267th to 274th Days of Year: 24.09.22 to 30.09.22 – Crazy and Power-Plus Equality 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/ Crazy Representations of Natural Numbers – The 10958 Problem Crazy Representations of Natural Numbers Using Factorial From 200001 to 300000 Inder J. Taneja, Patterned Selfie Fractions, Zenodo, October 27, 2019, pp. 1-267,  http://doi.org/10.5281/zenodo.3520096 Inder J. Taneja, Power-Type Semi-Selfie Numbers and Patterns, Zenodo, July … Continue reading 267th to 274th Days of Year: 24.09.22 to 30.09.22 – Crazy and Power-Plus Equality Representations

Different Styles of Magic Squares of Orders 8 and 10 Using Bordered Magic Rectangles and the Formula (a+b)^2

For the first time in this work, two new concepts in construction of magic square are considered: Using small blocks of magic or bordered magic rectangles. It is not always possible to write bordered magic rectangles for the non-sequential entries. In this case, the simple magic rectangles are considered. Using algebraic formula (a+b)2. The whole work contains magic squares of even … Continue reading Different Styles of Magic Squares of Orders 8 and 10 Using Bordered Magic Rectangles and the Formula (a+b)^2

259th to 266th Days of Year: 16.09.22 to 23.09.22 – Crazy Representations and Patterned Selfie Fractions

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/ Crazy Representations of Natural Numbers – The 10958 Problem Crazy Representations of Natural Numbers Using Factorial From 200001 to 300000 Inder J. Taneja, Patterned Selfie Fractions, Zenodo, October 27, 2019, pp. 1-267,  http://doi.org/10.5281/zenodo.3520096 Inder J. Taneja, Power-Type Semi-Selfie Numbers and Patterns, Zenodo, July … Continue reading 259th to 266th Days of Year: 16.09.22 to 23.09.22 – Crazy Representations and Patterned Selfie Fractions

251st to 258th Days of Year: 08.09.22 to 15.09.22 – Crazy and Power-Plus Equality 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/ Crazy Representations of Natural Numbers – The 10958 Problem Crazy Representations of Natural Numbers Using Factorial From 200001 to 300000 Inder J. Taneja, Patterned Selfie Fractions, Zenodo, October 27, 2019, pp. 1-267,  http://doi.org/10.5281/zenodo.3520096 Inder J. Taneja, Power-Type Semi-Selfie Numbers and Patterns, Zenodo, July … Continue reading 251st to 258th Days of Year: 08.09.22 to 15.09.22 – Crazy and Power-Plus Equality Representations

244th to 250th Days of Year: 01.09.22 to 07.09.22 – Crazy 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/ Crazy Representations of Natural Numbers – The 10958 Problem Crazy Representations of Natural Numbers Using Factorial From 200001 to 300000 Inder J. Taneja, Patterned Selfie Fractions, Zenodo, October 27, 2019, pp. 1-267,  http://doi.org/10.5281/zenodo.3520096 Inder J. Taneja, Power-Type Semi-Selfie Numbers and Patterns, Zenodo, July … Continue reading 244th to 250th Days of Year: 01.09.22 to 07.09.22 – Crazy and Semi-Selfie Representations

229tt to 236th Days of Year: 17.08.22 to 24.08.22 – Crazy 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/Crazy Representations of Natural Numbers – The 10958 ProblemCrazy Representations of Natural Numbers Using Factorial From 200001 to 300000Inder J. Taneja, Patterned Selfie Fractions, Zenodo, October 27, 2019, pp. 1-267,  http://doi.org/10.5281/zenodo.3520096Inder J. Taneja, Power-Type Semi-Selfie Numbers and Patterns, Zenodo, July 16, 2019, pp. 1-130, … Continue reading 229tt to 236th Days of Year: 17.08.22 to 24.08.22 – Crazy and Semi-Selfie Representations

221st to 228th Days of Year: 09.08.22 to 16.08.22 – Crazy and Semi-Selfie Representations

ByInder J. Taneja  AUG 11, 2022 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/Crazy Representations of Natural Numbers – The 10958 ProblemCrazy Representations of Natural Numbers Using Factorial From 200001 to 300000Inder J. Taneja, Patterned Selfie Fractions, Zenodo, October 27, 2019, pp. 1-267, http://doi.org/10.5281/zenodo.3520096Inder J. Taneja, Power-Type Semi-Selfie Numbers and Patterns, Zenodo, … Continue reading 221st to 228th Days of Year: 09.08.22 to 16.08.22 – Crazy and Semi-Selfie Representations

213th to 220th Days of Year: 01.08.22 to 08.08.22 – Crazy Representations and Patterns in Selfie Fractions

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/Crazy Representations of Natural Numbers – The 10958 ProblemCrazy Representations of Natural Numbers Using Factorial From 200001 to 300000Inder J. Taneja, Patterned Selfie Fractions, Zenodo, October 27, 2019, pp. 1-267, http://doi.org/10.5281/zenodo.3520096

206th, 207th, 208th, 209th, 210th, 211th and 212th Days of Year: 25.07.22, 26.07.22, 27.07.22, 28.07.22, 29.07.22, 30.07.22 and 31.07.22 – Crazy Representations and Power Plus Equalities

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/Crazy Representations of Natural Numbers – The 10958 ProblemCrazy Representations of Natural Numbers Using Factorial From 200001 to 300000Inder J. Taneja, Same Digits Equality Expressions: Power and Plus, Zenodo, January 03, 1-1729,  https://doi.org/10.5281/zenodo.3597506.

186th, 187th, 188th and 189th Days of Year: 05.07.22, 06.07.22, 07.07.22 and 08.07.22 – Crazy, Pythagorean Triples and Selfie Fractions

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/Crazy Representations of Natural Numbers – The 10958 ProblemCrazy Representations of Natural Numbers Using Factorial From 200001 to 300000Inder J. Taneja, Patterns in Pythagorean Triples Using Single and Double Variable Procedures, Zenodo, January 19, 2019, pp. 1-134, http://doi.org/10.5281/zenodo.2544519Inder J. Taneja, Multiple-Type Patterns and Pythagorean Triples, Zenodo, January … Continue reading 186th, 187th, 188th and 189th Days of Year: 05.07.22, 06.07.22, 07.07.22 and 08.07.22 – Crazy, Pythagorean Triples and Selfie Fractions

182nd, 183rd, 184th and 185th Days of Year: 01.07.22, 02.07.22, 03.07.22 and 04.07.22 – Crazy, Pythagorean Triples 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/Crazy Representations of Natural Numbers – The 10958 ProblemCrazy Representations of Natural Numbers Using Factorial From 200001 to 300000Inder J. Taneja, Patterns in Pythagorean Triples Using Single and Double Variable Procedures, Zenodo, January 19, 2019, pp. 1-134, http://doi.org/10.5281/zenodo.2544519Inder J. Taneja, Multiple-Type Patterns and Pythagorean Triples, Zenodo, January … Continue reading 182nd, 183rd, 184th and 185th Days of Year: 01.07.22, 02.07.22, 03.07.22 and 04.07.22 – Crazy, Pythagorean Triples and Semi-Selfie Representations

178th, 179th, 180th and 181st Days of Year: 27.06.22, 28.06.22, 29.06.22 and 30.06.22 – Crazy, Pandigital Type, and Pythagorean Triples Patterns

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/Crazy Representations of Natural Numbers – The 10958 ProblemCrazy Representations of Natural Numbers Using Factorial From 200001 to 300000Inder J. Taneja, Patterns in Pythagorean Triples Using Single and Double Variable Procedures, Zenodo, January 19, 2019, pp. 1-134, http://doi.org/10.5281/zenodo.2544519Inder J. Taneja, Multiple-Type Patterns and Pythagorean Triples, Zenodo, January … Continue reading 178th, 179th, 180th and 181st Days of Year: 27.06.22, 28.06.22, 29.06.22 and 30.06.22 – Crazy, Pandigital Type, and Pythagorean Triples Patterns

170th, 171st, 172nd and 173rd Days of Year: 19.06.22, 20.06.22, 21.06.22 and 22.06.22 – Crazy, Pythagorean Triples and Power-Plus and 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/Crazy Representations of Natural Numbers – The 10958 ProblemCrazy Representations of Natural Numbers Using Factorial From 200001 to 300000Inder J. Taneja, Patterns in Pythagorean Triples Using Single and Double Variable Procedures, Zenodo, January 19, 2019, pp. 1-134, http://doi.org/10.5281/zenodo.2544519Inder J. Taneja, Multiple-Type Patterns and Pythagorean Triples, Zenodo, January … Continue reading 170th, 171st, 172nd and 173rd Days of Year: 19.06.22, 20.06.22, 21.06.22 and 22.06.22 – Crazy, Pythagorean Triples and Power-Plus and Representations

166th, 167th, 168th and 169th Days of Year: 15.06.22, 16.06.22, 17.06.22 and 18.06.22 – Crazy, Power-Plus 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/Crazy Representations of Natural Numbers – The 10958 ProblemCrazy Representations of Natural Numbers Using Factorial From 200001 to 300000Inder J. Taneja, Patterns in Pythagorean Triples Using Single and Double Variable Procedures, Zenodo, January 19, 2019, pp. 1-134, http://doi.org/10.5281/zenodo.2544519Inder J. Taneja, Multiple-Type Patterns and Pythagorean Triples, Zenodo, January … Continue reading 166th, 167th, 168th and 169th Days of Year: 15.06.22, 16.06.22, 17.06.22 and 18.06.22 – Crazy, Power-Plus and Semi-Selfie Representations

162nd, 163rd, 164th and 165th Days of Year: 11.06.22, 12.06.22, 13.06.22 and 14.06.22 – Crazy Representations, Power-Plus and Pythagorean Triples Patterns

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/Crazy Representations of Natural Numbers – The 10958 ProblemCrazy Representations of Natural Numbers Using Factorial From 200001 to 300000Inder J. Taneja, Patterns in Pythagorean Triples Using Single and Double Variable Procedures, Zenodo, January 19, 2019, pp. 1-134, http://doi.org/10.5281/zenodo.2544519Inder J. Taneja, Multiple-Type Patterns and Pythagorean Triples, Zenodo, January … Continue reading 162nd, 163rd, 164th and 165th Days of Year: 11.06.22, 12.06.22, 13.06.22 and 14.06.22 – Crazy Representations, Power-Plus and Pythagorean Triples Patterns

Construction of Magic Squares With Blocks of Magic Rectangles

In this work, magic squares are written with equal and unequal sums blocks of magic rectangles. The magic squares studied are of orders 12, 15, 20, 21, 24, 27, 28, 30, 33, 35, 39 and 45. The equal sum blocks magic rectangles are for the magic squares of orders 12, 20, 24, 28 and 30. This lead us … Continue reading Construction of Magic Squares With Blocks of Magic Rectangles

133th, 134th, 135th and 136th Days of Year: 13.05.22, 14.05.22, 15.05.22 and 16.05.22 – Crazy Representations and Pythagorean Triples Patterns

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/Crazy Representations of Natural Numbers – The 10958 ProblemCrazy Representations of Natural Numbers Using Factorial From 200001 to 300000Inder J. Taneja, Patterns in Pythagorean Triples Using Single and Double Variable Procedures, Zenodo, January 19, 2019, pp. 1-134, http://doi.org/10.5281/zenodo.2544519Inder J. Taneja, Multiple-Type Patterns and Pythagorean Triples, Zenodo, January … Continue reading 133th, 134th, 135th and 136th Days of Year: 13.05.22, 14.05.22, 15.05.22 and 16.05.22 – Crazy Representations and Pythagorean Triples Patterns

Different Types of Multiple Style Magic Squares of Order 30

Recently, author wrote different types of magic squares for even orders. These are of type block-wise, bordered, block-bordered, block-wise bordered etc. or we can say that these are mix-type magic squares. The whole work can be downloaded at the following link: Inder J. Taneja, Different Types of Multiple Style Magic Squares of Order 30, Zenodo, May 01, 2022, pp. 1-40, https://doi.org/10.5281/zenodo.6515808. Below are 612 … Continue reading Different Types of Multiple Style Magic Squares of Order 30

Different Types of Multiple Style Magic Squares of Order 28

Recently, author wrote different types of magic squares for even orders. These are of type block-wise, bordered, block-bordered, block-wise bordered etc. or we can say that these are mix-type magic squares. In this case there are 324 magic squares of order 32. The work can be downloaded as the following link: Inder J. Taneja, Different Types of Multiple Style Magic … Continue reading Different Types of Multiple Style Magic Squares of Order 28