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

## Three Digit’s Days of December 2021 – Magic Square of Order Nine With Eights Days

References Inder J. Taneja, Magic Squares, https://inderjtaneja.com/2019/06/27/publications-magic-squares/

## 343rd, 344th, 345th and 346th Days of Year: 09.12.21, 10.12.21, 11.12.21 and 12.12.21 – Crazy Representations, Patterns in Selfie Fractions and Single Letter Representations

References 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, Patterned Selfie Fractions, Zenodo, October 27, 2019, pp. 1-267, http://doi.org/10.5281/zenodo.3520096.Inder J. Taneja. (2020). Patterned Single Letter Representations of Natural Numbers, Zenodo, July 02, 2020, pp. 1-110, http://doi.org/10.5281/zenodo.3928507 Advertisements

## Crazy Running Equality Expressions With Factorial and Square-Root

In previous works, authors wrote equality expressions in terms of 1 to 9 and 9 to 1 or 9 to 0 separated by single or double equality signs. These expressions are based on the idea of crazy representations of natural numbers. These equality expressions are based on basic operations along with factorial, square-root, Fibonacci sequence … Continue reading Crazy Running Equality Expressions With Factorial and Square-Root

## Crazy Representations of Natural Numbers Using Factorial: From 20001-100000

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. … Continue reading Crazy Representations of Natural Numbers Using Factorial: From 20001-100000

## 339th, 340th, 341th and 342th Days of Year: 05.12.2021, 06.12.2021, 07.12.2021 and 08.12.2021 – Crazy Representations, Pythagorean Triples and Semi-Selfie Expressions

References 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, Pythagorean Triples, https://inderjtaneja.com/category/pythagorean-triples/Inder J. Taneja, Factorial-Power Selfie Expressions, Zenodo, February 20, 2019, pp. 1-115, http://doi.org/10.5281/zenodo.2573569\Inder J. Taneja, Power-Type Semi-Selfie Numbers and Patterns, Zenodo, July 16, 2019, pp. 1-130, http://doi.org/10.5281/zenodo.3338366

## 335th, 336th, 337th and 338th Days of Year: 01.12.2021, 02.12.2021, 03.12.2021 and 04.12.2021 – Crazy Representations, Pythagorean Triples and Factorial-Power Representations

References 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, Pythagorean Triples, https://inderjtaneja.com/category/pythagorean-triples/Inder J. Taneja, Factorial-Power Selfie Expressions, Zenodo, February 20, 2019, pp. 1-115, http://doi.org/10.5281/zenodo.2573569

## 327th, 328th, 329th and 330th Days of Year: 23.11.2021, 24.11.2021, 25.11.2021 and 26.11.2021 – Pattern in Pythagorean Triples and Selfie Fractions

References Inder J. Taneja, Patterned Selfie Fractions, Zenodo, October 27, 2019, pp. 1-267, http://doi.org/10.5281/zenodo.3520096.Inder J. Taneja, Pythagorean Triples, https://inderjtaneja.com/category/pythagorean-triples/

## Three Digits Magic Squares of Orders 4 and 5 With Days 20.11.2021, 21.11.2021 and 22.11.2021

References Inder J. Taneja, Magic Squares, https://inderjtaneja.wordpress.com/category/magic-squares/

## 323th, 324th, 325th and 326th Days of Year: 19.11.21, 20.11.21, 21.11.21 and 22.11.21 – Crazy and Running Representations

References: 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, Running Expressions: Increasing and Decreasing Orders, https://inderjtaneja.wordpress.com/2017/05/24/running-expressions-increasing-and-decreasing-orders/