Prime-and-Double-Prime-Orders-Nested-Block-Magic-Squares-Generator-10to108

Orders 10–108 · 1971 verified border and inner-block arrangements

Created by Inder J. Taneja

Options

Choose an odd or even order, its concentric or cyclic border arrangement, and the inner division. Uses 1 through n² exactly once. Choose equal-sum or different-sum inner blocks. Every block has equal rows and equal columns within that block (a magic rectangle when the block is not square); the complete square and its central core are magic. Blocks marked equal all have the same total.

Magic square

Inner-block and nested-square verification

The selector identifies equal or different block sums, and magic, pandiagonal or semi-magic blocks. Every block has equal rows and equal columns within itself. Concentric borders preserve every nested square; cyclic borders preserve the complete square and central core.

Mathematical details

References

The following research by Inder J. Taneja provides the relevant block-wise, rectangular and bordered construction background. Each generated arrangement is checked for the properties stated in its options and verification results.

  1. Inder J. Taneja, Block-Bordered Magic Squares of Prime and Double Prime Numbers - I, Zenodo, August 18, 2020, pp. 1-81, doi.org/10.5281/zenodo.3990291.
  2. Inder J. Taneja, Block-Bordered Magic Squares of Prime and Double Prime Numbers - II, Zenodo, August 18, 2020, pp. 1-90, doi.org/10.5281/zenodo.3990293.
  3. Inder J. Taneja, Block-Bordered Magic Squares of Prime and Double Prime Numbers - III, Zenodo, September 01, 2020, pp. 1-93, doi.org/10.5281/zenodo.4011213.
  4. Inder J. Taneja, Block-Wise and Block-Bordered Magic and Bimagic Squares of Orders 10 to 47, Zenodo, January 14, 2021, pp. 1-185, doi.org/10.5281/zenodo.4437783.
  5. Inder J. Taneja, Bordered and Block-Wise Bordered Magic Squares: Odd Order Multiples, Zenodo, February 10, 2021, pp. 1-75, doi.org/10.5281/zenodo.4527739.
  6. Inder J. Taneja, Bordered and Block-Wise Bordered Magic Squares: Even Order Multiples, Zenodo, February 10, 2021, pp. 1-96, doi.org/10.5281/zenodo.4527746.
  7. Inder J. Taneja, Nested Magic Squares with Perfect Square Sums, Pythagorean Triples, and Borders Differences, Zenodo, June 14, 2019, pp. 1-59, doi.org/10.5281/zenodo.3246586.
  8. Inder J. Taneja, Symmetric Properties of Nested Magic Squares, Zenodo, June 29, 2019, pp. 1-55, doi.org/10.5281/zenodo.3262170.
  9. Inder J. Taneja, General Sum Symmetric and Positive Entries Nested Magic Squares, Zenodo, July 04, 2019, pp. 1-55, doi.org/10.5281/zenodo.3268877.
  10. Inder J. Taneja, Magic Squares with Perfect Square Sum of Entries: Orders 3 to 47, Zenodo, August 16, 2021, pp. 1-317, doi.org/10.5281/zenodo.5205214.