Bimagic Squares of Orders 121 and 1331: Blocks of Order 11

Whole the work is done manually on excel sheets.

Below are bimagic squares written in blocks multiples of orders 11. These are of orders 121 and 1331. The work is done manually by author in 2011. It is summarized in the following link.

Inder J. Taneja, Bimagic Squares of Bimagic Squares and an Open Problem, Febuarary 11, 2011, 2011, pp. 1-14, (22.02.2011), https://doi.org/10.48550/arXiv.1102.3052.

Before proceeding further below are the basic formulas to check the sums of magic and bimagic squares

• Magic Sum

• Bimagic Sum

where n is the order the magic square.

Bimagic Square of Order 121

In this case, we have

S_121×121:=885841; Sb_121×121:= 8646694001,

Blocks of order 11 are pandiagonal and of equal sums, S_11×11 :=80531. The magic squares of order 121 are also pandiagonal. See below the excel sheet for the order 121.

Excel sheet of Bimagic Square of Order 121

Bimagic Square of Order 1331: Blocks of Orders 11 and 121

Bimagic square of order 1331 with magic and bimagic sums:

S_1331×1331:=1178974511 and Sb_1331×1331:= 1392417235445951

Block of order 121 are also pandiagonal bimagic square with different bimagic, but equal magic sums, S_121×121:=107179501. Block of order 11 are also pandiagonal with equal sums S_11×11:=9743591.

The magic square of order 1331 is also pandiagonal. It is checked with software by H. White. See below excel sheet of the bimagic square of order 1331.

Excel sheet of Bimagic Square of Order 1331

Due to higher values in the excel the the bimagic sum is appearing as Sb_1331×1331:= 1392417235445950. Actually it is Sb_1331×1331:= 1392417235445951.

References

1. Inder J. Taneja, Bimagic Squares of Bimagic Squares and an Open Problem, Febuarary 11, 2011, 2011, pp. 1-14, (22.02.2011), https://doi.org/10.48550/arXiv.1102.3052.
2. Inder J. Taneja, Block-Wise Construction of Bimagic Squares: Multiples of Orders 8 and 16.
3. Inder J. Taneja, Block-Wise Construction of Bimagic Squares Multiples of 25: Orders 25, 125 and 625.
4. Inder J. Taneja, Block-Wise Construction of Bimagic Squares of Orders 49 and 343.
5. Inder J. Taneja, Block-Wise Construction of Bimagic Squares Multiples of 9: Orders 9, 81 and 729.
6. Inder J. Taneja, Block-Wise Construction of Bimagic Squares of Orders 121 and 1331.
7. Inder J. Taneja, Bimagic Squares of Orders 256, 512 and 1024: Blocks of Order 16.
8. Inder J. Taneja, Bimagic Squares of Orders 200 and 1000: Blocks of Order 8.
9. Inder J. Taneja, Bimagic Squares of Orders 400, 800, 1600 and 2000: Blocks of Order 16.
10. Inder J. Taneja, Bimagic Squares of Orders 100, 110 and 121: Blocks of Orders 10 and 11.
11. Inder J. Taneja, Universal and Upside-Down Magic and Bimagic Squares of Order 16
12. Inder J. Taneja, Universal and Upside-Down Magic and Bimagic Squares of Order 25