{"id":668,"date":"2022-02-13T06:13:57","date_gmt":"2022-02-13T09:13:57","guid":{"rendered":"https:\/\/numbers-magic.com\/?p=668"},"modified":"2026-02-27T12:55:17","modified_gmt":"2026-02-27T15:55:17","slug":"magic-squares","status":"publish","type":"post","link":"https:\/\/numbers-magic.com\/?p=668","title":{"rendered":"Work on Magic Squares"},"content":{"rendered":"\n

M1. <\/mark>Digital Fonts-Type Magic Squares<\/mark><\/h3>\n\n\n\n
    \n
  1. Inder J. Taneja<\/strong>, Digital Era: Magic Squares and 8th May 2010 (08.05.2010), May, 2010, pp. 1-4, https:\/\/arxiv.org\/abs\/1005.1384<\/a>.<\/mark><\/li>\n\n\n\n
  2. Inder J. Taneja<\/strong><\/mark>, Universal Bimagic Squares and the day 10th October 2010 (10.10.10), Oct, 2010, pp. 1-5, https:\/\/arxiv.org\/abs\/1010.2083<\/a>.<\/mark><\/li>\n\n\n\n
  3. Inder J. Taneja<\/strong><\/mark>, DIGITAL ERA: Universal Bimagic Squares, Oct, 2010, pp. 1-8, https:\/\/arxiv.org\/abs\/1010.2541<\/a>.<\/mark><\/li>\n\n\n\n
  4. Inder J. Taneja<\/strong><\/mark>, Upside Down Numerical Equation, Bimagic Squares, and the day September 11, Oct. 2010, pp. 1-7, https:\/\/arxiv.org\/abs\/1010.4186<\/a>.<\/mark><\/li>\n\n\n\n
  5. Inder J. Taneja<\/strong><\/mark>, 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<\/a>.<\/mark><\/li>\n\n\n\n
  6. Inder J. Taneja<\/strong><\/mark>, 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<\/a>.<\/mark><\/li>\n\n\n\n
  7. Inder J. Taneja<\/strong><\/mark>, Bimagic Squares of Bimagic Squares and an Open Problem, Feb. 2011, pp. 1-14, https:\/\/arxiv.org\/abs\/1102.3052<\/a>.<\/mark><\/li>\n\n\n\n
  8. Inder J. Taneja<\/strong><\/mark>, Representations of Genetic Tables, Bimagic Squares, Hamming Distances and Shannon Entropy, Jun. 2012, pp. 1-19, https:\/\/arxiv.org\/abs\/1206.2220<\/a>.<\/mark><\/li>\n<\/ol>\n\n\n\n

    M2. <\/mark>Selfie and Palindromic-Type Magic Squares<\/mark><\/h3>\n\n\n\n
      \n
    1. Inder J. Taneja<\/strong>, Selfie Palindromic Magic Squares, RGMIA Research Report Collection, 18<\/strong>(2015), Art. 98, pp. 1-15. http:\/\/rgmia.org\/papers\/v18\/v18a98.pdf<\/a>.<\/mark><\/li>\n\n\n\n
    2. Inder J. Taneja<\/strong><\/mark>, 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<\/a>.<\/mark><\/li>\n<\/ol>\n\n\n\n

      M3. <\/mark>Intervally Distributed Magic Squares<\/mark><\/h3>\n\n\n\n
        \n
      1. Inder J. Taneja<\/strong><\/mark>, Intervally Distributed, Palindromic, Selfie Magic Squares, and Double Colored Patterns, RGMIA Research Report Collection, 18<\/strong>(2015), Art. 127, pp. 1-45. http:\/\/rgmia.org\/papers\/v18\/v18a127.pdf<\/a>.<\/mark><\/li>\n\n\n\n
      2. Inder J. Taneja<\/strong>, Intervally Distributed, Palindromic and Selfie Magic Squares: Genetic Table and Colored Pattern – Orders 11 to 20, RGMIA Research Report Collection, 18<\/strong>(2015), Art. 140, pp. 1-43, http:\/\/rgmia.org\/papers\/v18\/v18a140.pdf<\/a>.<\/mark><\/li>\n\n\n\n
      3. Inder J. Taneja<\/strong><\/mark>, Intervally Distributed, Palindromic and Selfie Magic Squares – Orders 21 to 25, 18<\/strong>(2015), Art. 151, pp. 1-33, http:\/\/rgmia.org\/papers\/v18\/v18a151.pdf<\/a>.<\/mark><\/li>\n<\/ol>\n\n\n\n

        M4. <\/mark>Different Digits and Number Patterns Magic Squares<\/mark><\/h3>\n\n\n\n
          \n
        1. Inder J. Taneja<\/strong><\/mark>, Multi-Digits Magic Squares, RGMIA Research Report Collection, 18<\/strong>(2015), Art. 159, pp. 1-22. http:\/\/rgmia.org\/papers\/v18\/v18a159.pdf<\/a>. <\/mark><\/li>\n\n\n\n
        2. Inder J. Taneja<\/strong><\/mark>, Different Digits Magic Squares and Number Patterns, Zenodo<\/strong>, February 1, 2019, pp. 1-34, http:\/\/doi.org\/10.5281\/zenodo.2555327<\/a>.<\/mark><\/li>\n<\/ol>\n\n\n\n

          M5. <\/mark>Perfect Square Sums and Pythagorean Triples Magic Squares<\/mark><\/h3>\n\n\n\n
            \n
          1. Inder J. Taneja<\/strong><\/mark>, Magic Squares with Perfect Square Number Sums, Research Report Collection, 20<\/strong>(2017), Article 11, pp. 1-24, http:\/\/rgmia.org\/papers\/v20\/v20a11.pdf<\/a>. <\/mark><\/li>\n\n\n\n
          2. Inder J. Taneja<\/strong><\/mark>, Pythagorean Triples and Perfect Square Sum Magic Squares, RGMIA Research Report Collection, 20<\/strong>(2017), Art. 128, pp. 1-22, http:\/\/rgmia.org\/papers\/v20\/v20a128.pdf<\/a>.<\/mark><\/li>\n\n\n\n
          3. Inder J. Taneja<\/strong><\/mark>, Perfect Square Sum Magic Squares, Zenodo<\/strong>, April 29, 2019, pp. 1-65, http:\/\/doi.org\/10.5281\/zenodo.2653927<\/a>.<\/mark><\/li>\n\n\n\n
          4. Inder J. Taneja<\/strong><\/mark>, 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<\/a>.<\/li>\n\n\n\n
          5. Inder J. Taneja<\/strong><\/mark>, Bordered Magic Squares with Order Square Magic Sums, Zenodo, January 20, 2020, pp. 1-26, http:\/\/doi.org\/10.5281\/zenodo.3613690<\/a>.<\/li>\n\n\n\n
          6. Inder J. Taneja<\/strong><\/mark>, 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<\/a>.<\/li>\n\n\n\n
          7. Inder J. Taneja<\/strong><\/mark>, Generating Pythagorean Triples and Magic Squares: Orders 3 to 31, Zenodo, May 28, 2021, pp. 1-153, http:\/\/doi.org\/10.5281\/zenodo.4837491<\/a>.<\/li>\n\n\n\n
          8. Inder J. Taneja<\/strong><\/mark>, Sequential Pythagorean Triples and Perfect Square Sum Magic Squares, Zenodo, June 21, 2021, pp. 1-595, http:\/\/doi.org\/10.5281\/zenodo.5009204<\/a>.<\/li>\n\n\n\n
          9. Inder J. Taneja<\/strong><\/mark>, 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<\/a>.<\/li>\n<\/ol>\n\n\n\n

            M6. <\/mark>Magic Crosses, Letters and Numbers<\/mark><\/h3>\n\n\n\n
              \n
            1. Inder J. Taneja<\/strong>, Magic Crosses: Repeated and Non-repeated Entries, Zenodo<\/strong>, February 1, 2019, pp. 1-37, http:\/\/doi.org\/10.5281\/zenodo.2554623<\/a>.<\/mark><\/li>\n\n\n\n
            2. Inder J. Taneja<\/strong>, Representations of Letters and Numbers with Equal Sums Magic Squares of Orders 4 and 6, Zenodo<\/strong>, February 1, 2019, pp. 1-82, http:\/\/doi.org\/10.5281\/zenodo.2555287<\/a>.<\/mark><\/li>\n<\/ol>\n\n\n\n

              M7. <\/mark>Block-Wise Magic Squares<\/mark><\/h3>\n\n\n\n
                \n
              1. Inder J. Taneja<\/strong>, Block-Wise Constructions of Magic and Bimagic Squares of Orders 8 to 108, May 15, 2019, pp. 1-43, Zenodo<\/strong>, http:\/\/doi.org\/10.5281\/zenodo.2843326<\/a>.<\/mark><\/li>\n\n\n\n
              2. Inder J. Taneja<\/strong><\/mark>, Block-Wise Equal Sums Pandiagonal Magic Squares of Order 4k, Zenodo<\/strong>, January 31, 2019, pp. 1-17, http:\/\/doi.org\/10.5281\/zenodo.2554288<\/a>.<\/mark><\/li>\n\n\n\n
              3. Inder J. Taneja<\/strong><\/mark>, Magic Rectangles in Construction of Block-Wise Pandiagonal Magic Squares, Zenodo<\/strong>, January 31, 2019, pp. 1-49, http:\/\/doi.org\/10.5281\/zenodo.2554520<\/a><\/mark>.<\/li>\n\n\n\n
              4. Inder J. Taneja<\/strong><\/mark>, Block-Wise Equal Sums Magic Squares of Orders 3k and 6k, Zenodo<\/strong>, February 1, 2019, pp. 1-55, http:\/\/doi.org\/10.5281\/zenodo.2554895<\/a>.<\/mark><\/li>\n\n\n\n
              5. Inder J. Taneja<\/strong><\/mark>, Block-Wise Unequal Sums Magic Squares, Zenodo<\/strong>, February 1, 2019, pp. 1-52, http:\/\/doi.org\/10.5281\/zenodo.2555260<\/a>.<\/mark><\/li>\n\n\n\n
              6. Inder J. Taneja<\/strong><\/mark>, Block-Wise Magic and Bimagic Squares of Orders 12 to 36, Zenodo<\/strong>, February 1, 2019, pp. 1-53, http:\/\/doi.org\/10.5281\/zenodo.2555343<\/a>.<\/mark><\/li>\n\n\n\n
              7. Inder J. Taneja<\/strong><\/mark>, Block-Wise Magic and Bimagic Squares of Orders 39 to 45, Zenodo<\/strong>, February 2, 2019, pp. 1-73, http:\/\/doi.org\/10.5281\/zenodo.2555889<\/a>.<\/mark><\/li>\n\n\n\n
              8. Inder J. Taneja<\/strong><\/mark>, Magic Squares with Perfect Square Sum of Entries: Orders 3 to 31, Zenodo<\/strong>, July 19, 2021, pp. 1-181, http:\/\/doi.org\/10.5281\/zenodo.5115214<\/a>.<\/li>\n\n\n\n
              9. Inder J. Taneja<\/strong><\/mark>, Magic Squares with Perfect Square Sum of Entries: Orders 3 to 47. Zenodo<\/strong>. August 16, 2021, pp. 1-317, https:\/\/doi.org\/10.5281\/zenodo.5205214<\/a>.<\/li>\n<\/ol>\n\n\n\n

                M8.<\/mark> Block-Wise, Bordered and Block-Bordered Magic Squares<\/mark><\/h3>\n\n\n\n
                  \n
                1. Inder J. Taneja<\/strong>, Nested Magic Squares with Perfect Square Sums, Pythagorean Triples, and Borders Differences, Zenodo<\/strong>, June 14, 2019, pp. 1-59, http:\/\/doi.org\/10.5281\/zenodo.3246586<\/a>.<\/mark><\/li>\n\n\n\n
                2. Inder J. Taneja<\/strong><\/mark>, Symmetric Properties of Nested Magic Squares, Zenodo<\/strong>, June 29, 2019, pp. 1-55, http:\/\/doi.org\/10.5281\/zenodo.3262170<\/a><\/mark><\/li>\n\n\n\n
                3. Inder J. Taneja<\/strong><\/mark>, General Sum Symmetric and Positive Entries Nested Magic Squares, Zenodo<\/strong>, July 04, 2019, pp. 1-55, http:\/\/doi.org\/10.5281\/zenodo.3268877<\/a><\/mark><\/li>\n\n\n\n
                4. Inder J. Taneja<\/strong><\/mark>, Bordered Magic Squares with Order Square Magic Sums, Zenodo<\/strong>, January 20, 2020, pp. 1-26, http:\/\/doi.org\/10.5281\/zenodo.3613690<\/a><\/mark><\/li>\n\n\n\n
                5. Inder J. Taneja<\/strong><\/mark>, Fractional and Decimal Type Bordered Magic Squares with Magic Sum 2020. Zenodo<\/strong>, January 20, 2020, pp.1-25. http:\/\/doi.org\/10.5281\/zenodo.3613698<\/a><\/mark><\/li>\n\n\n\n
                6. Inder J. Taneja<\/strong><\/mark>, Fractional and Decimal Type Bordered Magic Squares with Magic Sum 2021, Zenodo<\/strong>, December 16, 2020, pp. 1-33, http:\/\/doi.org\/10.5281\/zenodo.4327333<\/a><\/mark><\/li>\n\n\n\n
                7. Inder J. Taneja<\/strong><\/mark>, Block-Bordered Magic Squares of Prime and Double Prime Numbers – I, Zenodo<\/strong>, August 18, 2020, pp. 1-81<\/mark><\/mark>, http:\/\/doi.org\/10.5281\/zenodo.3990291<\/a>. <\/mark><\/li>\n\n\n\n
                8. Inder J. Taneja<\/strong><\/mark>, Block-Bordered Magic Squares of Prime and Double Prime Numbers – II, Zenodo<\/strong>, August 18, 2020, http:\/\/doi.org\/10.5281\/zenodo.3990293<\/a>, pp. 1-90<\/mark><\/li>\n\n\n\n
                9. Inder J. Taneja<\/strong><\/mark>, Block-Bordered Magic Squares of Prime and Double Prime Numbers – III, Zenodo<\/strong>, September 01, 2020, pp. 1-93<\/mark><\/mark>, http:\/\/doi.org\/10.5281\/zenodo.4011213<\/a><\/mark>.<\/li>\n\n\n\n
                10. Inder J. Taneja<\/strong><\/mark>, Block-Wise and Block-Bordered Magic and Bimagic Squares with Magic Sums 21, 21^2 and 2021. Zenodo<\/strong>, December 16, 2020, pp. 1-118<\/mark><\/mark>, http:\/\/doi.org\/10.5281\/zenodo.4380343<\/a>.<\/mark><\/li>\n\n\n\n
                11. Inder J. Taneja<\/strong><\/mark>, Block-Wise and Block-Bordered Magic and Bimagic Squares of Orders 10 to 47. Zenodo<\/strong>, January 14, 2021, pp. 1-185, http:\/\/doi.org\/10.5281\/zenodo.4437783<\/a>.<\/li>\n\n\n\n
                12. Inder J. Taneja<\/strong><\/mark>, Bordered and Block-Wise Bordered Magic Squares: Odd Order Multiples. Zenodo<\/strong>. February 10, 2021, pp. 1-75, http:\/\/doi.org\/10.5281\/zenodo.4527739<\/a>.<\/li>\n\n\n\n
                13. Inder J. Taneja<\/strong><\/mark>, Bordered and Block-Wise Bordered Magic Squares: Even Order Multiples, Zenodo<\/strong>, February 10, 2021, pp. 1-96, http:\/\/doi.org\/10.5281\/zenodo.4527746<\/a>.<\/li>\n\n\n\n
                14. Inder J. Taneja<\/strong><\/mark>, Minimum Perfect Square Sum Bordered and Block-Wise Bordered Magic Squares: Orders 3 to 31, Zenodo<\/strong>, July 20, 2021, pp. 1-82, http:\/\/doi.org\/10.5281\/zenodo.5116408<\/a>.<\/li>\n\n\n\n
                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<\/a>.<\/li>\n\n\n\n
                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<\/a>.<\/li>\n<\/ol>\n\n\n\n

                  M9. Different Types of Magic Squares: Even Orders<\/mark><\/h3>\n\n\n\n
                    \n
                  1. Inder J. Taneja<\/strong>, Different Types of Magic Squares: Even Number Orders From 10 to 26, Zenodo<\/strong>, March 26, 2022, pp. 1-167, https:\/\/doi.org\/10.5281\/zenodo.6386742<\/a><\/mark>.<\/li>\n\n\n\n
                  2. Inder J. Taneja<\/strong>, Different Types of Multiple Style Magic Squares of Order 28, Zenodo<\/strong><\/mark>, May 01, 2022, pp. 1-25, https:\/\/doi.org\/10.5281\/zenodo.6510000<\/a>.<\/li>\n\n\n\n
                  3. Inder J. Taneja<\/strong>, Different Types of Multiple Style Magic Squares of Order 30, Zenodo<\/strong><\/mark>, May 01, 2022, pp. 1-40, https:\/\/doi.org\/10.5281\/zenodo.6515808<\/a>.<\/li>\n\n\n\n
                  4. Inder J. Taneja<\/strong>, Inder J. Taneja. (2022). Different Types of Multiple Style Magic Squares of Order 32, Zenodo<\/strong><\/mark>, May 01, pp. 1-52, https:\/\/doi.org\/10.5281\/zenodo.6509756<\/a>.<\/li>\n\n\n\n
                  5. Inder J. Taneja<\/strong>, Inder J. Taneja. (2022). Multiple Style Different Types of Magic Squares of Order 36, Zenodo<\/strong><\/mark>, April 27, 2022, pp. 1-53, https:\/\/doi.org\/10.5281\/zenodo.6499276<\/a>,<\/li>\n\n\n\n
                  6. Inder J. Taneja<\/strong>, Different Types of Multiple Style Magic Squares of Order 40, Zenodo<\/strong>, April 23, 2022, pp. 1-85, https:\/\/doi.org\/10.5281\/zenodo.6480559<\/a>.<\/li>\n<\/ol>\n\n\n\n

                    M10. Two <\/mark>Digits Upside-Down and Universal Magic and Bimagic Squares<\/mark><\/h3>\n\n\n\n
                      \n
                    1. Inder J. Taneja<\/strong>, Universal Palindromic Day and Two Digits Magic Squares, Zenodo<\/strong>, February 2, 2020, pp. 1-22, http:\/\/doi.org\/10.5281\/zenodo.3633852<\/a><\/mark>.<\/li>\n\n\n\n
                    2. Inder J. Taneja<\/strong><\/mark>, 2-Digits Universal and Upside-Down Palindromic Magic and Bimagic Squares: Orders 3 to 16, Zenodo<\/strong>, April 07, 2020, pp. 1-103, http:\/\/doi.org\/10.5281\/zenodo.3743362<\/a>.<\/mark><\/li>\n\n\n\n
                    3. Inder J. Taneja<\/strong><\/mark>, Universal Magic and Bimagic Squares of Orders 17 to 32 With Digits 1 and 8, Zenodo<\/strong>, May 30, 2020, http:\/\/doi.org\/10.5281\/zenodo.3866366<\/a>, pp. 1-103<\/mark><\/li>\n\n\n\n
                    4. Inder J. Taneja<\/strong><\/mark>, Universal Magic and Bimagic Squares of Orders 17 to 32 With Digits 2 and 5, Zenodo<\/strong>, May 30, 2020, http:\/\/doi.org\/10.5281\/zenodo.3866386<\/a>, pp. 1-113<\/mark><\/li>\n\n\n\n
                    5. Inder J. Taneja<\/strong><\/mark>, Upside-Down Magic and Bimagic Squares of Orders 17 to 32 With Digits 6 and 9, Zenodo<\/strong>, May 30, 2020, http:\/\/doi.org\/10.5281\/zenodo.3866396<\/a>, pp.1-98<\/mark><\/li>\n\n\n\n
                    6. Inder J. Taneja<\/strong><\/mark>, Universal Magic Squares of Type 4k, 6k and 12k Using the Digits 1 and 8, Zenodo<\/strong>, June 28, 2020, http:\/\/doi.org\/10.5281\/zenodo.3911452<\/a>, pp. 1-134<\/mark><\/li>\n\n\n\n
                    7. Inder J. Taneja<\/strong><\/mark>, Universal Magic Squares of Type 4k, 6k and 12k Using the Digits 2 and 5, Zenodo<\/strong>, June 28, 2020, http:\/\/doi.org\/10.5281\/zenodo.3911457<\/a>, pp. 1-133<\/mark><\/li>\n\n\n\n
                    8. Inder J. Taneja<\/strong><\/mark>, Upside-Down Magic Squares of Type 4k, 6k and 12k Using the Digits 6 and 9, Zenodo<\/strong>, June 28, 2020, http:\/\/doi.org\/10.5281\/zenodo.3911461<\/a>, pp. 1-135<\/mark><\/li>\n\n\n\n
                    9. Inder J. Taneja<\/strong><\/mark>, Universal Magic Squares of Orders 128, 126 and 120 With Digits 1 and 8, Zenodo<\/strong>, October 26, 2020, http:\/\/doi.org\/10.5281\/zenodo.4130393<\/a>, pp. 1-194<\/mark><\/li>\n\n\n\n
                    10. Inder J. Taneja<\/strong><\/mark>, Universal Magic Squares of Orders 128, 126 and 120 With Digits 2 and 5, Zenodo<\/strong>, October 31, 2020, http:\/\/doi.org\/10.5281\/zenodo.4148929<\/a>, pp. 1-194<\/mark><\/li>\n\n\n\n
                    11. Inder J. Taneja<\/strong><\/mark>, Upside-Down Magic Squares of Orders 128, 126 and 120 With Digits 6 and 9, Zenodo<\/strong>, October 31, 2020, http:\/\/doi.org\/10.5281\/zenodo.4167058<\/a>, pp. 1-194.<\/mark><\/li>\n\n\n\n
                    12. Inder J. Taneja<\/strong><\/mark>, Odd Order Multiples Universal Magic Squares With 1 and 8, Zenodo<\/strong><\/mark>, March 11, 2021, pp. 1-155, http:\/\/doi.org\/10.5281\/zenodo.4592579<\/a>.<\/li>\n\n\n\n
                    13. Inder J. Taneja<\/strong><\/mark>, Block-Wise Universal Bimagic and Semi-Bimagic Squares with Digits 1 and 8, Zenodo<\/strong><\/mark>, March 11, 2021, pp. 1-71, http:\/\/doi.org\/10.5281\/zenodo.4599246<\/a>. <\/li>\n<\/ol>\n\n\n\n

                      M11. Upside-down, Mirror Looking and Water Reflection Magic and Bimagic Squares<\/mark><\/h3>\n\n\n\n