Below are magic squares of order 30, 36 and 40 with 22. The magic square of order 30 is made with equal sums blocks of order 6. The blocks giving number 2 twice is made from bordered magic square of order 6. There are total 25 blocks of order 6 with equal sums … Continue reading Magic Squares of Orders 30, 36 and 40 With 22

# Representation of Numbers from 1 to 20000 in Terms of Palindromic Digits 1357-9-7531

During past years author worked with representations of numbers in terms of 1 to 9 and 9 to 1. These representations called as crazy representations, and are done from 1 to 200000. For details see the references. This work is little different. It brings crazy representations of numbers from 1 to 20000 in terms of palindrodic … Continue reading Representation of Numbers from 1 to 20000 in Terms of Palindromic Digits 1357-9-7531

# Magic Square of Order 40 With 22

Below is a a magic square of order 40 made from consecutive number 1 to 1600. It contains 16 equal sums bordered magic squares of order 8 and 36 equal sums pandiagonal magic squares of order 4. If we consider 16 pandiagonal magic squares of order 4 appearing in 16 bordered magic squares of order 8, then there are 52 pandiagonal magic squares of order … Continue reading Magic Square of Order 40 With 22

# Representation of Numbers from 1 to 10000 in Terms of Palindromic Digits 2022-2202

During past years author worked with representations of numbers in terms of 1 to 9 and 9 to 1. These representations called as crazy representations, and are done from 1 to 200000. For details see the references. This work is little different. It brings crazy representations of numbers from 1 to 10000 in terms of … Continue reading Representation of Numbers from 1 to 10000 in Terms of Palindromic Digits 2022-2202

# Magic Square of Order 36 With 22

Below is a a magic square of order 36 made from consecutive number 1 to 1296. It contains 14 equal sums bordered magic squares of order 8 and 25 equal sums pandiagonal magic squares of order 4. If we consider 14 pandiagonal magic squares of order 4 appearing in 14 bordered magic squares of order … Continue reading Magic Square of Order 36 With 22

# Block-Wise and Block-Bordered Magic Squares With Magic Sum 2022

During past years, author worked with magic squares in different situations. These are of digital-type, block-wise, block-bordered, bordered, creative-type, 2-digits, magic-crosses, magic letters and magic numbers, etc. The detailed study can be seen in the reference list. The magic square summing 2020, 2021 etc. are also studied with different properties. In this work, block-wise and … Continue reading Block-Wise and Block-Bordered Magic Squares With Magic Sum 2022

# Mathematical Beauty of 2022

This work brings representations of 2022 in different ways. These representations are of crazy-type, running numbers, single digit, single letter, Triangular, Fibonacci, palindromic-type, prime numbers, embedded, repeated digits, colored patterns, magic squares, patterned designs, etc. Interesting, this year there will be a day with 11 times repetition of single digit. It will happens on: 22h … Continue reading Mathematical Beauty of 2022

# Hardy-Ramanujan Number – 1729: Revised

This paper brings representations of 1729, a famous Hardy-Ramanujan number in different situations. These representations are of crazy-type, single digit, single letter, Selfie-type, running expressions, selfie fractions, equivalent fractions, Triangular, Fibonacci, fixed digits repetitions prime numbers patterns , Pythagorean triples, palindromic-type, polygonal-type, prime numbers, embedded, repeated, etc. Ideas toward magic squares are also extended. Some … Continue reading Hardy-Ramanujan Number – 1729: Revised

# Crazy Representations of Natural Numbers Using Factorial: From 100001-200000

In 2013-2014, author (click here) wrote natural numbers in increasing and decreasing orders of 1 to 9 using only basic operations. See below some examples: For more details and extension work by other see the following link: Inder J. Taneja, The Crazy Representations and 10958 Problem, https://inderjtaneja.com/2018/11/16/crazy-representations-of-natural-numbers-the-10958-problem/ The above study include the natural numbers till 30000. In … Continue reading Crazy Representations of Natural Numbers Using Factorial: From 100001-200000