Multiple Blocks Magic Squares Generator

Multiples of orders 3x3 to 14x14

Created by Inder J. Taneja

Options

Click a block size, then a block structure, then an order, then a sum type. Each square uses 1 through n*n exactly once; each choice states whether the block sums are equal or different, the block type, and whether the complete square is pandiagonal. Every block, core and inner division is verified.

1. Block size

2. Block structure

3. Order

4. Sum type and block type

Custom order and downloads

Block and inner-structure verification

Every selected block, core and inner division is verified according to its stated property. The complete square is also checked for equal rows, columns and both main diagonals.

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-Wise Constructions of Magic and Bimagic Squares of Orders 8 to 108, Zenodo, May 15, 2019, pp. 1-43, doi.org/10.5281/zenodo.2843326.
  2. Inder J. Taneja, Block-Wise Unequal Sums Magic Squares, Zenodo, February 1, 2019, pp. 1-52, doi.org/10.5281/zenodo.2555260.
  3. Inder J. Taneja, Block-Wise Equal Sums Magic Squares of Orders 3k and 6k, Zenodo, February 1, 2019, pp. 1-55, doi.org/10.5281/zenodo.2554895.
  4. Inder J. Taneja, Block-Wise Magic and Bimagic Squares of Orders 12 to 36, Zenodo, February 1, 2019, pp. 1-53, doi.org/10.5281/zenodo.2555343.
  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, Symmetric Properties of Nested Magic Squares, Zenodo, June 29, 2019, pp. 1-55, doi.org/10.5281/zenodo.3262170.
  7. Inder J. Taneja, Block-Wise Equal Sums Pandiagonal Magic Squares of Order 4k, Zenodo, January 31, 2019, pp. 1-17, doi.org/10.5281/zenodo.2554288.
  8. Inder J. Taneja, Magic Rectangles in Construction of Block-Wise Pandiagonal Magic Squares, Zenodo, January 31, 2019, pp. 1-49, doi.org/10.5281/zenodo.2554520.
  9. 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.
  10. Inder J. Taneja, Magic and Semi-Magic Squares with Blocks of Magic Rectangles, Zenodo, May 28, 2022, pp. 1-27, doi.org/10.5281/zenodo.6590637.
  11. Inder J. Taneja, Magic Rectangles in Construction of Magic and Block Bordered Magic Squares, Zenodo, June 03, 2022, pp. 1-70, doi.org/10.5281/zenodo.6621071.
  12. 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.
  13. 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.
  14. 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.
  15. 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.