Recreating Numbers and Magic Squares

Publications

Work on Magic Squares

ByInder J. Taneja

Feb 13, 2022

M1. Digital Fonts-Type Magic Squares

  1. Inder J. Taneja, Digital Era: Magic Squares and 8th May 2010 (08.05.2010), May, 2010, pp. 1-4, https://arxiv.org/abs/1005.1384.
  2. Inder J. Taneja, Universal Bimagic Squares and the day 10th October 2010 (10.10.10), Oct, 2010, pp. 1-5, https://arxiv.org/abs/1010.2083.
  3. Inder J. Taneja, DIGITAL ERA: Universal Bimagic Squares, Oct, 2010, pp. 1-8, https://arxiv.org/abs/1010.2541.
  4. Inder J. Taneja, Upside Down Numerical Equation, Bimagic Squares, and the day September 11, Oct. 2010, pp. 1-7, https://arxiv.org/abs/1010.4186.
  5. Inder J. Taneja, Equivalent Versions of “Khajuraho” and “Lo-Shu” Magic Squares and the day 1st October 2010 (01.10.2010), Nov. 2010, pp. 1-7, https://arxiv.org/abs/1011.0451.
  6. Inder J. Taneja, Upside Down Magic, Bimagic, Palindromic Squares and Pythagoras Theorem on a Palindromic Day – 11.02.2011, Feb. 2011, pp.1-9, https://arxiv.org/abs/1102.2394.
  7. Inder J. Taneja, Bimagic Squares of Bimagic Squares and an Open Problem, Feb. 2011, pp. 1-14, https://arxiv.org/abs/1102.3052.
  8. Inder J. Taneja, Representations of Genetic Tables, Bimagic Squares, Hamming Distances and Shannon Entropy, Jun. 2012, pp. 1-19, https://arxiv.org/abs/1206.2220.

M2. Selfie and Palindromic-Type Magic Squares

  1. Inder J. Taneja, Selfie Palindromic Magic Squares, RGMIA Research Report Collection, 18(2015), Art. 98, pp. 1-15. http://rgmia.org/papers/v18/v18a98.pdf.
  2. Inder 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.2555741.

M3. Intervally Distributed Magic Squares

  1. Inder J. Taneja, Intervally Distributed, Palindromic, Selfie Magic Squares, and Double Colored Patterns, RGMIA Research Report Collection, 18(2015), Art. 127, pp. 1-45. http://rgmia.org/papers/v18/v18a127.pdf.
  2. Inder J. Taneja, Intervally Distributed, Palindromic and Selfie Magic Squares: Genetic Table and Colored Pattern – Orders 11 to 20, RGMIA Research Report Collection, 18(2015), Art. 140, pp. 1-43, http://rgmia.org/papers/v18/v18a140.pdf.
  3. Inder J. Taneja, Intervally Distributed, Palindromic and Selfie Magic Squares – Orders 21 to 25, 18(2015), Art. 151, pp. 1-33, http://rgmia.org/papers/v18/v18a151.pdf.

M4. Different Digits and Number Patterns Magic Squares

  1. Inder J. Taneja, Multi-Digits Magic Squares, RGMIA Research Report Collection, 18(2015), Art. 159, pp. 1-22. http://rgmia.org/papers/v18/v18a159.pdf.
  2. Inder J. Taneja, Different Digits Magic Squares and Number Patterns, Zenodo, February 1, 2019, pp. 1-34, http://doi.org/10.5281/zenodo.2555327.

M5. Perfect Square Sums and Pythagorean Triples Magic Squares

  1. Inder J. Taneja, Magic Squares with Perfect Square Number Sums, Research Report Collection, 20(2017), Article 11, pp. 1-24, http://rgmia.org/papers/v20/v20a11.pdf.
  2. Inder J. Taneja, Pythagorean Triples and Perfect Square Sum Magic Squares, RGMIA Research Report Collection, 20(2017), Art. 128, pp. 1-22, http://rgmia.org/papers/v20/v20a128.pdf.
  3. Inder J. Taneja, Perfect Square Sum Magic Squares, Zenodo, April 29, 2019, pp. 1-65, http://doi.org/10.5281/zenodo.2653927.
  4. Inder J. Taneja, Nested Magic Squares with Perfect Square Sums, Pythagorean Triples, and Borders Differences, Zenodo, June 14, 2019, pp. 1-59, http://doi.org/10.5281/zenodo.3246586.
  5. Inder J. Taneja, Bordered Magic Squares with Order Square Magic Sums, Zenodo, January 20, 2020, pp. 1-26, http://doi.org/10.5281/zenodo.3613690.
  6. Inder J. Taneja, Block-Wise and Block-Bordered Magic Squares Generated by Pythagorean Triples: Orders 3 to 47, May 28, 2021, pp. 1-119, Zenodo, http://doi.org/10.5281/zenodo.4837454.
  7. Inder J. Taneja, Generating Pythagorean Triples and Magic Squares: Orders 3 to 31, Zenodo, May 28, 2021, pp. 1-153, http://doi.org/10.5281/zenodo.4837491.
  8. Inder J. Taneja, Sequential Pythagorean Triples and Perfect Square Sum Magic Squares, Zenodo, June 21, 2021, pp. 1-595, http://doi.org/10.5281/zenodo.5009204.
  9. Inder J. Taneja, Magic Squares with Perfect Square Sum of Entries: Orders 3 to 31, Zenodo, July 19, pp. 1-181, 2021, http://doi.org/10.5281/zenodo.5115214.

M6. Magic Crosses, Letters and Numbers

  1. Inder J. Taneja, Magic Crosses: Repeated and Non-repeated Entries, Zenodo, February 1, 2019, pp. 1-37, http://doi.org/10.5281/zenodo.2554623.
  2. Inder J. Taneja, Representations of Letters and Numbers with Equal Sums Magic Squares of Orders 4 and 6, Zenodo, February 1, 2019, pp. 1-82, http://doi.org/10.5281/zenodo.2555287.

M7. Block-Wise Magic Squares

  1. Inder J. Taneja, Block-Wise Constructions of Magic and Bimagic Squares of Orders 8 to 108, May 15, 2019, pp. 1-43, Zenodo, http://doi.org/10.5281/zenodo.2843326.
  2. Inder J. Taneja, Block-Wise Equal Sums Pandiagonal Magic Squares of Order 4k, Zenodo, January 31, 2019, pp. 1-17, http://doi.org/10.5281/zenodo.2554288.
  3. Inder J. Taneja, Magic Rectangles in Construction of Block-Wise Pandiagonal Magic Squares, Zenodo, January 31, 2019, pp. 1-49, http://doi.org/10.5281/zenodo.2554520.
  4. Inder J. Taneja, Block-Wise Equal Sums Magic Squares of Orders 3k and 6k, Zenodo, February 1, 2019, pp. 1-55, http://doi.org/10.5281/zenodo.2554895.
  5. Inder J. Taneja, Block-Wise Unequal Sums Magic Squares, Zenodo, February 1, 2019, pp. 1-52, http://doi.org/10.5281/zenodo.2555260.
  6. Inder J. Taneja, Block-Wise Magic and Bimagic Squares of Orders 12 to 36, Zenodo, February 1, 2019, pp. 1-53, http://doi.org/10.5281/zenodo.2555343.
  7. Inder J. Taneja, Block-Wise Magic and Bimagic Squares of Orders 39 to 45, Zenodo, February 2, 2019, pp. 1-73, http://doi.org/10.5281/zenodo.2555889.
  8. Inder J. Taneja, Magic Squares with Perfect Square Sum of Entries: Orders 3 to 31, Zenodo, July 19, 2021, pp. 1-181, http://doi.org/10.5281/zenodo.5115214.
  9. Inder J. Taneja, Magic Squares with Perfect Square Sum of Entries: Orders 3 to 47. Zenodo. August 16, 2021, pp. 1-317, https://doi.org/10.5281/zenodo.5205214.

M8. Block-Wise, Bordered and Block-Bordered Magic Squares

  1. Inder J. Taneja, Nested Magic Squares with Perfect Square Sums, Pythagorean Triples, and Borders Differences, Zenodo, June 14, 2019, pp. 1-59, http://doi.org/10.5281/zenodo.3246586.
  2. Inder J. Taneja, Symmetric Properties of Nested Magic Squares, Zenodo, June 29, 2019, pp. 1-55, http://doi.org/10.5281/zenodo.3262170
  3. Inder J. Taneja, General Sum Symmetric and Positive Entries Nested Magic Squares, Zenodo, July 04, 2019, pp. 1-55, http://doi.org/10.5281/zenodo.3268877
  4. Inder J. Taneja, Bordered Magic Squares with Order Square Magic Sums, Zenodo, January 20, 2020, pp. 1-26, http://doi.org/10.5281/zenodo.3613690
  5. Inder J. Taneja, Fractional and Decimal Type Bordered Magic Squares with Magic Sum 2020. Zenodo, January 20, 2020, pp.1-25. http://doi.org/10.5281/zenodo.3613698
  6. Inder J. Taneja, Fractional and Decimal Type Bordered Magic Squares with Magic Sum 2021, Zenodo, December 16, 2020, pp. 1-33, http://doi.org/10.5281/zenodo.4327333
  7. Inder J. Taneja, Block-Bordered Magic Squares of Prime and Double Prime Numbers – I, Zenodo, August 18, 2020, pp. 1-81, http://doi.org/10.5281/zenodo.3990291.
  8. Inder J. Taneja, Block-Bordered Magic Squares of Prime and Double Prime Numbers – II, Zenodo, August 18, 2020, http://doi.org/10.5281/zenodo.3990293, pp. 1-90
  9. Inder J. Taneja, Block-Bordered Magic Squares of Prime and Double Prime Numbers – III, Zenodo, September 01, 2020, pp. 1-93, http://doi.org/10.5281/zenodo.4011213.
  10. Inder J. Taneja, Block-Wise and Block-Bordered Magic and Bimagic Squares with Magic Sums 21, 21^2 and 2021. Zenodo, December 16, 2020, pp. 1-118, http://doi.org/10.5281/zenodo.4380343.
  11. Inder J. Taneja, Block-Wise and Block-Bordered Magic and Bimagic Squares of Orders 10 to 47. Zenodo, January 14, 2021, pp. 1-185, http://doi.org/10.5281/zenodo.4437783.
  12. Inder J. Taneja, Bordered and Block-Wise Bordered Magic Squares: Odd Order Multiples. Zenodo. February 10, 2021, pp. 1-75, http://doi.org/10.5281/zenodo.4527739.
  13. Inder J. Taneja, Bordered and Block-Wise Bordered Magic Squares: Even Order Multiples, Zenodo, February 10, 2021, pp. 1-96, http://doi.org/10.5281/zenodo.4527746.
  14. Inder J. Taneja, Minimum Perfect Square Sum Bordered and Block-Wise Bordered Magic Squares: Orders 3 to 31, Zenodo, July 20, 2021, pp. 1-82, http://doi.org/10.5281/zenodo.5116408.
  15. Inder J. Taneja, Magic and Semi-Magic Squares with Blocks of Magic Rectangles, May 28, 2022, pp. 1-27, Zenodo, https://doi.org/10.5281/zenodo.6590637.
  16. Inder J. Taneja, Magic Rectangles in Construction of Magic and Block Bordered Magic Squares, June 03, 2022, pp. 1-70, Zenodo, https://doi.org/10.5281/zenodo.6621071.

M9. Different Types of Magic Squares: Even Orders

  1. Inder J. Taneja, Different Types of Magic Squares: Even Number Orders From 10 to 26, Zenodo, March 26, 2022, pp. 1-167, https://doi.org/10.5281/zenodo.6386742.
  2. Inder J. Taneja, Different Types of Multiple Style Magic Squares of Order 28, Zenodo, May 01, 2022, pp. 1-25, https://doi.org/10.5281/zenodo.6510000.
  3. 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.
  4. Inder J. Taneja, Inder J. Taneja. (2022). Different Types of Multiple Style Magic Squares of Order 32, Zenodo, May 01, pp. 1-52, https://doi.org/10.5281/zenodo.6509756.
  5. Inder J. Taneja, Inder J. Taneja. (2022). Multiple Style Different Types of Magic Squares of Order 36, Zenodo, April 27, 2022, pp. 1-53, https://doi.org/10.5281/zenodo.6499276,
  6. Inder J. Taneja, Different Types of Multiple Style Magic Squares of Order 40, Zenodo, April 23, 2022, pp. 1-85, https://doi.org/10.5281/zenodo.6480559.

M10. Two Digits Upside-Down and Universal Magic and Bimagic Squares

  1. Inder J. Taneja, Universal Palindromic Day and Two Digits Magic Squares, Zenodo, February 2, 2020, pp. 1-22, http://doi.org/10.5281/zenodo.3633852.
  2. Inder J. Taneja, 2-Digits Universal and Upside-Down Palindromic Magic and Bimagic Squares: Orders 3 to 16, Zenodo, April 07, 2020, pp. 1-103, http://doi.org/10.5281/zenodo.3743362.
  3. Inder J. Taneja, Universal Magic and Bimagic Squares of Orders 17 to 32 With Digits 1 and 8, Zenodo, May 30, 2020, http://doi.org/10.5281/zenodo.3866366, pp. 1-103
  4. Inder J. Taneja, Universal Magic and Bimagic Squares of Orders 17 to 32 With Digits 2 and 5, Zenodo, May 30, 2020, http://doi.org/10.5281/zenodo.3866386, pp. 1-113
  5. Inder J. Taneja, Upside-Down Magic and Bimagic Squares of Orders 17 to 32 With Digits 6 and 9, Zenodo, May 30, 2020, http://doi.org/10.5281/zenodo.3866396, pp.1-98
  6. Inder J. Taneja, Universal Magic Squares of Type 4k, 6k and 12k Using the Digits 1 and 8, Zenodo, June 28, 2020, http://doi.org/10.5281/zenodo.3911452, pp. 1-134
  7. Inder J. Taneja, Universal Magic Squares of Type 4k, 6k and 12k Using the Digits 2 and 5, Zenodo, June 28, 2020, http://doi.org/10.5281/zenodo.3911457, pp. 1-133
  8. Inder J. Taneja, Upside-Down Magic Squares of Type 4k, 6k and 12k Using the Digits 6 and 9, Zenodo, June 28, 2020, http://doi.org/10.5281/zenodo.3911461, pp. 1-135
  9. Inder J. Taneja, Universal Magic Squares of Orders 128, 126 and 120 With Digits 1 and 8, Zenodo, October 26, 2020, http://doi.org/10.5281/zenodo.4130393, pp. 1-194
  10. Inder J. Taneja, Universal Magic Squares of Orders 128, 126 and 120 With Digits 2 and 5, Zenodo, October 31, 2020, http://doi.org/10.5281/zenodo.4148929, pp. 1-194
  11. Inder J. Taneja, Upside-Down Magic Squares of Orders 128, 126 and 120 With Digits 6 and 9, Zenodo, October 31, 2020, http://doi.org/10.5281/zenodo.4167058, pp. 1-194.
  12. Inder J. Taneja, Odd Order Multiples Universal Magic Squares With 1 and 8, Zenodo, March 11, 2021, pp. 1-155, http://doi.org/10.5281/zenodo.4592579.
  13. Inder J. Taneja, Block-Wise Universal Bimagic and Semi-Bimagic Squares with Digits 1 and 8, Zenodo, March 11, 2021, pp. 1-71, http://doi.org/10.5281/zenodo.4599246.

M11. Upside-down, Mirror Looking and Water Reflection Magic and Bimagic Squares

M11a. Different Styles of Magic Squares

Part 1: Pythagorean Theorem Style

  1. Inder J. Taneja, Different Styles of Magic Squares of Orders 8, 10 and 12 Using Bordered Magic Rectangles and the Formula (a+b)2, Zenodo, September 18, 2022, pp. 1-30, https://doi.org/10.5281/zenodo.7090737.
    Also see the following links:
    a) Different Styles of Magic Squares of Orders 8 and 10 Using Bordered Magic Rectangles and the Formula (a+b)^2.
    b) Different Styles of Magic Squares of Order 12 Using Bordered Magic Rectangles and the Formula (a+b)^2.
  2. Inder J. Taneja, Different Styles of Magic Squares of Order 14 Using Bordered Magic Rectangles and the Formula (a+b)2, Zenodo, September 18, 2022, pp. 1-45, https://doi.org/10.5281/zenodo.7090764.
    Also see the following links:
    Different Styles of Magic Squares of Order 14 Using Bordered Magic Rectangles and the Formula (a+b)^2.
  3. Inder J. Taneja, Different Styles of Magic Squares of Order 16 Using Bordered Magic Rectangles and the Formula (a+b)2, Zenodo, September 18, 2022, pp. 1-85, https://doi.org/10.5281/zenodo.7090770.
    Also see the following links:
    Different Styles of Magic Squares of Order 16 Using Bordered Magic Rectangles and the Formula (a+b)^2
  4. Inder J. Taneja, Different Styles of Magic Squares of Order 18 Using Bordered Magic Rectangles and the Formula (a+b)2, Zenodo, September 23, 2022, pp. 1-136, https://doi.org/10.5281/zenodo.7108694.
    Also see the following links:
    Different Styles of Magic Squares of Order 18 Using Bordered Magic Rectangles and the Formula (a+b)^2.

Part 2: Normal Style

  1. Inder J. Taneja, Different Styles of Magic Squares of Orders 6, 8, 10 and 12 Using Bordered Magic Rectangles, Zenodo, November 14, 2022, pp. 1-26, https://doi.org/10.5281/zenodo.7319985.
  2. Inder J. Taneja, Different Styles of Magic Squares of Order 14 Using Bordered Magic Rectangles, Zenodo, November 14, 2022, pp. 1-40, https://doi.org/10.5281/zenodo.7319787.
  3. Inder J. Taneja, Different Styles of Magic Squares of Order 16 Using Bordered Magic Rectangles, Zenodo, November 14, 2022, pp. 1-63, https://doi.org/10.5281/zenodo.7320116.
  4. Inder J. Taneja,, Different Styles of Magic Squares of Order 18 Using Bordered Magic Rectangles, Zenodo, November 14, 2022, pp. 1-85, https://doi.org/10.5281/zenodo.7320131.
  5. Inder J. Taneja,, Different Styles of Magic Squares of Order 20 Using Bordered Magic Rectangles, Zenodo, November 15, 2022, pp. 1-88, https://doi.org/10.5281/zenodo.7320877.

M12. Striped Magic Squares

M13. Different Types of Magic Rectangles and Magic Squares

Even Orders Magic Squares

  1. Inder J. Taneja, Different Types of Magic Rectangles, Zenodo, September 04, 2023, pp. 1-26, https://doi.org/10.5281/zenodo.8316719.
  2. Inder J. Taneja, Different Types of Magic Rectangles in Construction of Magic Squares of Orders 14 and 18, Zenodo, September 10, 2023, pp. 1-32, https://doi.org/10.5281/zenodo.8331709.
  3. Inder J. Taneja, Different Types of Magic Rectangles in Construction of Magic Squares of Order 22, Zenodo, September 10, 2023, pp. 1-36, https://doi.org/10.5281/zenodo.8331743.
  4. Inder J. Taneja, Different Types of Magic Rectangles in Construction of Magic Squares of Order 26, Zenodo, September 10, 2023, pp. 1-39, https://doi.org/10.5281/zenodo.8331750.
  5. Inder J. Taneja, Different Types of Magic Rectangles in Construction of Magic Squares of Order 30, Zenodo, September 10, 2023, pp. 1-44, https://doi.org/10.5281/zenodo.8331755.
  6. Inder J. Taneja, Different Types of Magic Rectangles in Construction of Magic Squares of Order 34, Zenodo, September 10, 2023, pp. 1-49, https://doi.org/10.5281/zenodo.8331759.
  7. Inder J. Taneja, Cornered Magic Squares in Construction of Magic Squares of Orders 16, 20, 24 and 28, Zenodo, September 10, 2023, pp. 1-35, https://doi.org/10.5281/zenodo.8332156.

Odd Orders Magic Squares

  1. Inder J. Taneja, Odd Order Magic Squares: Orders 3 to 15, Zenodo, June 15, 2023, pp. 1-43, https://doi.org/10.5281/zenodo.8043030.
  2. Inder J. Taneja, Magic Squares of Orders 17 and 19, Zenodo, June 15, 2023, pp. 1-38, https://doi.org/10.5281/zenodo.8043105.
  3. Inder J. Taneja, Magic Squares of Orders 21 and 23, Zenodo, June 15, 2023, pp. 1-43, https://doi.org/10.5281/zenodo.8043198.
  4. Inder J. Taneja, Magic Squares of Order 25, Zenodo, June 15, 2023, pp. 1-27, https://doi.org/10.5281/zenodo.8043228.
  5. Inder J. Taneja, Magic Squares of Order 27, Zenodo, August 06, 2023, pp. 1-32, https://doi.org/10.5281/zenodo.8218291.
  6. Inder J. Taneja, Magic Squares of Order 29, Zenodo, August 06, 2023, pp. 1-30, https://doi.org/10.5281/zenodo.8218771.
  7. Inder J. Taneja, Magic Squares of Order 31, Zenodo, August 06, 2023, pp. 1-35, https://doi.org/10.5281/zenodo.8219053.

M14. Bordered Magic Rectangles and Magic Squares

Normal

  1. Inder J. Taneja, Different Styles of Magic Squares of Orders 6, 8, 10 and 12 Using Bordered Magic Rectangles, Zenodo, November 14, 2022, pp. 1-26, https://doi.org/10.5281/zenodo.7319985.
  2. Inder J. Taneja, Different Styles of Magic Squares of Order 14 Using Bordered Magic Rectangles, Zenodo, November 14, 2022, pp. 1-40, https://doi.org/10.5281/zenodo.7319787.
  3. Inder J. Taneja, Different Styles of Magic Squares of Order 16 Using Bordered Magic Rectangles, Zenodo, Inder J. Taneja, 2022, pp. 1-63, https://doi.org/10.5281/zenodo.7320116.
  4. Inder J. Taneja, Different Styles of Magic Squares of Order 18 Using Bordered Magic Rectangles, Zenodo, November 14, 2022, pp. 1-85, https://doi.org/10.5281/zenodo.7320131.
  5. Inder J. Taneja, Different Styles of Magic Squares of Order 20 Using Bordered Magic Rectangles, Zenodo, November 14, 2022, pp. 1-88, https://doi.org/10.5281/zenodo.7320877.
  6. Inder J. Taneja, Few Examples of Magic Squares of Even Orders 6 to 18 Using Bordered Magic Rectangles, Zenodo, October 19, 2022, pp. 1-30, https://doi.org/10.5281/zenodo.7225854.
  7. Inder J. Taneja, Few Examples of Magic Squares of Even Orders 20 to 30 Using Bordered Magic Rectangles, Zenodo, October 19, 2022, pp. 1-100, https://doi.org/10.5281/zenodo.7225886.
  8. Inder J. Taneja, 8000+ Magic Squares of Order 22 in Different Styles, Models and Designs, Zenodo, April 08, pp. 1-135, https://doi.org/10.5281/zenodo.7809478.

Crossed

  1. Inder J. Taneja, Single Crossed Bordered Magic Rectangles and Magic Squares of Order 40, Zenodo, January 24, 2023, pp. 1-76, https://doi.org/10.5281/zenodo.7565946.
  2. Inder J. Taneja, Double Crossed Bordered Magic Rectangles and Magic Squares of Order 40, Zenodo, January 30, 2023, pp. 1-102, https://doi.org/10.5281/zenodo.7585787.
  3. Inder J. Taneja, Single-Cross Bordered Magic Rectangles and Magic Squares of Order 42, Zenodo, March 03, 2023, pp. 1-69, https://doi.org/10.5281/zenodo.7695939.
  4. Inder J. Taneja, Double-Cross Bordered Magic Rectangles and Magic Squares of Order 42, Zenodo, March 03, 2023, pp. 1-59, https://doi.org/10.5281/zenodo.7696070.
  5. Inder J. Taneja, Closed Double-Cross Bordered Magic Rectangles and Magic Squares of Order 42, Zenodo, March 03, 2023, pp. 1-28, https://doi.org/10.5281/zenodo.7696181.

Figures

  1. Inder J. Taneja, Figured Magic Squares of Orders 6, 10, 12, 14 and 16 Using Bordered Magic Rectangles: A Systematic Procedure, Zenodo, November 29, 2022, pp. 1-31, https://doi.org/10.5281/zenodo.7377674.
  2. Inder J. Taneja, Figured Magic Squares of Orders 18 and 20 Using Bordered Magic Rectangles: A Systematic Procedure, Zenodo, November 29, 2022, pp. 1-87, https://doi.org/10.5281/zenodo.7377689.
  3. Inder J. Taneja, Figured Magic Squares of Order 22 Using Bordered Magic Rectangles: A Systematic Procedure, Zenodo, November 29, 2022, pp. 1-61, https://doi.org/10.5281/zenodo.7377706.
  4. Inder J. Taneja, Figured Magic Squares of Order 24 Using Bordered Magic Rectangles: A Systematic Procedure, Zenodo, November 29, 2022, pp. 1-104, https://doi.org/10.5281/zenodo.7377779.
  5. Inder J. Taneja, Figured Magic Squares of Order 26 Using Bordered Magic Rectangles: A Systematic Procedure, Zenodo, November 29, 2022, pp. 1-88, https://doi.org/10.5281/zenodo.7377794.
  6. Inder J. Taneja, Figured Magic Squares of Order 28 Using Bordered Magic Rectangles: A Systematic Procedure, Zenodo, December 02, 2022, pp. 1-179, https://doi.org/10.5281/zenodo.7390666.
  7. Inder J. Taneja, Figured Magic Squares of Order 30 Using Bordered Magic Rectangles: A Systematic Procedure, Zenodo, December 02, 2022, pp. 1-179, https://doi.org/10.5281/zenodo.7390705.
  8. Inder J. Taneja, Figured Magic Squares of Order 32 Using Bordered Magic Rectangles: A Systematic Procedure, Zenodo, December 22, 2022, pp. 1-310, https://doi.org/10.5281/zenodo.7472891.
  9. Inder J. Taneja, Figured Magic Squares of Order 34 Using Bordered Magic Rectangles: A Systematic Procedure, Zenodo, December 27, 2022, pp. 1-193, https://doi.org/10.5281/zenodo.7486540.
  10. Inder J. Taneja, Figured Magic Squares of Order 36 Using Bordered Magic Rectangles: A Systematic Procedure, Zenodo, December 27, 2022, pp. 1-140, https://doi.org/10.5281/zenodo.7486548.
  11. Inder J. Taneja, Figured Magic Squares of Order 38 Using Bordered Magic Rectangles: A Systematic Procedure, Zenodo, January 03, 2023, pp. 1-133, https://doi.org/110.5281/zenodo.7500188.
  12. Inder J. Taneja, Figured Magic Squares of Order 40 Using Bordered Magic Rectangles: A Systematic Procedure, Zenodo, January 03, 2023, pp. 1-157, https://doi.org/10.5281/zenodo.7500192.
  13. Inder J. Taneja, Magic Squares of Order 42 Using Bordered Magic Rectangles: A Systematic Procedure, Zenodo, March 03, 2023, pp. 1-92, https://doi.org/10.5281/zenodo.7695834.

M15. Multiple Orders Bordered Magic Squares

Even Orders Magic Squares

  1. Inder J. Taneja, Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 4, Zenodo, August 31, 2021, pp. 1-148, https://doi.org/10.5281/zenodo.5347897.
  2. Inder J. Taneja, Bordered Magic Squares Multiples of 6, Zenodo, July 25, 2023, pp. 1-32, https://doi.org/10.5281/zenodo.8184983.
  3. Inder J. Taneja, Bordered and Pandiagonal Magic Squares Multiples of 8, Zenodo, July 26, 2023, pp. 1-58, https://doi.org/10.5281/zenodo.8187791.
  4. Inder J. Taneja, Bordered Magic Squares Multiples of 10, Zenodo, July 26, pp. 1-40, https://doi.org/10.5281/zenodo.8187888.
  5. Inder J. Taneja, Bordered and Pandiagonal Magic Squares Multiples of 12, Zenodo, July 27, 2023, pp. 1-31, https://doi.org/10.5281/zenodo.8188293.
  6. Inder J. Taneja, Bordered Magic Squares Multiples of 14, Zenodo, July 27, pp. 1-33, https://doi.org/10.5281/zenodo.8188395.
  7. Inder J. Taneja, Bordered and Pandiagonal Magic Squares Multiples of 16, Zenodo, July 27, pp. 1-30, https://doi.org/10.5281/zenodo.8190884.
  8. Inder J. Taneja, Bordered Magic Squares Multiples of 18, Zenodo, July 28, pp. 1-31, https://doi.org/10.5281/zenodo.8191223.
  9. Inder J. Taneja, Bordered and Pandiagonal Magic Squares Multiples of 20, Zenodo, July 28, pp. 1-45, https://doi.org/10.5281/zenodo.8191426.

Odd Orders Magic Squares

  1. Inder J. Taneja, Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 3, Zenodo, May 05, pp. 1-29, 2023, https://doi.org/10.5281/zenodo.7898383.
  2. Inder J. Taneja, Bordered and Pandiagonal Magic Squares Multiples of 5, Zenodo, July 23, 2023, pp. 1-36, https://doi.org/10.5281/zenodo.8175759.
  3. Inder J. Taneja, Bordered and Pandiagonal Magic Squares Multiples of 7, Zenodo, July 23, pp. 1-34, 2023, https://doi.org/10.5281/zenodo.8176061.
  4. Inder J. Taneja, Bordered Magic Squares Multiples of 9, Zenodo, July 23, 2023, pp. 1-28, https://doi.org/10.5281/zenodo.8176357.
  5. Inder J. Taneja, Bordered Magic Squares Multiples of 11, Zenodo, July 24, pp. 1-34, 2023, https://doi.org/10.5281/zenodo.8176475.
  6. Inder J. Taneja, Bordered Magic Squares Multiples of 13, Zenodo, July 24, pp. 1-32, 2023, https://doi.org/10.5281/zenodo.8178879.
  7. Inder J. Taneja, Bordered Magic Squares Multiples of 15, Zenodo, July 24, pp. 1-35, 2023, https://doi.org/10.5281/zenodo.8178935.
  8. Inder J. Taneja, Bordered Magic Squares Multiples of 17, Zenodo, July 25, pp. 1-26, 2023, https://doi.org/10.5281/zenodo.8180706.
  9. Inder J. Taneja, Bordered Magic Squares Multiples of 19, Zenodo, July 25, pp. 1-31, 2023, https://doi.org/10.5281/zenodo.8180919.

Mixed Orders Magic Squares

  1. Inder J. Taneja, Multiple Orders Bordered Magic Squares, Zenodo, Jun 9, 2023, pp. 1-43,
    https://doi.org/10.5281/zenodo.8019330.

M16. Double Digits and Cornered Magic Squares

Double Digits Magic Squares

  1. Inder J. Taneja, Two Digits Bordered Magic Squares Multiples of 4: Orders 8 to 24, Zenodo, April, 26, 2023, pp. 1-43, https://doi.org/10.5281/zenodo.7866956.
  2. Inder J. Taneja, Two Digits Bordered Magic Squares of Orders 28 and 32, Zenodo, April, 26, 2023, pp. 1-36, https://doi.org/10.5281/zenodo.7866981.
  3. Inder J. Taneja, Two Digits Bordered Magic Squares of Orders 10, 14, 18 and 22, Zenodo, April, 30, 2023, pp. 1-43, https://doi.org/10.5281/zenodo.7880931.
  4. Inder J. Taneja, Two Digits Bordered Magic Squares of Orders 26 and 30, Zenodo, April, 30, 2023, pp. 1-45, https://doi.org/10.5281/zenodo.7880937.
  5. Inder J. Taneja, Two Digits Bordered Magic Squares of Orders 36 and 40, Zenodo, May, 04, 2023, pp. 1-41, https://doi.org/10.5281/zenodo.7896709.
  6. Inder J. Taneja, Two Digits Bordered Magic Squares of Orders 34 and 38, Zenodo, May 10, 2023, pp. 1-45, https://doi.org/10.5281/zenodo.7922571.
  7. Inder J. Taneja, New Concepts in Magic Squares: Double Digits Bordered Magic Squares of Orders 7 to 108, Zenodo, August 09, 2023, pp. 1-30, https://doi.org/10.5281/zenodo.8230214.

Cornered Magic Squares

  1. Inder J. Taneja, Cornered Magic Squares of Order 6, Zenodo, May 23, 2023, pp. 1-23, https://doi.org/10.5281/zenodo.7960679.
  2. Inder J. Taneja, Cornered Magic Squares of Orders 5 to 13, Zenodo, June 03, 2023, pp. 1-71, https://doi.org/10.5281/zenodo.8000467.
  3. Inder J. Taneja, Cornered Magic Squares of Orders 14 to 24, Zenodo, June 03, 2023, pp. 1-39, https://doi.org/10.5281/zenodo.8000471.
  4. Inder J. Taneja, New Concepts in Magic Squares: Cornered Magic Squares of Orders 5 to 81, Zenodo, August 09, 2023, pp. 1-27, https://doi.org/10.5281/zenodo.8231157.
  5. Inder J. Taneja, Cornered Magic Squares in Construction of Magic Squares of Orders 16, 20, 24 and 28, August 23, 2023, https://numbers-magic.com/?p=10172
  6. Inder J. Taneja, Striped and Semi-Striped Cornered Magic Squares of Orders 6 to 50 – Recreating Numbers and Magic Squares, March 17, 2025.
  7. Inder J. Taneja, New Concepts in Magic Squares: Cornered Magic Squares of Orders 5 to 108, Zenodo, January 29, 2025, pp. 1-33, https://doi.org/10.5281/zenodo.14759238.

M17. Creative Magic Squares

  1. Inder J. Taneja, Creative Magic Squares: Single Digit Representations, Zenodo, March 25, 2021, pp. 1-165, http://doi.org/10.5281/zenodo.4637121
  2. Inder J. Taneja, Creative Magic Squares: Single Letter Representations, Zenodo, March 25, 2021, pp. 1-41, http://doi.org/10.5281/zenodo.4637125
  3. Inder J. Taneja, Creative Magic Squares: Permutable Base-Power Digits Representations, Zenodo, April 03, 2021, pp. 1-44, http://doi.org/10.5281/zenodo.4661586.
  4. Inder J. Taneja, Creative Magic Squares: Increasing and Decreasing Orders Crazy Representations, Zenodo, May 26, 2021, pp. 1-54, http://doi.org/10.5281/zenodo.4813030.
  5. Inder J. Taneja, Creative Magic Squares: Area Representations, Zenodo, June 22, pp. 1-45, 2021, http://doi.org/10.5281/zenodo.5009224.
  6. Inder J. Taneja, Creative Magic Squares: Area Representations with Fraction Numbers Entries, Zenodo, August 16, 2021, 1-77, https://doi.org/10.5281/zenodo.5209502.

M18. Bimagic Squares

  1. Inder J. Taneja, Block-Wise Construction of Bimagic Squares: Multiples of Orders 8 and 16.
  2. Inder J. Taneja, Block-Wise Construction of Bimagic Squares Multiples of 25: Orders 25, 125 and 625.
  3. Inder J. Taneja, Block-Wise Construction of Bimagic Squares Multiples of 9: Orders 9, 81 and 729.
  4. Inder J. Taneja, Block-Wise Construction of Bimagic Squares of Orders 121 and 1331.
  5. Inder J. Taneja, Bimagic Squares of Orders 256, 512 and 1024: Blocks of Order 16.
  6. Inder J. Taneja, Bimagic Squares of Orders 200 and 1000: Blocks of Order 8.
  7. Inder J. Taneja, Bimagic Squares of Orders 400, 800, 1600 and 2000: Blocks of Order 16.
  8. Inder J. Taneja, Bimagic Squares of Orders 100, 110 and 121: Blocks of Orders 10 and 11.

M19. Magic Cubes

M20. Reduced Entries Magic Squares

Part 1: Day and Dates of the Year – 2025 in Terms of Magic Squares

Part 2: Reduced Entries Agebraic Magic Squares

Part 3: Agebraic Magic Squares: Double-Digits, Cornered and Striped

M21. Different Types and Aspects of Magic Squares

M22. Work on S. Ramanujan and Hardy-Ramanujan Number 1729

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By Inder J. Taneja

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One thought on “Work on Magic Squares”

  1. Dear Dr. Taneja,
    For reasons that are not relevant here, my attention was drawn to the topic of “magic squares.” As a result of my own contemplation, I arrived at an algorithm that can be used to construct a magic square of any size.
    After I had finished developing the algorithm, I found a huge number of online resources discussing a wide range of aspects of magic squares. It seems to me that I have not “reinvented the wheel” or replicated already well-known results. Since you appear to be one of the most active researchers in this field, I have decided to share with you a short summary of my findings (which includes several necessary terminological definitions). I would be very interested in your professional opinion on whether they are of any interest to the wider “magic” community.
    Any answer you give will be received with understanding.
    I would like to receive your reply to my personal email if possible.
    Abstract
    All squares discussed hereafter are magic.
    A square M×M is called Normal if it is filled with M^2 consecutive numbers, not necessarily starting with 1.
    A normal square is called Composite if it contains at least one smaller normal square within itself (naturally, excluding itself and the trivial 1×1 square).
    A square that is not composite is called Simple or Primitive.
    An algorithm is proposed for the construction of a normal square in the case where the number M is any composite number, i.e., it can be represented as the product of two factors, K_1 and K_2, where each factor can also be a composite number (the only exception being numbers M whose factors include only one “2”).
    The algorithm allows for the construction of two composite squares of size M×M=(K_1⋅K_2)×(K_1⋅K_2), consisting of K_1^2 normal simple squares of size K_2×K_2 or K_2^2 normal simple squares of size K_1×K_1.
    The development of the algorithm leads to the possibility of constructing a hierarchical system of Hyper-Squares with an arbitrarily complex structure of nested composite and/or simple squares, which are always distinct.

    Reply

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